Type: Package
Date: 2022-05-13
Version: 1.1.0
Title: Time Varying Mediation Analysis
Description: Provides functions for estimating mediation effects that vary over time as described in Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.
RoxygenNote: 7.1.2
Depends: R (≥ 4.0.0)
Imports: stats (≥ 4.0.2), dplyr (≥ 1.0.2), ggplot2 (≥ 3.3.2), locpol (≥ 0.7-0)
Suggests: knitr, rmarkdown
License: GPL-3
URL: https://github.com/dcoffman/tvmediation/wiki
BugReports: https://github.com/dcoffman/tvmediation/issues
LazyData: true
VignetteBuilder: knitr
Encoding: UTF-8
NeedsCompilation: no
Packaged: 2022-05-21 15:38:02 UTC; yajna
Author: Donna Coffman ORCID iD [aut, cre], Xizhen Cai ORCID iD [aut], Yajnaseni Chakraborti ORCID iD [aut], Harry Zobel [ctb]
Maintainer: Donna Coffman <dcoffman@temple.edu>
Repository: CRAN
Date/Publication: 2022-05-25 06:40:02 UTC

Function to transpose the data from long to wide format

Description

Transposing a dataset with repeated measurements/responses for each subject from longitudinal to wide format.

Usage

LongToWide(subject.id, time.sequence, outcome, verbose = FALSE)

Arguments

subject.id

a column of subject identifiers

time.sequence

a column of time points

outcome

a column to be transposed

verbose

TRUE or FALSE (default = FALSE) prints output to screen (OPTIONAL INPUT)

Details

If data is not sorted by subject.id, a warning message will appear. The function will then sort the data by subject.id. It is recommended that the user sorts the data prior to using this function.

Value

mat.wide

a matrix in wide format, in which each column is the outcome for each subject and each row is the time sequence

Examples

# CREATING A TRANSPOSED MATRIX FOR MEDIATOR `WantToSmokeLst15min`
data(smoker)
mat.wide <- LongToWide(smoker$SubjectID,
                       smoker$timeseq,
                       smoker$WantToSmokeLst15min)

Bootstrap function for computing CIs for coefficients for a continuous outcome and two treatment groups

Description

Part of the set of internal functions for estimating bootstrapped CIs for the coefficients of the mediation model for continuous outcome and two treatment groups.

Usage

bootci_coeff_2trt(trt, t.seq, M, Y, t.est, deltat, replicates)

Arguments

trt

a vector indicating treatment group

t.seq

a vector of time points for each observation

M

matrix of mediator values in wide format

Y

matrix of outcome values in wide format

t.est

time points at which to make the estimation. Default = t.seq

deltat

a small constant which controls the time-lag of the effect of the mediator on the outcome.

replicates

number of replicates for bootstrapping confidence intervals. Default = 1000

Value

CI.upper.alpha

CI upper limit for coefficient hat.alpha

CI.lower.alpha

CI lower limit for coefficient hat.alpha

CI.upper.gamma

CI upper limit for coefficient hat.gamma

CI.lower.gamma

CI lower limit for coefficient hat.gamma

CI.upper.beta

CI upper limit for coefficient hat.beta

CI.lower.beta

CI lower limit for coefficient hat.beta

CI.upper.tau

CI upper limit for coefficient hat.tau

CI.lower.tau

CI lower limit for coefficient hat.tau

Bootstrap samples to estimate confidence intervals for coefficients for a continuous outcome and three treatment groups.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for the coefficients of the mediation model for a continuous outcome and three treatment groups.

Usage

bootci_coeff_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est,
  original.coeff,
  boot.sample = 1000
)

Arguments

T1

a vector indicating assignment to treatment 1

T2

a vector indicating assignment to treatment 2

t.seq

a vector of time points for each observation

mediator

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

t.est

time points at which to make the estimation. Default = t.seq

original.coeff

a list of the estimated coefficients.

boot.sample

number of replicates for bootstrapping confidence intervals. Default = 1000.

Value

alw1

CI lower limit for estimated Treatment 1 effect on mediator

aup1

CI upper limit for estimated Treatment 1 effect on mediator

alw2

CI lower limit for estimated Treatment 2 effect on mediator

aup2

CI upper limit for estimated Treatment 2 effect on mediator

glw1

CI lower limit for estimated Treatment 1 direct effect on outcome

gup1

CI upper limit for estimated Treatment 1 direct effect on outcome

glw2

CI lower limit for estimated Treatment 2 direct effect on outcome

gup2

CI upper limit for estimated Treatment 2 direct effect on outcome

tlw1

CI lower limit for estimated Treatment 1 total effect on outcome

tup1

CI upper limit for estimated Treatment 1 total effect on outcome

tlw2

CI lower limit for estimated Treatment 2 total effect on outcome

tup2

CI upper limit for estimated Treatment 2 total effect on outcome

blw

CI lower limit for estimated effect of mediator on outcome

bup

CI upper limit for estimated effect of mediator on outcome

Bootstrap samples to estimate confidence intervals for binary outcome coefficients.

Description

Internal function for estimating bootstrapped confidence intervals for the coefficients of the mediation model for a binary outcome.

Usage

bootci_coeff_binary(
  treatment,
  t.seq,
  m,
  outcome,
  span = 0.75,
  replicates = 1000
)

Arguments

treatment

a vector indicating treatment group

t.seq

a vector of unique time points for each observation

m

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

span

Numeric value of the span to be used for LOESS regression. Default = 0.75.

replicates

Number of replicates for bootstrapping confidence intervals. Default = 1000.

Value

t.seq

time points of estimation

CI.lower.a

CI lower limit for alpha_hat

CI.upper.a

CI upper limit for alpha_hat

CI.lower.g

CI lower limit for gamma_hat

CI.upper.g

CI upper limit for gamma_hat

CI.lower.b

CI lower limit for beta_hat

CI.upper.b

CI upper limit for beta_hat

CI.lower.t

CI lower limit for tau_hat

CI.upper.t

CI upper limit for tau_hat

Bootstrap samples to estimate confidence intervals for continuous outcome and three treatment groups.

Description

Internal function for estimating bootstrapped confidence intervals for the mediation effect of continuous outcome and three treatment groups when user argument CI="boot".

Usage

bootci_tvm_3trt(boot.sample, orig.data, t.est)

Arguments

boot.sample

number of replicates for bootstrapping confidence intervals. Default = 1000.

orig.data

a list of original data T1, T2, mediator, outcome and t.seq.

t.est

time points at which to make the estimation. Default = t.seq.

Value

plw1

CI lower limit for estimated mediation effect of T1

pup1

CI upper limit for estimated mediation effect of T1

plw2

CI lower limit for estimated mediation effect of T2

pup2

CI upper limit for estimated mediation effect of T2

orig.se1.all

estimated standard errors for the mediation effect of T1

orig.se2.all

estimated standard errors for the mediation effect of T2

orig.mediation1

time varying mediation effect for T1

orig.mediation2

time varying mediation effect for T2

Bootstrap samples to estimate confidence intervals for the mediation effect for a binary outcome.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for the mediation effect for a binary outcome when user argument CI="boot".

Usage

bootci_tvmb(
  treatment,
  t.seq,
  m,
  outcome,
  coeff_data,
  span = 0.75,
  replicates = 1000
)

Arguments

treatment

a vector indicating treatment group

t.seq

a vector of unique time points for each observation

m

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

coeff_data

a merged dataset of indirect and direct effects and CIs estimated from bootci_coeff_binary

span

Numeric value of the span to be used for LOESS regression. Default = 0.75.

replicates

number of replicates for bootstrapping CIs. Default = 1000.

Value

timeseq

time points of estimation

alpha_hat

time-varying treatment effect on the mediator

CI.lower.a

CI lower limit for estimated coefficient alpha_hat

CI.upper.a

CI upper limit for estimated coefficient alpha_hat

gamma_hat

time-varying treatment effect on the outcome (direct effect)

CI.lower.g

CI lower limit for estimated coefficient gamma_hat

CI.upper.g

CI upper limit for estimated coefficient gamma_hat

beta_hat

time-varying effect of the mediator on the outcome

CI.lower.b

CI lower limit for estimated coefficient beta_hat

CI.upper.b

CI upper limit for estimated coefficient beta_hat

tau_hat

time-varying treatment effect on outcome (total effect)

CI.lower.t

CI lower limit for estimated coefficient tau_hat

CI.upper.t

CI upper limit for estimated coefficient tau_hat

medEffect

time varying mediation effect

CI.lower

CI lower limit for medEffect

CI.upper

CI upper limit for medEffect

Function to estimate coefficients at time t

Description

Part of the set of internal functions called within the tvmcurve_3trt function to assist in the estimation of time varying mediation effect.

Usage

coeff(j, T1, T2, x, y)

Arguments

j

a number indicating time point of observation

T1

a vector indicating assignment to treatment 1

T2

a vector indicating assignment to treatment 2

x

matrix of mediator values in wide format

y

matrix of outcome outcomes in wide format

Value

coeff.est

estimated coefficients of the mediation model

nomissing.index

index of complete cases

Bootstrapping samples to estimate mediation effects confidence intervals for continuous outcome and two treatment (exposure) groups.

Description

Part of the set of internal functions for estimating bootstrapped confidence intervals for continuous outcome and two treatment groups when user argument CI="boot".

Usage

estBootCIs(trt, t.seq, M, Y, t.est, deltat, replicates)

Arguments

trt

a vector indicating treatment group

t.seq

a vector of time points at each obs

M

matrix of mediator values

Y

matrix of outcome values

t.est

time points at which to make the estimation

deltat

a small constant which controls the time-lag of the effect of the mediator on the outcome, half the time between two time points

replicates

number of replicates for bootstrapping confidence intervals.

Value

boot.sebootstrapped standard error for the estimated mediation effect

CI.upperpercentile bootstrapped CI upper limit for the estimated mediation effect

CI.lowerpercentile bootstrapped CI lower limit for the estimated mediation effect

Function to estimate coefficients at time t.

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of the time varying mediation effect.

Usage

estCoeff(newMO.j.est)

Arguments

newMO.j.est

a list containing mean centered mediators and outcomes

Value

coeff.est

estimated coefficients of the mediation model

Function to compute new Mediator and Outcome using time t and t-1 mean centered on the individual.

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of time varying mediation effect.

Usage

newMediatorOutcome(trt, M, Y)

Arguments

trt

numeric binary treatment group indicator for each individual

M

(t.seq x N) matrix where N = number of observations. Column 1 is mediator at time t-1. Column 2 is mediator at time t.

Y

(Nx1) matrix were N = number of observations. Column 1 is outcome at time t-1.

Value

newMO

list containing new mediators, outcomes, and index of complete cases

Wisconsin Smokers' Health Study 2

Description

The dataset is simulated based on the Wisconsin Smokers' Health Study 2.

Usage

data(smoker)

Format

A data frame with 40,130 observations on 12 variables.

  1. SubjectID: Subject ID

  2. treatment: Treatment group (2 = patch, 3 = varenicline, 4 = combination nicotine replacement therapy)

  3. patch: Received patch (0 = No, 1 = Yes)

  4. varenicline: Received varenicline (0 = No, 1 = Yes)

  5. comboNRT: Received combination nicotine replacement therapy (0 = No, 1 = Yes)

  6. DaysFromTQD: Number of days from quit date

  7. time.of.day: Time of day (0 = am, 1 = pm)

  8. timeseq: Number of days from quit date (.5 indicates pm)

  9. WantToSmokeLst15min: How did you feel in the last 15 min: wanting to smoke (1 = not at all, 7 = extremely)

  10. NegMoodLst15min: How did you feel in the last 15 min: Negative mood (1 = not at all, 7 = extremely)

  11. cessFatig: Cessation fatigue - I am tired of trying to quit smoking (1 = strongly disagree, 7 = strongly agree)

  12. CigCount: Cigarettes smoked over entire day

  13. smoke_status: Did you smoke (0 = No, 1 = Yes)

See Also

tvmb, tvma_3trt tvma, LongToWide

Examples

data(smoker)

Function to compute local polynomial estimation using rule of thumb for bandwidth selection

Description

Part of the set of internal functions called within the tvma function to assist in the estimation of the time varying mediation effect.

Usage

smoothest(t.seq, t.coeff, t.est, deltat)

Arguments

t.seq

a vector of time points at each observation

t.coeff

estimated coefficients

t.est

time points at which to make the estimation

deltat

a small constant which controls the time-lag of the effect of the mediator on the outcome, half the time between two time points

Value

bw_alpha

a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for alpha coefficient.

bw_gamma

a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for gamma coefficient.

bw_beta

a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for beta coefficient.

bw_beta

a number computed via Fan and Gijbels' (1996) rule of thumb for bandwidth selector for tau coefficient.

hat.alpha

estimated treatment effect on mediator

hat.gamma

estimated treatment effect on outcome, adjusted for mediator

hat.beta

estimated mediator effect on outcome

hat.tau

estimated treatment effect on outcome, not adjusting for mediator

est.M

estimated mediation effect, product of hat.alpha and hat.beta

Time Varying Mediation Function: Continuous Outcome and Two Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors for two treatment groups and a continuous outcome.

Usage

tvma(
  treatment,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)

Arguments

treatment

a vector indicating treatment group

t.seq

a vector of time points for each observation

mediator

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

t.est

a vector of time points at which to estimate. Default = t.seq (OPTIONAL ARGUMENT)

plot

TRUE or FALSE for producing plots. Default = "FALSE" (OPTIONAL ARGUMENT)

CI

"none" or "boot" method of deriving confidence intervals. Default = "boot" (OPTIONAL ARGUMENT)

replicates

number of replicates for bootstrapping confidence intervals. Default = 1000 (OPTIONAL ARGUMENT)

verbose

TRUE or FALSE for printing results to screen. Default = "FALSE" (OPTIONAL ARGUMENT)

Value

hat.alpha

estimated time-varying treatment effect on mediator

CI.lower.alpha

CI lower limit for estimated coefficient hat.alpha

CI.upper.alpha

CI upper limit for estimated coefficient hat.alpha

hat.gamma

estimated time-varying treatment effect on outcome (direct effect)

CI.lower.gamma

CI lower limit for estimated coefficient hat.gamma

CI.upper.gamma

CI upper limit for estimated coefficient hat.gamma

hat.beta

estimated time-varying effect of the mediator on outcome

CI.lower.beta

CI lower limit for estimated coefficient hat.beta

CI.upper.beta

CI upper limit for estimated coefficient hat.beta

hat.tau

estimated time-varying treatment effect on outcome (total effect)

CI.lower.tau

CI lower limit for estimated coefficient hat.tau

CI.upper.tau

CI upper limit for estimated coefficient hat.tau

est.M

time varying mediation effect

boot.se.m

estimated standard error for est.M

CI.lower

CI lower limit for est.M

CI.upper

CI upper limit for est.M

Plot Returns

  1. Alpha_CI plot for hat.alpha with CIs over t.est

  2. Gamma_CI plot for hat.gamma with CIs over t.est

  3. Beta_CI plot for hat.beta with CIs over t.est

  4. Tau_CI plot for hat.tau with CIs over t.est

  5. MedEff plot for est.M over t.est

  6. MedEff_CI plot for est.M with CIs over t.est

Note

  1. ** IMPORTANT ** An alternate way of formatting the data and calling the function is documented in detail in the tutorial for the tvmb() function.

References

  1. Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.

  2. Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.

  3. Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.

  4. Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.

  5. Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.

  6. B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDING COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$cessFatig)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[,c("SubjectID","varenicline")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma(trt, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma(trt, t.seq, mediator, outcome,
                t.est = c(0.2, 0.4, 0.6, 0.8),
                replicates = 250)
## End(Not run)

Time Varying Mediation Function: Continuous Outcome and Three Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors for three treatment groups and a continuous outcome.

Usage

tvma_3trt(
  T1,
  T2,
  t.seq,
  mediator,
  outcome,
  t.est = t.seq,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  grpname = "T",
  verbose = FALSE
)

Arguments

T1

a vector indicating assignment to treatment 1

T2

a vector indicating assignment to treatment 2

t.seq

a vector of time points for each observation

mediator

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

t.est

a vector of time points at which to make the estimation. Default = t.seq. (OPTIONAL ARGUMENT)

plot

TRUE or FALSE for plotting mediation effect. Default = "FALSE". (OPTIONAL ARGUMENT)

CI

"none" or "boot" method of deriving confidence intervals. Default = "boot". (OPTIONAL ARGUMENT)

replicates

number of replicates for bootstrapping confidence intervals. Default = 1000. (OPTIONAL ARGUMENT)

grpname

name of the treatment arms (exposure groups) to be displayed in the results. Default = "T". (OPTIONAL ARGUMENT)

verbose

TRUE or FALSE for printing results to screen. Default = "FALSE". (OPTIONAL ARGUMENT)

Value

hat.alpha1

estimated Treatment 1 effect on mediator

CI.lower.alpha1

CI lower limit for estimated coefficient hat.alpha1

CI.upper.alpha1

CI upper limit for estimated coefficient hat.alpha1

hat.alpha2

estimated Treatment 2 effect on mediator

CI.lower.alpha2

CI lower limit for estimated coefficient hat.alpha2

CI.upper.alpha2

CI upper limit for estimated coefficient hat.alpha2

hat.gamma1

estimated Treatment 1 direct effect on outcome

CI.lower.gamma1

CI lower limit for estimated coefficient hat.gamma1

CI.upper.gamma1

CI upper limit for estimated coefficient hat.gamma1

hat.gamma2

estimated Treatment 2 direct effect on outcome

CI.lower.gamma2

CI lower limit for estimated coefficient hat.gamma2

CI.upper.gamma2

CI upper limit for estimated coefficient hat.gamma2

hat.tau1

estimated Treatment 1 total effect on outcome

CI.lower.tau1

CI lower limit for estimated coefficient hat.tau1

CI.upper.tau1

CI upper limit for estimated coefficient hat.tau1

hat.tau2

estimated Treatment 2 total effect on outcome

CI.lower.tau2

CI lower limit for estimated coefficient hat.tau2

CI.upper.tau2

CI upper limit for estimated coefficient hat.tau2

hat.beta

estimated mediator effect on outcome

CI.lower.beta

CI lower limit for estimated coefficient hat.beta

CI.upper.beta

CI upper limit for estimated coefficient hat.beta

hat.mediation1

time varying mediation effect for Treatment 1 on outcome

SE_MedEff1

estimated standard errors of hat.mediation1

CI.upper.T1

CI upper limit for hat.mediation1

CI.lower.T1

CI lower limit for hat.mediation1

hat.mediation2

time varying mediation effect for Treatment 2 on outcome

SE_MedEff2

estimated standard errors of hat.mediation2

CI.upper.T2

CI upper limit for hat.mediation2

CI.lower.T2

CI lower limit for hat.mediation2

Plot Returns

  1. plot1_a1 plot for hat.alpha1 with CIs over t.est

  2. plot2_a2 plot for hat.alpha2 with CIs over t.est

  3. plot3_g1 plot for hat.gamma1 with CIs over t.est

  4. plot4_g2 plot for hat.gamma2 with CIs over t.est

  5. plot5_t1 plot for hat.tau1 with CIs over t.est

  6. plot6_t2 plot for hat.tau2 with CIs over t.est

  7. plot7_b plot for hat.beta with CIs over t.est

  8. MedEff_T1 plot for hat.mediation1 over t.est

  9. MedEff_T2 plot for hat.mediation2 over t.est

  10. MedEff_CI_T1 plot for hat.mediation1 with CIs over t.est

  11. MedEff_CI_T2 plot for hat.mediation2 with CIs over t.est

References

  1. Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.

  2. Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.

  3. Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.

  4. Cai X, Coffman DL, Piper ME, Li R. Estimation and inference for the mediation effect in a time-varying mediation model. BMC Med Res Methodol. 2022;22(1):1-12.

  5. Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.

  6. B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker$SubjectID,
                        smoker$timeseq, 
                        smoker$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker$SubjectID,
                      smoker$timeseq,
                      smoker$cessFatig)

# GENERATE TWO BINARY TREATMENT VARIABLES
NRT1 <- as.numeric(unique(smoker[,c("SubjectID","varenicline")])[,2])-1
NRT2 <- as.numeric(unique(smoker[,c("SubjectID","comboNRT")])[,2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome)

# COMPUTE TIME VARYING MEDIATION ANALYSIS FOR SPECIFIED POINTS IN TIME USING 250 REPLICATES
results <- tvma_3trt(NRT1, NRT2, t.seq, mediator, outcome,
                     t.est = c(0.2, 0.4, 0.6, 0.8),
                     replicates = 250)
## End(Not run)

Time Varying Mediation Function: Binary Outcome and Two Treatment Groups

Description

Function to estimate the time-varying mediation effect and bootstrap standard errors, involving two treatment groups and binary outcome.

Usage

tvmb(
  treatment,
  t.seq,
  mediator,
  outcome,
  span = 0.75,
  plot = FALSE,
  CI = "boot",
  replicates = 1000,
  verbose = FALSE
)

Arguments

treatment

a vector indicating treatment group

t.seq

a vector of unique time points for each observation

mediator

matrix of mediator values in wide format

outcome

matrix of outcome values in wide format

span

Numeric value of the span to be used for LOESS regression. Default = 0.75.

plot

TRUE or FALSE for producing plots. Default = "FALSE". (OPTIONAL ARGUMENT)

CI

"none" or "boot" method of deriving confidence intervals. Default = "boot". (OPTIONAL ARGUMENT)

replicates

Number of replicates for bootstrapping confidence intervals. Default = 1000. (OPTIONAL ARGUMENT)

verbose

TRUE or FALSE for printing results to screen. Default = "FALSE". (OPTIONAL ARGUMENT)

Value

timeseq

time points of estimation

alpha_hat

estimated treatment effect on mediator

CI.lower.a

CI lower limit for estimated coefficient alpha_hat

CI.upper.a

CI upper limit for estimated coefficient alpha_hat

gamma_hat

estimated treatment effect on outcome (direct effect)

CI.lower.g

CI lower limit for estimated coefficient gamma_hat

CI.upper.g

CI upper limit for estimated coefficient gamma_hat

beta_hat

estimated mediator effect on outcome

CI.lower.b

CI lower limit for estimated coefficient beta_hat

CI.upper.b

CI upper limit for estimated coefficient beta_hat

tau_hat

estimated treatment effect on outcome (total effect)

CI.lower.t

CI lower limit for estimated coefficient tau_hat

CI.upper.t

CI upper limit for estimated coefficient tau_hat

medEffect

time varying mediation effect

CI.lower

CI lower limit for medEffect

CI.upper

CI upper limit for medEffect

Plot Returns

  1. plot1_a plot for alpha_hat with CIs over t.seq

  2. plot2_g plot for gamma_hat with CIs over t.seq

  3. plot3_b plot for beta_hat with CIs over t.seq

  4. plot4_t plot for tau_hat with CIs over t.seq

  5. MedEff plot for medEffect over t.seq

  6. MedEff_CI plot for medEffect with CIs over t.seq

  7. bootstrap plot for estimated medEffect from bootstrapped samples over t.seq

Note

  1. Currently supports 2 treatment groups

  2. ** IMPORTANT ** An alternate way of formatting the data and calling the function is documented in detail in the tutorial for the tvmb() function.

References

  1. Fan, J. and Gijbels, I. Local polynomial modelling and its applications: Monographs on statistics and applied probability 66. CRC Press; 1996.

  2. Fan J, Zhang W. Statistical Estimation in Varying Coefficient Models. The Annals of Statistics. 1999;27(5):1491-1518.

  3. Fan J, Zhang JT. Two-step estimation of functional linear models with applications to longitudinal data. Journal of the Royal Statistical Society: Series B (Statistical Methodology). 2000;62(2):303-322.

  4. Baker TB, Piper ME, Stein JH, et al. Effects of Nicotine Patch vs Varenicline vs Combination Nicotine Replacement Therapy on Smoking Cessation at 26 Weeks: A Randomized Clinical Trial. JAMA. 2016;315(4):371.

  5. B. Efron, R. Tibshirani. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science. 1986;1(1):54-75.

Examples

## Not run: data(smoker)

# REDUCE DATA SET TO ONLY 2 TREATMENT CONDITIONS (EXCLUDE COMBINATION NRT)
smoker.sub <- smoker[smoker$treatment != 4, ]

# GENERATE WIDE FORMATTED MEDIATORS
mediator <- LongToWide(smoker.sub$SubjectID,
                       smoker.sub$timeseq,
                       smoker.sub$NegMoodLst15min)

# GENERATE WIDE FORMATTED OUTCOMES
outcome <- LongToWide(smoker.sub$SubjectID,
                      smoker.sub$timeseq,
                      smoker.sub$smoke_status)

# GENERATE A BINARY TREATMENT VARIABLE
trt <- as.numeric(unique(smoker.sub[, c("SubjectID","varenicline")])[, 2])-1

# GENERATE A VECTOR OF UNIQUE TIME POINTS
t.seq <- sort(unique(smoker.sub$timeseq))

# COMPUTE TIME VARYING MEDIATION ANALYSIS USING BOOTSTRAPPED CONFIDENCE INTERVALS
results <- tvmb(trt, t.seq, mediator, outcome)
## End(Not run)

Main function for time varying mediation function for continuous outcome and three treatment arms (i.e., exposure groups).

Description

Part of the set of internal functions to estimate the time-varying mediation effect and bootstrap standard errors for three treatment groups and continuous outcome.

Usage

tvmcurve_3trt(T1, T2, t.seq, x, y, t.est)

Arguments

T1

a vector indicating assignment to treatment 1

T2

a vector indicating assignment to treatment 2

t.seq

a vector of time points for each observation

x

matrix of mediator values in wide format

y

matrix of outcome values in wide format

t.est

time points at which to make the estimation. Default = t.seq

Value

hat.alpha1

estimated Treatment 1 effect on mediator

hat.alpha2

estimated Treatment 2 effect on mediator

hat.gamma1

estimated Treatment 1 direct effect on outcome

hat.gamma2

estimated Treatment 2 direct effect on outcome

hat.tau1

estimated Treatment 1 total effect on outcome

hat.tau2

estimated Treatment 2 total effect on outcome

hat.beta

estimated mediator effect on outcome

hat.mediation1

time varying mediation effect for Treatment 1 on outcome

hat.mediation2

time varying mediation effect for Treatment 2 on outcome