Type:	Package
Title:	Utility-Based Optimal Phase II/III Drug Development Planning
Version:	1.0.2
Author:	Stella Erdmann [aut], Johannes Cepicka [aut], Marietta Kirchner [aut], Meinhard Kieser [aut], Lukas D. Sauer [aut, cre]
Maintainer:	Lukas D. Sauer <sauer@imbi.uni-heidelberg.de>
Description:	Plan optimal sample size allocation and go/no-go decision rules for phase II/III drug development programs with time-to-event, binary or normally distributed endpoints when assuming fixed treatment effects or a prior distribution for the treatment effect, using methods from Kirchner et al. (2016) <doi:10.1002/sim.6624> and Preussler (2020). Optimal is in the sense of maximal expected utility, where the utility is a function taking into account the expected cost and benefit of the program. It is possible to extend to more complex settings with bias correction (Preussler S et al. (2020) <doi:10.1186/s12874-020-01093-w>), multiple phase III trials (Preussler et al. (2019) <doi:10.1002/bimj.201700241>), multi-arm trials (Preussler et al. (2019) <doi:10.1080/19466315.2019.1702092>), and multiple endpoints (Kieser et al. (2018) <doi:10.1002/pst.1861>).
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 3.5.0), doParallel, parallel, foreach, iterators
Imports:	mvtnorm, cubature, msm, MASS, stats, progressr
URL:	https://github.com/Sterniii3/drugdevelopR, https://sterniii3.github.io/drugdevelopR/
BugReports:	https://github.com/Sterniii3/drugdevelopR/issues
Suggests:	rmarkdown, knitr, testthat (≥ 3.0.0), covr, kableExtra, magrittr, devtools
VignetteBuilder:	knitr
Config/testthat/parallel:	true
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2025-01-14 08:52:18 UTC; or415
Repository:	CRAN
Date/Publication:	2025-01-14 12:50:01 UTC

drugdevelopR: Utility-Based Optimal Phase II/III Drug Development Planning

Description

Plan optimal sample size allocation and go/no-go decision rules for phase II/III drug development programs with time-to-event, binary or normally distributed endpoints when assuming fixed treatment effects or a prior distribution for the treatment effect, using methods from Kirchner et al. (2016) doi:10.1002/sim.6624 and Preussler (2020). Optimal is in the sense of maximal expected utility, where the utility is a function taking into account the expected cost and benefit of the program. It is possible to extend to more complex settings with bias correction (Preussler S et al. (2020) doi:10.1186/s12874-020-01093-w), multiple phase III trials (Preussler et al. (2019) doi:10.1002/bimj.201700241), multi-arm trials (Preussler et al. (2019) doi:10.1080/19466315.2019.1702092), and multiple endpoints (Kieser et al. (2018) doi:10.1002/pst.1861).

Author(s)

Maintainer: Lukas D. Sauer sauer@imbi.uni-heidelberg.de (ORCID)

Authors:

• Stella Erdmann erdmann@imbi.uni-heidelberg.de

• Johannes Cepicka

• Marietta Kirchner

• Meinhard Kieser

See Also

Useful links:

• https://github.com/Sterniii3/drugdevelopR

• https://sterniii3.github.io/drugdevelopR/

• Report bugs at https://github.com/Sterniii3/drugdevelopR/issues

Expected probability of a successful program deciding between two or three phase III trials in a time-to-event setting

Description

The function EPsProg23() calculates the expected probability of a successful program in a time-to-event setting. This function follows a special decision rule in order to determine whether two or three phase III trials should be conducted. First, two phase III trials are performed. Depending on their success, the decision for a third phase III trial is made:

• If both trials are successful, no third phase III trial will be conducted.

• If only one of the two trials is successful and the other trial has a treatment effect that points in the same direction, a third phase III trial will be conducted with a sample size of N3 = N3(ymin), which depends on an assumed minimal clinical relevant effect (ymin). The third trial then has to be significant at level alpha

• If only one of the two trials is successful and the treatment effect of the other points in opposite direction or if none of the two trials are successful, then no third trial is performed and the drug development development program is not successful. In the utility function, this will lead to a utility of -9999.

Usage

EPsProg23(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2, case, size, ymin)

Arguments

Value

The output of the function EPsProg23() is the expected probability of a successful program.

Examples

res <- EPsProg23(HRgo = 0.8, d2 = 50,  alpha = 0.025, beta = 0.1, 
                                  w = 0.3, hr1 =  0.69, hr2 = 0.81, 
                                  id1 = 280, id2 = 420, case = 2, size = "small",
                                  ymin = 0.5)

Expected probability of a successful program deciding between two or three phase III trials for a binary distributed outcome

Description

The function EPsProg23_binary() calculates the expected probability of a successful program with a normally distributed outcome. This function follows a special decision rule in order to determine whether two or three phase III trials should be conducted. First, two phase III trials are performed. Depending on their success, the decision for a third phase III trial is made:

• If both trials are successful, no third phase III trial will be conducted.

• If only one of the two trials is successful and the other trial has a treatment effect that points in the same direction, a third phase III trial will be conducted with a sample size of N3 = N3(ymin), which depends on an assumed minimal clinical relevant effect (ymin). The third trial then has to be significant at level alpha

• If only one of the two trials is successful and the treatment effect of the other points in opposite direction or if none of the two trials are successful, then no third trial is performed and the drug development development program is not successful. In the utility function, this will lead to a utility of -9999.

Usage

EPsProg23_binary(
  RRgo,
  n2,
  alpha,
  beta,
  w,
  p0,
  p11,
  p12,
  in1,
  in2,
  case,
  size,
  ymin
)

Arguments

Value

The output of the function EPsProg23_binary() is the expected probability of a successful program.

Examples

res <- EPsProg23_binary(RRgo = 0.8, n2 = 50,  alpha = 0.025, beta = 0.1, 
                                 w = 0.6,  p0 = 0.3, p11 =  0.3, p12 = 0.5, 
                                 in1 = 300, in2 = 600, case = 2, size = "small",
                                 ymin = 0.5)

Expected probability of a successful program deciding between two or three phase III trials for a normally distributed outcome

Description

The function EPsProg23_normal() calculates the expected probability of a successful program with a normally distributed outcome. This function follows a special decision rule in order to determine whether two or three phase III trials should be conducted. First, two phase III trials are performed. Depending on their success, the decision for a third phase III trial is made:

• If both trials are successful, no third phase III trial will be conducted.

• If only one of the two trials is successful and the other trial has a treatment effect that points in the same direction, a third phase III trial will be conducted with a sample size of N3 = N3(ymin), which depends on an assumed minimal clinical relevant effect (ymin). The third trial then has to be significant at level alpha

• If only one of the two trials is successful and the treatment effect of the other points in opposite direction or if none of the two trials are successful, then no third trial is performed and the drug development development program is not successful. In the utility function, this will lead to a utility of -9999.

Usage

EPsProg23_normal(
  kappa,
  n2,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  case,
  size,
  ymin
)

Arguments

Value

The output of the function EPsProg23_normal() is the expected probability of a successful program.

Examples

EPsProg23_normal(kappa = 0.1, n2 = 50, alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 case = 2, size = "small", ymin = 0.5)

Expected probability of a successful program for bias adjustment programs with time-to-event outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the following functions, which each describe a specific case:

• EPsProg_L(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• EPsProg_L2(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• EPsProg_R(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• EPsProg_R2(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

EPsProg_L(
  HRgo,
  d2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  hr1,
  hr2,
  id1,
  id2,
  fixed
)

EPsProg_L2(
  HRgo,
  d2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  hr1,
  hr2,
  id1,
  id2,
  fixed
)

EPsProg_R(
  HRgo,
  d2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  hr1,
  hr2,
  id1,
  id2,
  fixed
)

EPsProg_R2(
  HRgo,
  d2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  hr1,
  hr2,
  id1,
  id2,
  fixed
)

Arguments

Value

The output of the functions EPsProg_L(), EPsProg_L2(), EPsProg_R() and EPsProg_R2() is the expected probability of a successful program.

Examples

res <- EPsProg_L(HRgo = 0.8, d2 = 50, Adj = 0.4, 
                           alpha = 0.025, beta = 0.1, 
                           step1 = 1, step2 = 0.95, 
                           w = 0.3, hr1 = 0.69, hr2 = 0.81,
                           id1 = 280, id2 = 420, fixed = FALSE)
          res <- EPsProg_L2(HRgo = 0.8, d2 = 50, Adj = 0.4, 
                           alpha = 0.025, beta = 0.1, 
                           step1 = 1, step2 = 0.95, 
                           w = 0.3, hr1 = 0.69, hr2 = 0.81,
                           id1 = 280, id2 = 420, fixed = FALSE)
          res <- EPsProg_R(HRgo = 0.8, d2 = 50, Adj = 0.9, 
                           alpha = 0.025, beta = 0.1, 
                           step1 = 1, step2 = 0.95, 
                           w = 0.3, hr1 = 0.69, hr2 = 0.81,
                           id1 = 280, id2 = 420, fixed = FALSE)
          res <- EPsProg_R2(HRgo = 0.8, d2 = 50, Adj = 0.9, 
                           alpha = 0.025, beta = 0.1, 
                           step1 = 1, step2 = 0.95, 
                           w = 0.3, hr1 = 0.69, hr2 = 0.81,
                           id1 = 280, id2 = 420, fixed = FALSE)

Expected probability of a successful program for bias adjustment programs with binary distributed outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the following functions, which each describe a specific case:

• EPsProg_binary_L(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• EPsProg_binary_L2(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• EPsProg_binary_R(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• EPsProg_binary_R2(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

EPsProg_binary_L(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)

EPsProg_binary_L2(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)

EPsProg_binary_R(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)

EPsProg_binary_R2(
  RRgo,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  fixed
)

Arguments

Value

The output of the functions EPsProg_binary_L(), EPsProg_binary_L2(), EPsProg_binary_R() and EPsProg_binary_R2() is the expected probability of a successful program.

Examples

res <- EPsProg_binary_L(RRgo = 0.8, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_L2(RRgo = 0.8, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_R(RRgo = 0.8, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)
          res <- EPsProg_binary_R2(RRgo = 0.8, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, 
                                 step1 = 1, step2 = 0.95, p0 = 0.6,  w = 0.3,
                                 p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                                 fixed = FALSE)

Expected probability of a successful program for bias adjustment programs with normally distributed outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the following functions, which each describe a specific case:

• EPsProg_normal_L(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• EPsProg_normal_L2(): calculates the expected probability of a successful for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• EPsProg_normal_R(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• EPsProg_normal_R2(): calculates the expected probability of a successful for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

EPsProg_normal_L(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_L2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_R(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

EPsProg_normal_R2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  step1,
  step2,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

Arguments

Value

The output of the functions EPsProg_normal_L(), EPsProg_normal_L2(), EPsProg_normal_R() and EPsProg_normal_R2() is the expected probability of a successful program.

Examples

res <- EPsProg_normal_L(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_L2(kappa = 0.1, n2 = 50, Adj = 0, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_R(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)
          res <- EPsProg_normal_R2(kappa = 0.1, n2 = 50, Adj = 1, 
                                 alpha = 0.025, beta = 0.1, w = 0.3,
                                 step1 = 0, step2 = 0.5,
                                 Delta1 = 0.375, Delta2 = 0.625, 
                                 in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, fixed = FALSE)

Expected probability of a successful program for multiple endpoints and normally distributed outcomes

Description

This function calculates the probability that our drug development program is successful. Successful is defined as both endpoints showing a statistically significant positive treatment effect in phase III.

Usage

EPsProg_multiple_normal(
  kappa,
  n2,
  alpha,
  beta,
  Delta1,
  Delta2,
  sigma1,
  sigma2,
  step11,
  step12,
  step21,
  step22,
  in1,
  in2,
  fixed,
  rho,
  rsamp
)

Arguments

Value

The output of the function EPsProg_multiple_normal() is the expected probability of a successfull program, when going to phase III.

Expected probability of a successful program for multiple endpoints in a time-to-event setting

Description

This function calculates the probability that our drug development program is successful. Successful is defined as at least one endpoint showing a statistically significant positive treatment effect in phase III.

Usage

EPsProg_multiple_tte(
  HRgo,
  n2,
  alpha,
  beta,
  ec,
  hr1,
  hr2,
  id1,
  id2,
  step1,
  step2,
  fixed,
  rho,
  rsamp
)

Arguments

Value

The output of the function EPsProg_multiple_tte() is the expected probability of a successful program, when going to phase III.

Expected probability of a successful program for multitrial programs in a time-to-event setting

Description

These functions calculate the expected probability of a successful program given the parameters. Each function represents a specific strategy, e.g. the function EpsProg3() calculates the expected probability if three phase III trials are performed. The parameter case specifies how many of the trials have to be successful, i.e. how many trials show a significantly relevant positive treatment effect.

Usage

EPsProg2(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2, case, size, fixed)

EPsProg3(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2, case, size, fixed)

EPsProg4(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2, case, size, fixed)

Arguments

Details

The following cases can be investigated by the software:

• Two phase III trials

  • Case 1: Strategy 1/2; at least one trial significant, the treatment effect of the other one at least showing in the same direction

  • Case 2: Strategy 2/2; both trials significant

• Three phase III trials

  • Case 2: Strategy 2/3; at least two trials significant, the treatment effect of the other one at least showing in the same direction

  • Case 3: Strategy 3/3; all trials significant

• Four phase III trials

  • Case 3: Strategy 3/4; at least three trials significant, the treatment effect of the other one at least showing in the same direction

Value

The output of the function EPsProg2(), EPsProg3() and EPsProg4() is the expected probability of a successful program when performing several phase III trials (2, 3 or 4 respectively)

Examples

EPsProg2(HRgo = 0.8, d2 = 50,  alpha = 0.025, beta = 0.1, 
                                 w = 0.3, hr1 =  0.69, hr2 = 0.81, 
                                 id1 = 210, id2 = 420, case = 2, size = "small",
                                 fixed = FALSE)
          EPsProg3(HRgo = 0.8, d2 = 50,  alpha = 0.025, beta = 0.1, 
                                 w = 0.3, hr1 =  0.69, hr2 = 0.81, 
                                 id1 = 210, id2 = 420, case = 2, size = "small",
                                 fixed = TRUE)
          EPsProg4(HRgo = 0.8, d2 = 50,  alpha = 0.025, beta = 0.1, 
                                 w = 0.3, hr1 =  0.69, hr2 = 0.81, 
                                 id1 = 210, id2 = 420, case = 3, size = "small",
                                 fixed = TRUE)

Expected probability of a successful program for multitrial programs with binary distributed outcomes

Description

These functions calculate the expected probability of a successful program given the parameters. Each function represents a specific strategy, e.g. the function EpsProg3_binary() calculates the expected probability if three phase III trials are performed. The parameter case specifies how many of the trials have to be successful, i.e. how many trials show a significantly relevant positive treatment effect.

Usage

EPsProg2_binary(
  RRgo,
  n2,
  alpha,
  beta,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  case,
  size,
  fixed
)

EPsProg3_binary(
  RRgo,
  n2,
  alpha,
  beta,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  case,
  size,
  fixed
)

EPsProg4_binary(
  RRgo,
  n2,
  alpha,
  beta,
  p0,
  w,
  p11,
  p12,
  in1,
  in2,
  case,
  size,
  fixed
)

Arguments

Details

The following cases can be investigated by the software:

• Two phase III trials

  • Case 1: Strategy 1/2; at least one trial significant, the treatment effect of the other one at least showing in the same direction

  • Case 2: Strategy 2/2; both trials significant

• Three phase III trials

  • Case 2: Strategy 2/3; at least two trials significant, the treatment effect of the other one at least showing in the same direction

  • Case 3: Strategy 3/3; all trials significant

• Four phase III trials

  • Case 3: Strategy 3/4; at least three trials significant, the treatment effect of the other one at least showing in the same direction

Value

The output of the function EPsProg2_binary(), EPsProg3_binary() and EPsProg4_binary() is the expected probability of a successful program when performing several phase III trials (2, 3 or 4 respectively)

Examples

EPsProg2_binary(RRgo = 0.8, n2 = 50,  alpha = 0.025, beta = 0.1, 
                                 p0 = 0.6,  w = 0.3, p11 =  0.3, p12 = 0.5, 
                                 in1 = 300, in2 = 600, case = 2, size = "small",
                                 fixed = FALSE)
          EPsProg3_binary(RRgo = 0.8, n2 = 50,  alpha = 0.025, beta = 0.1, 
                                 p0 = 0.6,  w = 0.3, p11 =  0.3, p12 = 0.5, 
                                 in1 = 300, in2 = 600, case = 2, size = "small",
                                 fixed = FALSE)
          EPsProg4_binary(RRgo = 0.8, n2 = 50,  alpha = 0.025, beta = 0.1, 
                                 p0 = 0.6,  w = 0.3, p11 =  0.3, p12 = 0.5, 
                                 in1 = 300, in2 = 600, case = 3, size = "small",
                                 fixed = FALSE)

Expected probability of a successful program for multitrial programs with normally distributed outcomes

Description

These functions calculate the expected probability of a successful program given the parameters. Each function represents a specific strategy, e.g. the function EpsProg3_normal() calculates the expected probability if three phase III trials are performed. The parameter case specifies how many of the trials have to be successful, i.e. how many trials show a significantly relevant positive treatment effect.

Usage

EPsProg2_normal(
  kappa,
  n2,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  case,
  size,
  fixed
)

EPsProg3_normal(
  kappa,
  n2,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  case,
  size,
  fixed
)

EPsProg4_normal(
  kappa,
  n2,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  case,
  size,
  fixed
)

Arguments

Details

The following cases can be investigated by the software:

• Two phase III trials

  • Case 1: Strategy 1/2; at least one trial significant, the treatment effect of the other one at least showing in the same direction

  • Case 2: Strategy 2/2; both trials significant

• Three phase III trials

  • Case 2: Strategy 2/3; at least two trials significant, the treatment effect of the other one at least showing in the same direction

  • Case 3: Strategy 3/3; all trials significant

• Four phase III trials

  • Case 3: Strategy 3/4; at least three trials significant, the treatment effect of the other one at least showing in the same direction

Value

The output of the function EPsProg2_normal(), EPsProg3_normal() and EPsProg4_normal() is the expected probability of a successful program when performing several phase III trials (2, 3 or 4 respectively).

Examples

EPsProg2_normal(kappa = 0.1, n2 = 50, alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 case = 2, size = "small", fixed = FALSE)
          EPsProg3_normal(kappa = 0.1, n2 = 50, alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 case = 2, size = "small", fixed = TRUE)
          EPsProg4_normal(kappa = 0.1, n2 = 50, alpha = 0.025, beta = 0.1, w = 0.3,
                                 Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                                 a = 0.25, b = 0.75, 
                                 case = 3, size = "small", fixed = TRUE)                      

Expected probability of a successful program for time-to-event outcomes

Description

Expected probability of a successful program for time-to-event outcomes

Usage

EPsProg_tte(
  HRgo,
  d2,
  alpha,
  beta,
  step1,
  step2,
  w,
  hr1,
  hr2,
  id1,
  id2,
  gamma,
  fixed
)

Arguments

Value

The output of the functions EPsProg_tte() is the expected probability of a successful program.

Examples

res <- EPsProg_tte(HRgo = 0.8, d2 = 50, 
                           alpha = 0.025, beta = 0.1, 
                           step1 = 1, step2 = 0.95, 
                           w = 0.3, hr1 = 0.69, hr2 = 0.81,
                           id1 = 280, id2 = 420,
                           gamma = 0, fixed = FALSE)

Expected sample size for phase III for bias adjustment programs and time-to-event outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the functions Ed3_L(), Ed3_L2(), Ed3_R() and Ed3_R2(). Each function describes a specific case:

• Ed3_L(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• Ed3_L2(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• Ed3_R(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• Ed3_R2(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

Ed3_L(HRgo, d2, Adj, alpha, beta, w, hr1, hr2, id1, id2, fixed)

Ed3_L2(HRgo, d2, Adj, alpha, beta, w, hr1, hr2, id1, id2, fixed)

Ed3_R(HRgo, d2, Adj, alpha, beta, w, hr1, hr2, id1, id2, fixed)

Ed3_R2(HRgo, d2, Adj, alpha, beta, w, hr1, hr2, id1, id2, fixed)

Arguments

Value

The output of the functions Ed3_L, Ed3_L2, Ed3_R and Ed3_R2 is the expected number of participants in phase III.

Examples

res <-  Ed3_L(HRgo = 0.8, d2 = 50, Adj = 0.4,
                        alpha = 0.025, beta = 0.1, w = 0.3, 
                        hr1 =  0.69, hr2 = 0.81, 
                        id1 = 280, id2 = 420, fixed = FALSE)
          res <-  Ed3_L2(HRgo = 0.8, d2 = 50, Adj = 0.4,
                        alpha = 0.025, beta = 0.1, w = 0.3, 
                        hr1 =  0.69, hr2 = 0.81, 
                        id1 = 280, id2 = 420, fixed = FALSE)
          res <- Ed3_R(HRgo = 0.8, d2 = 50, Adj = 0.9,
                        alpha = 0.025, beta = 0.1, w = 0.3, 
                        hr1 =  0.69, hr2 = 0.81, 
                        id1 = 280, id2 = 420, fixed = FALSE)
          res <- Ed3_R2(HRgo = 0.8, d2 = 50, Adj = 0.9,
                        alpha = 0.025, beta = 0.1, w = 0.3, 
                        hr1 =  0.69, hr2 = 0.81, 
                        id1 = 280, id2 = 420, fixed = FALSE)
                              

Expected sample size for phase III for time-to-event outcomes

Description

Expected sample size for phase III for time-to-event outcomes

Usage

Ed3_tte(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2, fixed)

Arguments

Value

The output of the the functions Ed3_tte is the expected number of events in phase III.

Examples

res <-  Ed3_tte(HRgo = 0.8, d2 = 50,
                        alpha = 0.025, beta = 0.1, w = 0.3, 
                        hr1 =  0.69, hr2 = 0.81, 
                        id1 = 280, id2 = 420, fixed = FALSE)

Expected sample size for phase III for bias adjustment programs and binary distributed outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the functions En3_binary_L(), En3_binary_L2(), En3_binary_R() and En3_binary_R2(). Each function describes a specific case:

• En3_binary_L(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• En3_binary_L2(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• En3_binary_R(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• En3_binary_R2(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

En3_binary_L(RRgo, n2, Adj, alpha, beta, p0, w, p11, p12, in1, in2, fixed)

En3_binary_L2(RRgo, n2, Adj, alpha, beta, p0, w, p11, p12, in1, in2, fixed)

En3_binary_R(RRgo, n2, Adj, alpha, beta, p0, w, p11, p12, in1, in2, fixed)

En3_binary_R2(RRgo, n2, Adj, alpha, beta, p0, w, p11, p12, in1, in2, fixed)

Arguments

Value

The output of the functions En3_binary_L, En3_binary_L2, En3_binary_R and En3_binary_R2 is the expected number of participants in phase III.

Examples

res <- En3_binary_L(RRgo = 0.8, n2 = 50, Adj = 0, 
                              alpha = 0.025, beta = 0.1, p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)
          res <-  En3_binary_L2(RRgo = 0.8, n2 = 50, Adj = 0, 
                              alpha = 0.025, beta = 0.1, p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)
          res <- En3_binary_R(RRgo = 0.8, n2 = 50, Adj = 1, 
                              alpha = 0.025, beta = 0.1, p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)
          res <- En3_binary_R2(RRgo = 0.8, n2 = 50, Adj = 1, 
                              alpha = 0.025, beta = 0.1, p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)
                              

Expected sample size for phase III for bias adjustment programs and normally distributed outcomes

Description

To discount for overoptimistic results in phase II when calculating the optimal sample size in phase III, it is necessary to use the functions En3_normal_L(), En3_normal_L2(), En3_normal_R() and En3_normal_R2(). Each function describes a specific case:

• En3_normal_L(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval), however the go-decision is not affected by the bias adjustment

• En3_normal_L2(): calculates the optimal sample size for an additive adjustment factor (i.e. adjust the lower bound of the one-sided confidence interval) when the go-decision is also affected by the bias adjustment

• En3_normal_R(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor), however the go-decision is not affected by the bias adjustment

• En3_normal_R2(): calculates the optimal sample size for a multiplicative adjustment factor (i.e. use estimate with a retention factor) when the go-decision is also affected by the bias adjustment

Usage

En3_normal_L(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

En3_normal_L2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

En3_normal_R(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

En3_normal_R2(
  kappa,
  n2,
  Adj,
  alpha,
  beta,
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  fixed
)

Arguments

Value

The output of the functions En3_normal_L, En3_normal_L2, En3_normal_R and En3_normal_R2 is the expected number of participants in phase III.

Examples

res <- En3_normal_L(kappa = 0.1, n2 = 50, Adj = 0, 
                              alpha = 0.025, beta = 0.1, w = 0.3,
                              Delta1 = 0.375, Delta2 = 0.625, 
                              in1 = 300, in2 = 600, 
                              a = 0.25, b = 0.75, fixed = FALSE)
          res <- En3_normal_L2(kappa = 0.1, n2 = 50, Adj = 0, 
                              alpha = 0.025, beta = 0.1, w = 0.3,
                              Delta1 = 0.375, Delta2 = 0.625, 
                              in1 = 300, in2 = 600, 
                              a = 0.25, b = 0.75, fixed = TRUE)
          res <- En3_normal_R(kappa = 0.1, n2 = 50, Adj = 1, 
                              alpha = 0.025, beta = 0.1, w = 0.3,
                              Delta1 = 0.375, Delta2 = 0.625, 
                              in1 = 300, in2 = 600, 
                              a = 0.25, b = 0.75, fixed = FALSE)
          res <- En3_normal_R2(kappa = 0.1, n2 = 50, Adj = 1, 
                              alpha = 0.025, beta = 0.1, w = 0.3,
                              Delta1 = 0.375, Delta2 = 0.625, 
                              in1 = 300, in2 = 600, 
                              a = 0.25, b = 0.75, fixed = FALSE)

Expected probability to do third phase III trial

Description

In the setting of Case 2: Strategy 2/2( + 1); at least two trials significant (and the treatment effect of the other one at least showing in the same direction) this function calculates the probability that a third phase III trial is necessary.

Usage

Epgo23(HRgo, d2, alpha, beta, w, hr1, hr2, id1, id2)

Arguments

Value

The output of the function Epgo23() is the probability to a third phase III trial.

Examples

res <- Epgo23(HRgo = 0.8, d2 = 50,  w = 0.3, alpha = 0.025, beta = 0.1,
                               hr1 =  0.69, hr2 = 0.81, id1 = 280, id2 = 420)

Expected probability to do third phase III trial

Description

In the setting of Case 2: Strategy 2/2( + 1); at least two trials significant (and the treatment effect of the other one at least showing in the same direction) this function calculates the probability that a third phase III trial is necessary.

Usage

Epgo23_binary(RRgo, n2, alpha, beta, p0, w, p11, p12, in1, in2)

Arguments

Value

The output of the function Epgo23_binary() is the probability to a third phase III trial.

Examples

res <- Epgo23_binary(RRgo = 0.8, n2 = 50,  p0 = 0.3, w = 0.3, alpha = 0.025, beta = 0.1,
                               p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600)

Expected probability to do third phase III trial

Description

In the setting of Case 2: Strategy 2/2( + 1); at least two trials significant (and the treatment effect of the other one at least showing in the same direction) this function calculates the probability that a third phase III trial is necessary.

Usage

Epgo23_normal(kappa, n2, alpha, beta, a, b, w, Delta1, Delta2, in1, in2)

Arguments

Value

The output of the function Epgo23_normal() is the probability to a third phase III trial.

Examples

Epgo23_normal(kappa = 0.1, n2 = 50, w = 0.3, alpha = 0.025, beta = 0.1, a = 0.25, b=0.75,
                               Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600)

Expected probability to go to phase III for bias adjustment programs with time-to-event outcomes

Description

In the case we do not only want do discount for overoptimistic results in phase II when calculating the sample size in phase III, but also when deciding whether to go to phase III or not the functions Epgo_L2 and Epgo_R2 are necessary. The function Epgo_L2 uses an additive adjustment parameter (i.e. adjust the lower bound of the one-sided confidence interval), the function Epgo_R2 uses a multiplicative adjustment parameter (i.e. use estimate with a retention factor)

Usage

Epgo_L2(HRgo, d2, Adj, w, hr1, hr2, id1, id2, fixed)

Epgo_R2(HRgo, d2, Adj, w, hr1, hr2, id1, id2, fixed)

Arguments

Value

The output of the functions Epgo_L2 and Epgo_R2 is the expected probability to go to phase III with conservative decision rule and sample size calculation.

Examples

res <- Epgo_L2(HRgo = 0.8, d2 = 50, Adj = 0.4,  
                                w = 0.3, hr1 = 0.69, hr2 = 0.81, 
                                id1 = 280, id2 = 420, fixed = FALSE)
          res <- Epgo_R2(HRgo = 0.8, d2 = 50, Adj = 0.9,  
                                w = 0.3, hr1 = 0.69, hr2 = 0.81, 
                                id1 = 280, id2 = 420, fixed = FALSE)

Expected probability to go to phase III for bias adjustment programs with binary distributed outcomes

Description

In the case we do not only want do discount for overoptimistic results in phase II when calculating the sample size in phase III, but also when deciding whether to go to phase III or not the functions Epgo_binary_L2 and Epgo_binary_R2 are necessary. The function Epgo_binary_L2 uses an additive adjustment parameter (i.e. adjust the lower bound of the one-sided confidence interval), the function Epgo_binary_R2 uses a multiplicative adjustment parameter (i.e. use estimate with a retention factor)

Usage

Epgo_binary_L2(RRgo, n2, Adj, p0, w, p11, p12, in1, in2, fixed)

Epgo_binary_R2(RRgo, n2, Adj, p0, w, p11, p12, in1, in2, fixed)

Arguments

Value

The output of the functions Epgo_binary_L2 and Epgo_binary_R2 is the expected number of participants in phase III with conservative decision rule and sample size calculation.

Examples

res <- Epgo_binary_L2(RRgo = 0.8, n2 = 50, Adj = 0,  p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)
          res <- Epgo_binary_R2(RRgo = 0.8, n2 = 50, Adj = 1,  p0 = 0.6,  w = 0.3,
                              p11 =  0.3, p12 = 0.5, in1 = 300, in2 = 600, 
                              fixed = FALSE)

Expected probability to go to phase III for bias adjustment programs with normally distributed outcomes

Description

In the case we do not only want do discount for overoptimistic results in phase II when calculating the sample size in phase III, but also when deciding whether to go to phase III or not the functions Epgo_normal_L2 and Epgo_normal_R2 are necessary. The function Epgo_normal_L2 uses an additive adjustment parameter (i.e. adjust the lower bound of the one-sided confidence interval), the function Epgo_normal_R2 uses a multiplicative adjustment parameter (i.e. use estimate with a retention factor)

Usage

Epgo_normal_L2(kappa, n2, Adj, w, Delta1, Delta2, in1, in2, a, b, fixed)

Epgo_normal_R2(kappa, n2, Adj, w, Delta1, Delta2, in1, in2, a, b, fixed)

Arguments

Value

The output of the functions Epgo_normal_L2 and Epgo_normal_R2 is the expected number of participants in phase III with conservative decision rule and sample size calculation.

Examples

res <- Epgo_normal_L2(kappa = 0.1, n2 = 50, Adj = 0, w = 0.3,
                               Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                               a = 0.25, b = 0.75, fixed = FALSE)
          res <- Epgo_normal_R2(kappa = 0.1, n2 = 50, Adj = 1, w = 0.3,
                               Delta1 = 0.375, Delta2 = 0.625, in1 = 300, in2 = 600, 
                               a = 0.25, b = 0.75, fixed = FALSE)

Expected probability to go to phase III for time-to-event outcomes

Description

Expected probability to go to phase III for time-to-event outcomes

Usage

Epgo_tte(HRgo, d2, w, hr1, hr2, id1, id2, fixed)

Arguments

Value

The output of the functions Epgo_tte() is the expected probability to go to phase III.

Examples

res <- Epgo_tte(HRgo = 0.8, d2 = 50,  
                                w = 0.3, hr1 = 0.69, hr2 = 0.81, 
                                id1 = 280, id2 = 420, fixed = FALSE)

Expected sample size for phase III for multiarm programs with binary distributed outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III given the cases and strategies listed below. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiarm_binary() function

Usage

Ess_binary(RRgo, n2, alpha, beta, p0, p11, p12, strategy, case)

Arguments

Value

the function Ess_binary() returns the expected sample size for phase III when going to phase III

Examples

res <- Ess_binary(RRgo = 0.8 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            p0 = 0.6, p11 =  0.3, p12 = 0.5,strategy = 3, case = 31)

Expected sample size for phase III for multiple endpoints with normally distributed outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiple_normal() function

Usage

Ess_multiple_normal(
  kappa,
  n2,
  alpha,
  beta,
  Delta1,
  Delta2,
  in1,
  in2,
  sigma1,
  sigma2,
  fixed,
  rho,
  rsamp
)

Arguments

Value

the output of the function Ess_multiple_normal is the expected number of participants in phase III

Expected sample size for phase III for multiple endpoints with normally distributed outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiple_tte() function

Usage

Ess_multiple_tte(HRgo, n2, alpha, beta, hr1, hr2, id1, id2, fixed, rho)

Arguments

Value

the output of the function Ess_multiple_tte() is the expected number of participants in phase III

Expected sample size for phase III for multiarm programs with normally distributed outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III given the cases and strategies listed below. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiarm_normal() function

Usage

Ess_normal(kappa, n2, alpha, beta, Delta1, Delta2, strategy, case)

Arguments

Value

The function Ess_normal() returns the expected sample size for phase III when going to phase III when outcomes are normally distributed and we consider multiarm programs, i.e. several phase III trials with different doses or different treatments are performed

Examples

res <- Ess_normal(kappa = 0.1 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            Delta1 = 0.375, Delta2 = 0.625, strategy = 3, case = 31)

Expected sample size for phase III for multiarm programs with time-to-event outcomes

Description

Given phase II results are promising enough to get the "go"-decision to go to phase III this function now calculates the expected sample size for phase III given the cases and strategies listed below. The results of this function are necessary for calculating the utility of the program, which is then in a further step maximized by the optimal_multiarm() function

Usage

Ess_tte(HRgo, n2, alpha, beta, ec, hr1, hr2, strategy, case)

Arguments

Value

the function Ess_tte() returns the expected sample size for phase III when going to phase III

Examples

res <- Ess_tte(HRgo = 0.8 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            ec = 0.6, hr1 = 0.7, hr2 = 0.8, strategy = 2, case = 21)

Probability of a successful program for multiarm programs with binary distributed outcomes

Description

Given we get the "go"-decision in phase II, this functions now calculates the probability that the results of the confirmatory trial (phase III) are significant, i.e. we have a statistically relevant positive effect of the treatment.

Usage

PsProg_binary(
  RRgo,
  n2,
  alpha,
  beta,
  p0,
  p11,
  p12,
  step1,
  step2,
  strategy,
  case
)

Arguments

Value

The function PsProg_binary() returns the probability of a successful program

Examples

res <- PsProg_binary(RRgo = 0.8 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            p0 = 0.6, p11 =  0.3, p12 = 0.5, step1 = 1, step2 = 0.95,
                            strategy = 3, case = 31)

Probability of a successful program for multiarm programs with normally distributed outcomes

Description

Given we get the "go"-decision in phase II, this functions now calculates the probability that the results of the confirmatory trial (phase III) are significant, i.e. we have a statistically relevant positive effect of the treatment.

Usage

PsProg_normal(
  kappa,
  n2,
  alpha,
  beta,
  Delta1,
  Delta2,
  step1,
  step2,
  strategy,
  case
)

Arguments

Value

The function PsProg_normal() returns the probability of a successful program.

Examples

res <- PsProg_normal(kappa = 0.1 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            Delta1 = 0.375, Delta2 = 0.625,  step1 = 0, step2 = 0.5,
                            strategy = 3, case = 31)

Probability of a successful program for multiarm programs with time-to-event outcomes

Description

Given we get the "go"-decision in phase II, this functions now calculates the probability that the results of the confirmatory trial (phase III) are significant, i.e. we have a statistically relevant positive effect of the treatment.

Usage

PsProg_tte(HRgo, n2, alpha, beta, ec, hr1, hr2, step1, step2, strategy, case)

Arguments

Value

The function PsProg_tte() returns the probability of a successful program

Examples

res <- PsProg_tte(HRgo = 0.8 ,n2 = 50 ,alpha = 0.05, beta = 0.1,
                            ec = 0.6, hr1 = 0.7, hr2 = 0.8, step1 = 1, step2 = 0.95,
                            strategy = 2, case = 21)

Expected probability to go to phase III for time-to-event outcomes

Description

If choosing skipII = TRUE, the program calculates the expected utility for the case when phase II is skipped and compares it to the situation when phase II is not skipped. This function calculates the expected sample size for phase III for time-to-event outcomes using a median prior.

Usage

d3_skipII_tte(alpha, beta, median_prior)

Arguments

Value

The output of the functions d3_skipII_tte() is the expected number of events in phase III when skipping phase II.

Examples

res <- d3_skipII_tte(alpha = 0.05, beta = 0.1, median_prior = 0.35)

Density of the bivariate normal distribution

Description

Density of the bivariate normal distribution

Usage

dbivanorm(x, y, mu1, mu2, sigma1, sigma2, rho)

dbivanorm(x, y, mu1, mu2, sigma1, sigma2, rho)

Arguments

Value

The Function dbivanorm() will return the density of a bivariate normal distribution.

Utility based optimal phase II/III drug development planning

Description

The drugdevelopR package enables utility based planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules. The assumed true treatment effects can be assumed fixed (planning is then also possible via user friendly R Shiny App: drugdevelopR) or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

drugdevelopR()

drugdevelopR package and R Shiny App

The drugdevelopR package provides the functions to plan optimal phase II/III drug development programs with

• time-to-event endpoint (optimal_tte),

• binary endpoint (optimal_binary) and

• normally distributed endpoint (optimal_normal),

where the treatment effect is assumed fixed or modelled by a prior. In these settings, optimal phase II/III drug development planning with fixed assumed treatment effects can also be done with the help of the R Shiny application basic. Extensions to the basic setting are

• optimal planning of programs including methods for discounting of phase II results (function: optimal_bias, App: bias),

• optimal planning of programs with several phase III trials (function: optimal_multitrial, App: multitrial) and

• optimal planning of programs with multiple arms (function: optimal_multiarm, App: multiarm).

The R Shiny App drugdevelopR serves as homepage, navigating the different parts of drugdevelopR via links.

References

Kirchner, M., Kieser, M., Goette, H., & Schueler, A. (2016). Utility-based optimization of phase II/III programs. Statistics in Medicine, 35(2), 305-316.

Preussler, S., Kieser, M., and Kirchner, M. (2019). Optimal sample size allocation and go/no-go decision rules for phase II/III programs where several phase III trials are performed. Biometrical Journal, 61(2), 357-378.

Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal designs for phase II/III drug development programs including methods for discounting of phase II results. Submitted to peer-review journal.

Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal designs for multi-arm Phase II/III drug development programs. Submitted to peer-review journal.

Construct a drugdevelopResult object from a data frame

Description

This is a short wrapper for adding the "drugdevelopR" string to the list of S3 classes of a data frame.

Usage

drugdevelopResult(x, ...)

Arguments

Value

the same data frame, equipped with class "drugdevelopResult"

Density for the maximum of two normally distributed random variables

Description

The function fmax() will return the value of f(z), which is the value of the density function of the maximum of two normally distributed random variables.

Usage

fmax(z, mu1, mu2, sigma1, sigma2, rho)

Arguments

Details

Z = max(X,Y) with X ~ N(mu1,sigma1^2), Y ~ N(mu2,sigma2^2)

f(z)=f1(-z)+f2(-z)

Value

The function fmax() will return the value of f(z), which is the value of the density function of the maximum of two normally distributed random variables.

Density for the minimum of two normally distributed random variables

Description

The function fmin() will return the value of f(z), which is the value of the density function of the minimum of two normally distributed random variables.

Usage

fmin(y, mu1, mu2, sigma1, sigma2, rho)

Arguments

Details

Z= min(X,Y) with X ~ N(mu1,sigma1^2), Y ~ N(mu2,sigma2^2)

f(z)=f1(z)+f2(z)

Value

The function fmin() will return the value of f(z), which is the value of the density function of the minimum of two normally distributed random variables.

Generate sample for Monte Carlo integration in the multiple setting

Description

Generate sample for Monte Carlo integration in the multiple setting

Usage

get_sample_multiple_normal(Delta1, Delta2, in1, in2, rho)

Arguments

Value

a randomly generated data frame

Generate sample for Monte Carlo integration in the multiple setting

Description

Generate sample for Monte Carlo integration in the multiple setting

Usage

get_sample_multiple_tte(hr1, hr2, id1, id2, rho)

Arguments

Value

a randomly generated data frame

Optimal phase II/III drug development planning for time-to-event endpoints when discounting phase II results

Description

The function optimal_bias of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for time-to-event endpoints (Preussler et. al, 2020). The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased). The assumed true treatment effects can be assumed fixed (planning is then also possible via user friendly R Shiny App: bias) or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_bias(
  w,
  hr1,
  hr2,
  id1,
  id2,
  d2min,
  d2max,
  stepd2,
  hrgomin,
  hrgomax,
  stephrgo,
  adj = "both",
  lambdamin = NULL,
  lambdamax = NULL,
  steplambda = NULL,
  alphaCImin = NULL,
  alphaCImax = NULL,
  stepalphaCI = NULL,
  alpha,
  beta,
  xi2,
  xi3,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Method

Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)

Adj

optimal adjustment parameter (lambda or alphaCI according to Method)

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

optimal threshold value for the decision rule to go to phase III

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.

Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2020). Optimal designs for phase II/III drug development programs including methods for discounting of phase II results. Submitted to peer-review journal.

Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.

Examples

# Activate progress bar (optional)
## Not run: 
progressr::handlers(global = TRUE)

## End(Not run)
# Optimize

optimal_bias(w = 0.3,                       # define parameters for prior
  hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420,      # (https://web.imbi.uni-heidelberg.de/prior/)
  d2min = 20, d2max = 100, stepd2 = 5,               # define optimization set for d2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05,     # define optimization set for HRgo
  adj = "both",                                      # choose type of adjustment
  lambdamin = 0.2, lambdamax = 1, steplambda = 0.05, # define optimization set for lambda
  alphaCImin = 0.025, alphaCImax = 0.5,
  stepalphaCI = 0.025,                               # define optimization set for alphaCI
  alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7,   # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,           # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 1,                                        # define lower boundary for "small"
  stepm1 = 0.95,                                     # "medium"
  stepl1 = 0.85,                                     # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                   # define expected benefits 
  fixed = FALSE,                                     # true treatment effects are fixed/random
  num_cl = 1)                                        # number of coresfor parallelized computing 
  

Optimal phase II/III drug development planning when discounting phase II results with binary endpoint

Description

The function optimal_bias_binary of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for binary endpoints (Preussler et. al, 2020). The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased). The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_bias_binary(
  w,
  p0,
  p11,
  p12,
  in1,
  in2,
  n2min,
  n2max,
  stepn2,
  rrgomin,
  rrgomax,
  steprrgo,
  adj = "both",
  lambdamin = NULL,
  lambdamax = NULL,
  steplambda = NULL,
  alphaCImin = NULL,
  alphaCImax = NULL,
  stepalphaCI = NULL,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Method

Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)

Adj

optimal adjustment parameter (lambda or alphaCI according to Method)

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

RRgo

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_bias_binary(w = 0.3,                 # define parameters for prior
  p0 = 0.6, p11 =  0.3, p12 = 0.5,
  in1 = 30, in2 = 60,                                 # (https://web.imbi.uni-heidelberg.de/prior/)
  n2min = 20, n2max = 100, stepn2 = 10,               # define optimization set for n2
  rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05,      # define optimization set for RRgo
  adj = "both",                                       # choose type of adjustment
  alpha = 0.025, beta = 0.1,                          # drug development planning parameters
  lambdamin = 0.2, lambdamax = 1, steplambda = 0.05,  # define optimization set for lambda
  alphaCImin = 0.025, alphaCImax = 0.5,
  stepalphaCI = 0.025,                                # define optimization set for alphaCI
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,            # fixed and variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                         # set constraints
  steps1 = 1,                                         # define lower boundary for "small"
  stepm1 = 0.95,                                      # "medium"
  stepl1 = 0.85,                                      # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                    # define expected benefits
  fixed = TRUE,                                       # true treatment effects are fixed/random
  num_cl = 1)                                         # number of cores for parallelized computing
  

Generic function for optimizing drug development programs with bias adjustment

Description

Generic function for optimizing drug development programs with bias adjustment

Usage

optimal_bias_generic(
  adj = "both",
  lambdamin = NULL,
  lambdamax = NULL,
  steplambda = NULL,
  alphaCImin = NULL,
  alphaCImax = NULL,
  stepalphaCI = NULL
)

Arguments

Optimal phase II/III drug development planning when discounting phase II results with normally distributed endpoint

Description

The function optimal_bias_normal of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules including methods for discounting of phase II results for normally distributed endpoints (Preussler et. al, 2020). The discounting may be necessary as programs that proceed to phase III can be overoptimistic about the treatment effect (i.e. they are biased). The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_bias_normal(
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  adj = "both",
  lambdamin = NULL,
  lambdamax = NULL,
  steplambda = NULL,
  alphaCImin = NULL,
  alphaCImax = NULL,
  stepalphaCI = NULL,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Method

Type of adjustment: "multipl." (multiplicative adjustment of effect size), "add." (additive adjustment of effect size), "multipl2." (multiplicative adjustment of effect size and threshold), "add2." (additive adjustment of effect size and threshold)

Adj

optimal adjustment parameter (lambda or alphaCI according to Method)

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

Kappa

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_bias_normal(w=0.3,             # define parameters for prior
  Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600,    # (https://web.imbi.uni-heidelberg.de/prior/)
  a = 0.25, b = 0.75,
  n2min = 20, n2max = 100, stepn2 = 10,                # define optimization set for n2
  kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02,   # define optimization set for kappa
  adj = "both",                                        # choose type of adjustment
  lambdamin = 0.2, lambdamax = 1, steplambda = 0.05,   # define optimization set for lambda
  alphaCImin = 0.025, alphaCImax = 0.5,
  stepalphaCI = 0.025,                                 # define optimization set for alphaCI
  alpha = 0.025, beta = 0.1,                           # drug development planning parameters
  c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20,           # fixed and variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                          # set constraints
  steps1 = 0,                                          # define lower boundary for "small"
  stepm1 = 0.5,                                        # "medium"
  stepl1 = 0.8,                                        # and "large" effect size categories
  b1 = 3000, b2 = 8000, b3 = 10000,                    # define expected benefits
  fixed = TRUE,                                        # true treatment effects are fixed/random
  num_cl = 1)                                          # number of coresfor parallelized computing 
                                          

Optimal phase II/III drug development planning with binary endpoint

Description

The optimal_binary function of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules for binary endpoints. In this case, the treatment effect is measured by the risk ratio (RR). The assumed true treatment effects can be assumed to be fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_binary(
  w,
  p0,
  p11,
  p12,
  in1,
  in2,
  n2min,
  n2max,
  stepn2,
  rrgomin,
  rrgomax,
  steprrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  skipII = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

RRgo

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: 
progressr::handlers(global = TRUE)

## End(Not run)
# Optimize

optimal_binary(w = 0.3,                             # define parameters for prior
  p0 = 0.6, p11 =  0.3, p12 = 0.5,
  in1 = 30, in2 = 60,                               # (https://web.imbi.uni-heidelberg.de/prior/)
  n2min = 20, n2max = 100, stepn2 = 4,              # define optimization set for n2
  rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05,    # define optimization set for RRgo
  alpha = 0.025, beta = 0.1,                        # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,          # fixed and variable costs for phase II/III,
  K = Inf, N = Inf, S = -Inf,                       # set constraints
  steps1 = 1,                                       # define lower boundary for "small"
  stepm1 = 0.95,                                    # "medium"
  stepl1 = 0.85,                                    # and "large" treatment effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                  # define expected benefits
  gamma = 0,                                        # population structures in phase II/III
  fixed = FALSE,                                    # true treatment effects are fixed/random
  skipII = FALSE,                                   # choose if skipping phase II is an option
  num_cl = 2)                                       # number of cores for parallelized computing
  

Generic function for optimizing programs with binary endpoints

Description

Generic function for optimizing programs with binary endpoints

Usage

optimal_binary_generic(
  w,
  p0,
  p11,
  p12,
  in1,
  in2,
  n2min,
  n2max,
  stepn2,
  rrgomin,
  rrgomax,
  steprrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Generic function for optimizing drug development programs

Description

Generic function for optimizing drug development programs

Usage

optimal_generic(beta, alpha, c2, c3, c02, c03, K, N, S, b1, b2, b3, num_cl)

Arguments

Optimal phase II/III drug development planning for multi-arm programs with time-to-event endpoint

Description

The function optimal_multiarm of the drugdevelopR package enables planning of multi-arm phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules (Preussler et. al, 2019) for time-to-event endpoints. So far, only three-arm trials with two treatments and one control are supported. The assumed true treatment effects are assumed fixed (planning is also possible via user-friendly R Shiny App: multiarm). Fast computing is enabled by parallel programming.

Usage

optimal_multiarm(
  hr1,
  hr2,
  ec,
  n2min,
  n2max,
  stepn2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  strategy,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Strategy

Strategy, 1: "only best promising" or 2: "all promising"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

optimal threshold value for the decision rule to go to phase III

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg2

probability of a successful program with two arms in phase III

sProg3

probability of a successful program with three arms in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal Designs for Multi-Arm Phase II/III Drug Development Programs. Submitted to peer-review journal.

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multiarm(hr1 = 0.75, hr2 = 0.80,    # define assumed true HRs 
  ec = 0.6,                                          # control arm event rate
  n2min = 30, n2max = 90, stepn2 = 6,                # define optimization set for n2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05,     # define optimization set for HRgo
  alpha = 0.025, beta = 0.1,                         # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,           # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 1,                                        # define lower boundary for "small"
  stepm1 = 0.95,                                     # "medium"
  stepl1 = 0.85,                                     # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                   # define expected benefit 
  strategy = 1,                                      # choose strategy: 1, 2 or 3
  num_cl = 1)                                        # number of cores for parallelized computing 
  

Optimal phase II/III drug development planning for multi-arm programs with binary endpoint

Description

The optimal_multiarm_binary function enables planning of multi-arm phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules. For binary endpoints the treatment effect is measured by the risk ratio (RR). So far, only three-arm trials with two treatments and one control are supported. The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_multiarm_binary(
  p0,
  p11,
  p12,
  n2min,
  n2max,
  stepn2,
  rrgomin,
  rrgomax,
  steprrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  strategy,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Strategy

Strategy, 1: "only best promising" or 2: "all promising"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

RRgo

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg2

probability of a successful program with two arms in phase III

sProg3

probability of a successful program with three arms in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multiarm_binary( p0 = 0.6, 
  p11 =  0.3, p12 = 0.5, 
  n2min = 20, n2max = 100, stepn2 = 4,               # define optimization set for n2
  rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05,     # define optimization set for RRgo
  alpha = 0.025, beta = 0.1,                         # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,           # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 1,                                        # define lower boundary for "small"
  stepm1 = 0.95,                                     # "medium"
  stepl1 = 0.85,                                     # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                   # define expected benefits 
  strategy = 1, num_cl = 1)                          # number of cores for parallelized computing 
  

Generic function for optimizing multi-arm programs

Description

Generic function for optimizing multi-arm programs

Usage

optimal_multiarm_generic(
  n2min,
  n2max,
  stepn2,
  beta,
  alpha,
  c2,
  c3,
  c02,
  c03,
  K,
  N,
  S,
  b1,
  b2,
  b3,
  strategy,
  num_cl
)

Arguments

Optimal phase II/III drug development planning for multi-arm programs with normally distributed endpoint

Description

The optimal_multiarm_normal function enables planning of multi-arm phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules. For normally distributed endpoints, the treatment effect is measured by the standardized difference in means (Delta). So far, only three-arm trials with two treatments and one control are supported. The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_multiarm_normal(
  Delta1,
  Delta2,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  strategy,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Strategy

Strategy, 1: "only best promising" or 2: "all promising"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

Kappa

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg2

probability of a successful program with two arms in phase III

sProg3

probability of a successful program with three arms in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multiarm_normal(Delta1 = 0.375, Delta2 = 0.625,     
  n2min = 20, n2max = 100, stepn2 = 4,                 # define optimization set for n2
  kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02,   # define optimization set for kappa
  alpha = 0.025, beta = 0.1,                           # drug development planning parameters
  c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20,           # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                          # set constraints
  steps1 = 0,                                          # define lower boundary for "small"
  stepm1 = 0.5,                                        # "medium"
  stepl1 = 0.8,                                        # and "large" effect size categories
  b1 = 3000, b2 = 8000, b3 = 10000,                    # define expected benefits 
  strategy = 1,
  num_cl = 1)                                          # number of cores for parallelized computing 
  

Generic function for optimizing drug development programs with multiple endpoints

Description

This function is only used for documentation generation.

Usage

optimal_multiple_generic(rho, alpha, n2min, n2max, stepn2, fixed)

Arguments

Value

No return value

Optimal phase II/III drug development planning for programs with multiple normally distributed endpoints

Description

The function optimal_multiple_normal of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules for two-arm trials with two normally distributed endpoints and one control group (Preussler et. al, 2019).

Usage

optimal_multiple_normal(
  Delta1,
  Delta2,
  in1,
  in2,
  sigma1,
  sigma2,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  rho,
  fixed,
  relaxed = FALSE,
  num_cl = 1
)

Arguments

Details

For this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and all endpoints show a statistically significant treatment effect in phase III. For example, this situation is found in Alzheimer’s disease trials, where a drug should show significant results in improving cognition (cognitive endpoint) as well as in improving activities of daily living (functional endpoint).

The effect size categories small, medium and large are applied to both endpoints. In order to define an overall effect size from the two individual effect sizes, the function implements two different combination rules:

• A strict rule (relaxed = FALSE) assigning a large overall effect in case both endpoints show an effect of large size, a small overall effect in case that at least one of the endpoints shows a small effect, and a medium overall effect otherwise, and

• A relaxed rule (relaxed = TRUE) assigning a large overall effect if at least one of the endpoints shows a large effect, a small effect if both endpoints show a small effect, and a medium overall effect otherwise.

Fast computing is enabled by parallel programming.

Monte Carlo simulations are applied for calculating utility, event count and other operating characteristics in this setting. Hence, the results are affected by random uncertainty.

Value

The output of the function is a data.frame object containing the optimization results:

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

Kappa

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Meinhard Kieser, Marietta Kirchner, Eva Dölger, Heiko Götte (2018). Optimal planning of phase II/III programs for clinical trials with multiple endpoints

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

set.seed(123) # This function relies on Monte Carlo integration
optimal_multiple_normal(Delta1 = 0.75,
  Delta2 = 0.80, in1=300, in2=600,                   # define assumed true HRs
  sigma1 = 8, sigma2= 12,                            # variances for both endpoints
  n2min = 30, n2max = 90, stepn2 = 10,               # define optimization set for n2
  kappamin = 0.05, kappamax = 0.2, stepkappa = 0.05, # define optimization set for HRgo
  alpha = 0.025, beta = 0.1,                         # planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,           # fixed/variable costs: phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 0,                                        # define lower boundary for "small"
  stepm1 = 0.5,                                      # "medium"
  stepl1 = 0.8,                                      # and "large" effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                   # define expected benefit
  rho = 0.5, relaxed = TRUE,                         # strict or relaxed rule
  fixed = TRUE,                                      # treatment effect
  num_cl = 1)                                        # parallelized computing
  

Optimal phase II/III drug development planning for programs with multiple time-to-event endpoints

Description

The function optimal_multiple_tte of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules (Preussler et. al, 2019) in a two-arm trial with two time-to-event endpoints.

Usage

optimal_multiple_tte(
  hr1,
  hr2,
  id1,
  id2,
  n2min,
  n2max,
  stepn2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  b11,
  b21,
  b31,
  b12,
  b22,
  b32,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  rho,
  fixed = TRUE,
  num_cl = 1
)

Arguments

Details

In this setting, the drug development program is defined to be successful if it proceeds from phase II to phase III and at least one endpoint shows a statistically significant treatment effect in phase III. For example, this situation is found in oncology trials, where overall survival (OS) and progression-free survival (PFS) are the two endpoints of interest.

The gain of a successful program may differ according to the importance of the endpoint that is significant. If endpoint 1 is significant (no matter whether endpoint 2 is significant or not), then the gains b11, b21 and b31 will be used for calculation of the utility. If only endpoint 2 is significant, then b12, b22 and b32 will be used. This also matches the oncology example, where OS (i.e. endpoint 1) implicates larger expected gains than PFS alone (i.e. endpoint 2).

Fast computing is enabled by parallel programming.

Monte Carlo simulations are applied for calculating utility, event count and other operating characteristics in this setting. Hence, the results are affected by random uncertainty. The extent of uncertainty is discussed in (Kieser et al. 2018).

Value

The output of the function is a data.frame object containing the optimization results:

OP

probability that one endpoint is significant

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

optimal threshold value for the decision rule to go to phase III

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Kieser, M., Kirchner, M. Dölger, E., Götte, H. (2018).Optimal planning of phase II/III programs for clinical trials with multiple endpoints, Pharm Stat. 2018 Sep; 17(5):437-457.

Preussler, S., Kirchner, M., Goette, H., Kieser, M. (2019). Optimal Designs for Multi-Arm Phase II/III Drug Development Programs. Submitted to peer-review journal.

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

set.seed(123) # This function relies on Monte Carlo integration
optimal_multiple_tte(hr1 = 0.75,
  hr2 = 0.80, id1 = 210, id2 = 420,          # define assumed true HRs
  n2min = 30, n2max = 90, stepn2 = 6,        # define optimization set for n2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05, # define optimization set for HRgo
  alpha = 0.025, beta = 0.1,                 # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,   # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                # set constraints
  steps1 = 1,                                # define lower boundary for "small"
  stepm1 = 0.95,                             # "medium"
  stepl1 = 0.85,                             # and "large" effect size categories
  b11 = 1000, b21 = 2000, b31 = 3000,
  b12 = 1000, b22 = 1500, b32 = 2000,        # define expected benefits (both scenarios)
  rho = 0.6, fixed = TRUE,                   # correlation and treatment effect
  num_cl = 1)                                # number of cores for parallelized computing
 

Optimal phase II/III drug development planning where several phase III trials are performed for time-to-event endpoints

Description

The function optimal_multitrial of the drugdevelopR package enables planning of phase II/III drug development programs with time-to-event endpoints for programs with several phase III trials (Preussler et. al, 2019). Its main output values are the optimal sample size allocation and optimal go/no-go decision rules. The assumed true treatment effects can be assumed to be fixed (planning is then also possible via user friendly R Shiny App: multitrial) or can be modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_multitrial(
  w,
  hr1,
  hr2,
  id1,
  id2,
  d2min,
  d2max,
  stepd2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  xi2,
  xi3,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  b1,
  b2,
  b3,
  case,
  strategy = TRUE,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function is a data.frame object containing the optimization results:

Case

Case: "number of significant trials needed"

Strategy

Strategy: "number of trials to be conducted in order to achieve the goal of the case"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

optimal threshold value for the decision rule to go to phase III

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 1, as proposed by IQWiG (2016))

sProg2

probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.95, as proposed by IQWiG (2016))

sProg3

probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.85, as proposed by IQWiG (2016))

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

Effect sizes

In other settings, the definition of "small", "medium" and "large" effect sizes can be user-specified using the input parameters steps1, stepm1 and stepl1. Due to the complexity of the multitrial setting, this feature is not included for this setting. Instead, the effect sizes were set to to predefined values as explained under sProg1, sProg2 and sProg3 in the Value section.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Preussler, S., Kieser, M., and Kirchner, M. (2019). Optimal sample size allocation and go/no-go decision rules for phase II/III programs where several phase III trials are performed. Biometrical Journal, 61(2), 357-378.

Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multitrial(w = 0.3,                # define parameters for prior
  hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420,     # (https://web.imbi.uni-heidelberg.de/prior/)
  d2min = 20, d2max = 100, stepd2 = 5,              # define optimization set for d2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05,    # define optimization set for HRgo
  alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7,  # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,          # fixed and variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                       # set constraints
  b1 = 1000, b2 = 2000, b3 = 3000,                  # expected benefit for each effect size
  case = 1, strategy = TRUE,                        # chose Case and Strategy
  fixed = TRUE,                                     # true treatment effects are fixed/random
  num_cl = 1)                                       # number of cores for parallelized computing

Optimal phase II/III drug development planning where several phase III trials are performed

Description

The optimal_multitrial_binary function enables planning of phase II/III drug development programs with several phase III trials for the same binary endpoint. The main output values are optimal sample size allocation and go/no-go decision rules. For binary endpoints, the treatment effect is measured by the risk ratio (RR).

Usage

optimal_multitrial_binary(
  w,
  p0,
  p11,
  p12,
  in1,
  in2,
  n2min,
  n2max,
  stepn2,
  rrgomin,
  rrgomax,
  steprrgo,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  b1,
  b2,
  b3,
  case,
  strategy = TRUE,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Details

The assumed true treatment effects can be assumed fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package.

Fast computing is enabled by parallel programming.

Value

The output of the function is a data.frame object containing the optimization results:

Case

Case: "number of significant trials needed"

Strategy

Strategy: "number of trials to be conducted in order to achieve the goal of the case"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

RRgo

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 1, as proposed by IQWiG (2016))

sProg2

probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.95, as proposed by IQWiG (2016))

sProg3

probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.85, as proposed by IQWiG (2016))

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

Effect sizes

In other settings, the definition of "small", "medium" and "large" effect sizes can be user-specified using the input parameters steps1, stepm1 and stepl1. Due to the complexity of the multitrial setting, this feature is not included for this setting. Instead, the effect sizes were set to to predefined values as explained under sProg1, sProg2 and sProg3 in the Value section.

References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multitrial_binary(w = 0.3,         # define parameters for prior
  p0 = 0.6, p11 =  0.3, p12 = 0.5,
  in1 = 30, in2 = 60,                             # (https://web.imbi.uni-heidelberg.de/prior/)
  n2min = 20, n2max = 100, stepn2 = 4,            # define optimization set for n2
  rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05,  # define optimization set for RRgo
  alpha = 0.025, beta = 0.1,                      # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,        # fixed and variable costs for phase II/III,
  K = Inf, N = Inf, S = -Inf,                     # set constraints
  b1 = 1000, b2 = 2000, b3 = 3000,                # expected benefit for a each effect size
  case = 1, strategy = TRUE,                      # chose Case and Strategy                                   
  fixed = TRUE,                                   # true treatment effects are fixed/random
  num_cl = 1)                                     # number of cores for parallelized computing
  

Generic function for optimizing multi-trial programs

Description

Generic function for optimizing multi-trial programs

Usage

optimal_multitrial_generic(case, strategy = TRUE)

Arguments

Effect sizes

In other settings, the definition of "small", "medium" and "large" effect sizes can be user-specified using the input parameters steps1, stepm1 and stepl1. Due to the complexity of the multitrial setting, this feature is not included for this setting. Instead, the effect sizes were set to to predefined values as explained under sProg1, sProg2 and sProg3 in the Value section.

Optimal phase II/III drug development planning where several phase III trials are performed

Description

The optimal_multitrial_normal function enables planning of phase II/III drug development programs with several phase III trials for the same normally distributed endpoint. Its main output values are optimal sample size allocation and go/no-go decision rules. For normally distributed endpoints, the treatment effect is measured by the standardized difference in means (Delta). The assumed true treatment effects can be assumed fixed or modelled by a prior distribution.

Usage

optimal_multitrial_normal(
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  b1,
  b2,
  b3,
  case,
  strategy = TRUE,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Details

The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Value

The output of the function is a data.frame object containing the optimization results:

Case

Case: "number of significant trials needed"

Strategy

Strategy: "number of trials to be conducted in order to achieve the goal of the case"

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

Kappa

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III (lower boundary in HR scale is set to 0, as proposed by Cohen (1988))

sProg2

probability of a successful program with "medium" treatment effect in phase III (lower boundary in HR scale is set to 0.5, as proposed Cohen (1988))

sProg3

probability of a successful program with "large" treatment effect in phase III (lower boundary in HR scale is set to 0.8, as proposed Cohen (1988))

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

Effect sizes

In other settings, the definition of "small", "medium" and "large" effect sizes can be user-specified using the input parameters steps1, stepm1 and stepl1. Due to the complexity of the multitrial setting, this feature is not included for this setting. Instead, the effect sizes were set to to predefined values as explained under sProg1, sProg2 and sProg3 in the Value section.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_multitrial_normal(w = 0.3,           # define parameters for prior
  Delta1 = 0.375, Delta2 = 0.625,
  in1 = 300, in2 = 600,                               # (https://web.imbi.uni-heidelberg.de/prior/)
  a = 0.25, b = 0.75,
  n2min = 20, n2max = 100, stepn2 = 4,                # define optimization set for n2
  kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02,  # define optimization set for kappa
  alpha = 0.025, beta = 0.1,                          # drug development planning parameters
  c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20,          # fixed and variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                         # set constraints
  b1 = 3000, b2 = 8000, b3 = 10000,                   # expected benefit for each effect size                                         
  case = 1, strategy = TRUE,                          # chose Case and Strategy
  fixed = TRUE,                                       # true treatment effects are fixed/random
  num_cl = 1)                                         # number of cores for parallelized computing
  

Optimal phase II/III drug development planning with normally distributed endpoint

Description

The function optimal_normal of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules for normally distributed endpoints. The treatment effect is measured by the standardized difference in means. The assumed true treatment effects can be assumed to be fixed or modelled by a prior distribution. The R Shiny application prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_normal(
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  skipII = FALSE,
  num_cl = 1
)

Arguments

Value

The output of the function optimal_normal is a data.frame containing the optimization results:

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

Kappa

optimal threshold value for the decision rule to go to phase III

n2

total sample size for phase II

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters.

Taking cat(comment()) of the data.frame object lists the used optimization sequences, start and finish date of the optimization procedure. Taking attr(,"trace") returns the utility values of all parameter combinations visited during optimization

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences.

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize

optimal_normal(w=0.3,                       # define parameters for prior
  Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600,  # (https://web.imbi.uni-heidelberg.de/prior/)
  a = 0.25, b = 0.75,
  n2min = 20, n2max = 100, stepn2 = 4,               # define optimization set for n2
  kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, # define optimization set for kappa
  alpha = 0.025, beta = 0.1,                          # drug development planning parameters
  c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20,         # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                        # set constraints
  steps1 = 0,                                        # define lower boundary for "small"
  stepm1 = 0.5,                                      # "medium"
  stepl1 = 0.8,                                      # and "large" effect size categories
  b1 = 3000, b2 = 8000, b3 = 10000,                  # benefit for each effect size category
  gamma = 0,                                         # population structures in phase II/III
  fixed = FALSE,                                     # true treatment effects are fixed/random
  skipII = FALSE,                                    # skipping phase II
  num_cl = 1)                                        # number of cores for parallelized computing

Generic function for optimizing normally distributed endpoints

Description

Generic function for optimizing normally distributed endpoints

Usage

optimal_normal_generic(
  w,
  Delta1,
  Delta2,
  in1,
  in2,
  a,
  b,
  n2min,
  n2max,
  stepn2,
  kappamin,
  kappamax,
  stepkappa,
  alpha,
  beta,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 0,
  stepm1 = 0.5,
  stepl1 = 0.8,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Function for generating documentation of return values

Description

Generates the documentation of the return value of an optimal function including some custom text.

Usage

optimal_return_doc(type, setting = "basic")

Arguments

Value

string containing the documentation of the return value.

Optimal phase II/III drug development planning with time-to-event endpoint

Description

The function optimal_tte of the drugdevelopR package enables planning of phase II/III drug development programs with optimal sample size allocation and go/no-go decision rules for time-to-event endpoints (Kirchner et al., 2016). The assumed true treatment effects can be assumed to be fixed or modelled by a prior distribution. When assuming fixed true treatment effects, planning can also be done with the user-friendly R Shiny app basic. The app prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_tte(
  w,
  hr1,
  hr2,
  id1,
  id2,
  d2min,
  d2max,
  stepd2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  xi2,
  xi3,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  skipII = FALSE,
  num_cl = 1
)

Arguments

Format

data.frame containing the optimization results (see Value)

Value

The output of the function is a data.frame object containing the optimization results:

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

optimal threshold value for the decision rule to go to phase III

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

n2

total sample size for phase II; rounded to the next even natural number

n3

total sample size for phase III; rounded to the next even natural number

n

total sample size in the program; n = n2 + n3

K

maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

pgo

probability to go to phase III

sProg

probability of a successful program

sProg1

probability of a successful program with "small" treatment effect in phase III

sProg2

probability of a successful program with "medium" treatment effect in phase III

sProg3

probability of a successful program with "large" treatment effect in phase III

K2

expected costs for phase II

K3

expected costs for phase III

and further input parameters. Taking cat(comment()) of the data frame lists the used optimization sequences, start and finish time of the optimization procedure. The attribute attr(,"trace") returns the utility values of all parameter combinations visited during optimization.

References

Kirchner, M., Kieser, M., Goette, H., & Schueler, A. (2016). Utility-based optimization of phase II/III programs. Statistics in Medicine, 35(2), 305-316.

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, last access 15.05.19.

Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.

See Also

optimal_binary, optimal_normal, optimal_bias, optimal_multitrial and optimal_multiarm

Examples

# Activate progress bar (optional)
## Not run: 
progressr::handlers(global = TRUE)

## End(Not run)
# Optimize

optimal_tte(w = 0.3,                    # define parameters for prior
  hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420,   # (https://web.imbi.uni-heidelberg.de/prior/)
  d2min = 20, d2max = 100, stepd2 = 5,            # define optimization set for d2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05,  # define optimization set for HRgo
  alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,        # fixed/variable costs for phase II/III
  K = Inf, N = Inf, S = -Inf,                     # set constraints
  steps1 = 1,                                     # define lower boundary for "small"
  stepm1 = 0.95,                                  # "medium"
  stepl1 = 0.85,                                  # and "large" treatment effect size categories
  b1 = 1000, b2 = 2000, b3 = 3000,                # expected benefit for each effect size category
  gamma = 0,                                      # population structures in phase II/III
  fixed = FALSE,                                  # true treatment effects are fixed/random
  skipII = FALSE,                                 # skipping phase II 
  num_cl = 1)                                     # number of cores for parallelized computing 

Generic function for optimal planning of time-to-event endpoints

Description

Generic function for optimal planning of time-to-event endpoints

Usage

optimal_tte_generic(
  w,
  hr1,
  hr2,
  id1,
  id2,
  d2min,
  d2max,
  stepd2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  xi2,
  xi3,
  c2,
  c3,
  c02,
  c03,
  K = Inf,
  N = Inf,
  S = -Inf,
  steps1 = 1,
  stepm1 = 0.95,
  stepl1 = 0.85,
  b1,
  b2,
  b3,
  gamma = 0,
  fixed = FALSE,
  num_cl = 1
)

Arguments

Probability that endpoint OS significant

Description

This function calculate the probability that the endpoint OS is statistically significant. In the context of cancer research OS stands for overall survival, a positive treatment effect in this endpoints is thus sufficient for a successful program.

Usage

os_tte(HRgo, n2, alpha, beta, hr1, hr2, id1, id2, fixed, rho, rsamp)

Arguments

Value

The output of the function os_tte() is the probability that endpoint OS significant.

Probability to go to phase III for multiarm programs with binary distributed outcomes

Description

Given our parameters this function calculates the probability to go to phase III after the second phase was conducted. The considered strategies are as follows:

• 1. Strategy: Only best promising treatment goes to phase III

Usage

pgo_binary(RRgo, n2, p0, p11, p12, strategy, case)

Arguments

Value

The function pgo_binary() returns the probability to go to phase III.

Examples

res <- pgo_binary(RRgo = 0.8 ,n2 = 50 ,p0 = 0.6, p11 =  0.3, p12 = 0.5,strategy = 2, case = 31)

Probability to go to phase III for multiple endpoints with normally distributed outcomes

Description

This function calculated the probability that we go to phase III, i.e. that results of phase II are promising enough to get a successful drug development program. Successful means that both endpoints show a statistically significant positive treatment effect in phase III.

Usage

pgo_multiple_normal(
  kappa,
  n2,
  Delta1,
  Delta2,
  in1,
  in2,
  sigma1,
  sigma2,
  fixed,
  rho,
  rsamp
)

Arguments

Value

The output of the function pgo_multiple_normal() is the probability to go to phase III.

Probability to go to phase III for multiple endpoints in the time-to-event setting

Description

This function calculates the probability that we go to phase III, i.e. that results of phase II are promising enough to get a successful drug development program. Successful means that at least one endpoint shows a statistically significant positive treatment effect in phase III.

Usage

pgo_multiple_tte(HRgo, n2, hr1, hr2, id1, id2, fixed, rho)

Arguments

Value

The output of the function pgo_multiple_tte() is the probability to go to phase III.

Probability to go to phase III for multiarm programs with normally distributed outcomes

Description

Given our parameters this function calculates the probability to go to phase III after the second phase was conducted. The considered strategies are as follows:

• 1. Strategy: Only best promising treatment goes to phase III

Usage

pgo_normal(kappa, n2, Delta1, Delta2, strategy, case)

Arguments

Value

The function pgo_normal() returns the probability to go to phase III for multiarm programs with normally distributed outcomes

Examples

res <- pgo_normal(kappa = 0.1, n2 = 50, Delta1 = 0.375, Delta2 = 0.625, strategy = 2, case = 31)

Probability to go to phase III for multiarm programs with time-to-event outcomes

Description

Given our parameters this function calculates the probability to go to phase III after the second phase was conducted. The considered strategies are as follows:

• 1. Strategy: Only best promising treatment goes to phase III

Usage

pgo_tte(HRgo, n2, ec, hr1, hr2, strategy, case)

Arguments

Value

The function pgo_tte() returns the probability to go to phase III.

Examples

res <- pgo_tte(HRgo = 0.8, n2 = 48 , ec = 0.6, hr1 = 0.7, hr2 = 0.8, strategy = 2, case = 31)

Probability of a successful program, when going to phase III for multiple endpoint with normally distributed outcomes

Description

After getting the "go"-decision to go to phase III, i.e. our results of phase II are over the predefined threshold kappa, this function calculates the probability, that our program is successfull, i.e. that both endpoints show a statistically significant positive treatment effect in phase III.

Usage

posp_normal(
  kappa,
  n2,
  alpha,
  beta,
  Delta1,
  Delta2,
  sigma1,
  sigma2,
  in1,
  in2,
  fixed,
  rho,
  rsamp
)

Arguments

Value

The output of the function posp_normal() is the probability of a successful program, when going to phase III.

Printing a drugdevelopResult Object

Description

Displays details about the optimal results from a drugdevelopResult object.

Usage

## S3 method for class 'drugdevelopResult'
print(x, sequence = FALSE, ...)

Arguments

Examples

# Activate progress bar (optional)
## Not run: progressr::handlers(global = TRUE)
# Optimize
res <- optimal_normal(w=0.3,                       
  Delta1 = 0.375, Delta2 = 0.625, in1=300, in2=600,  
  a = 0.25, b = 0.75,
  n2min = 20, n2max = 100, stepn2 = 4,               
  kappamin = 0.02, kappamax = 0.2, stepkappa = 0.02, 
  alpha = 0.025, beta = 0.1,                       
  c2 = 0.675, c3 = 0.72, c02 = 15, c03 = 20,   
  K = Inf, N = Inf, S = -Inf,                        
  steps1 = 0,                                      
  stepm1 = 0.5,                                      
  stepl1 = 0.8,                                      
  b1 = 3000, b2 = 8000, b3 = 10000,                  
  gamma = 0,                                         
  fixed = FALSE,                                    
  skipII = FALSE,                                    
  num_cl = 1)
# Print results
print(res)                                  

Helper function for printing a drugdevelopResult Object

Description

Helper function for printing a drugdevelopResult Object

Usage

print_drugdevelopResult_helper(x, ...)

Arguments

Value

No return value, called for printing to the console using cat()

Prior distribution for time-to-event outcomes

Description

If we do not assume the treatment effects to be fixed, i.e. fixed = FALSE, the function prior_tte allows us to model the treatment effect following a prior distribution. For more details concerning the definition of a prior distribution, see the vignette on priors as well as the Shiny app.

Usage

prior_tte(x, w, hr1, hr2, id1, id2)

Arguments

Value

The output of the functions Epgo_tte() is the expected number of participants in phase III with conservative decision rule and sample size calculation.

Examples

res <- prior_tte(x = 0.5, w = 0.5, hr1 = 0.69, hr2 = 0.88, id1 = 240, id2 = 420)

Probabilty that effect in endpoint one is larger than in endpoint two

Description

This function calculated the probability that the treatment effect in endpoint one (or endpoint x) is larger than in endpoint two (or endpoint y), i.e. P(x>y) = P(x-y>0)

Usage

pw(n2, hr1, hr2, id1, id2, fixed, rho)

Arguments

Details

Z=X-Y is normally distributed with expectation mu_x - mu_y and variance sigma_x + sigma_y- 2 rho sdx sdy

Value

The output of the function pw() is the probability that endpoint one has a better result than endpoint two

Total sample size for phase III trial with l treatments and equal allocation ratio for binary outcomes

Description

Depending on the results of phase II and our strategy ,i.e. whether we proceed only with the best promising treatment (l = 1) or with all promising treatments (l = 2), this program calculates the number of participants in phase III.

l=1: according to Schoenfeld to guarantee power for the log rank test to detect treatment effect of phase II;

l=2: according to Dunnett to guarantee y any-pair power (Horn & Vollandt)

Usage

ss_binary(alpha, beta, p0, p11, y, l)

Arguments

Value

the function ss_binary() returns the total sample size for phase III trial with l treatments and equal allocation ratio

Examples

res <- ss_binary(alpha = 0.05, beta = 0.1, p0 = 0.6, p11 = 0.3, y = 0.5, l = 1)

Total sample size for phase III trial with l treatments and equal allocation ratio for normally distributed outcomes

Description

Depending on the results of phase II and our strategy ,i.e. whether we proceed only with the best promising treatment (l = 1) or with all promising treatments (l = 2), this program calculates the number of participants in phase III.

l=1: according to Schoenfeld to guarantee power for the log rank test to detect treatment effect of phase II;

l=2: according to Dunnett to guarantee y any-pair power (Horn & Vollandt)

Usage

ss_normal(alpha, beta, y, l)

Arguments