Type:	Package
Title:	Process Performance Qualification (PPQ) Plans in Chemistry, Manufacturing and Controls (CMC) Statistical Analysis
Version:	1.1.0
Maintainer:	Yalin Zhu <yalin.zhu@merck.com>
Depends:	R (≥ 3.2.0)
Imports:	ggplot2, plotly
Description:	Assessment for statistically-based PPQ sampling plan, including calculating the passing probability, optimizing the baseline and high performance cutoff points, visualizing the PPQ plan and power dynamically. The analytical idea is based on the simulation methods from the textbook Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Methods for CMC Applications. In Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry (pp. 227-250). Springer, Cham.
License:	GPL-3
Suggests:	knitr, rmarkdown, devtools
VignetteBuilder:	knitr
NeedsCompilation:	no
RoxygenNote:	7.1.0
Encoding:	UTF-8
URL:	https://allenzhuaz.github.io/PPQplan/, https://github.com/allenzhuaz/PPQplan
BugReports:	https://github.com/allenzhuaz/PPQplan/issues
LazyData:	true
Language:	en-US
Packaged:	2020-10-08 02:01:06 UTC; zhuyal
Author:	Yalin Zhu [aut, cre], Merck & Co., Inc. [cph]
Repository:	CRAN
Date/Publication:	2020-10-08 04:30:06 UTC

Heatmap/Contour Plot for Assessing Power of the CQA PPQ Plan Using General Multiplier.

Description

The function for plotting the heatmap to evaluate the PPQ plan based on the specification test, given lower and upper specification limits.

Usage

PPQ_ctplot(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, k, test.point)

Arguments

Value

Heatmap (or Contour Plot) for PPQ Assessment.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

PPQ_pp and PPQ_occurve.

Examples

## Not run: 
mu <- seq(1.6,3.4,0.05)
sigma <- seq(0.05,0.8,0.01)
PPQ_ctplot(attr.name = "Total Protein", attr.unit = "mg/mL", Llim=1.5, Ulim=3.5,
mu = mu, sigma = sigma, k=2.373)

## Example verifying simulation resutls in the textbook page 249
mu <- seq(95, 105, 0.1)
sigma <- seq(0.2, 5, 0.1)
PPQ_ctplot(attr.name = "Composite Assay", attr.unit = "%LC", Llim=95, Ulim=105,
mu = mu, sigma = sigma, k=2.373)
mu <- seq(90, 110, 0.5)
PPQ_ctplot(attr.name = "Composite Assay", attr.unit = "%LC", Llim=90, Ulim=110,
mu = mu, sigma = sigma, k=2.373)

mu <- seq(95,105,0.1)
sigma <- seq(0.1,2.5,0.1)
PPQ_ctplot(attr.name = "Sterile Concentration Assay", attr.unit = "%", Llim=95, Ulim=105,
mu = mu, sigma = sigma, k=2.373)
test <- data.frame(mean=c(97,98.3,102.5), sd=c(0.55, 1.5, 1.2))
PPQ_ctplot(attr.name = "Sterile Concentration Assay", attr.unit = "%", Llim=95, Ulim=105,
mu = mu, sigma = sigma, k=2.373, test.point=test)

## End(Not run)

Heatmap/Contour Plot for Dynamically Assessing Power of the CQA PPQ Plan Using General Multiplier.

Description

The function for dynamically plotting (ggplot) the heatmap to evaluate the PPQ plan based on the specification test, given lower and upper specification limits.

Usage

PPQ_ggplot(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, k,
test.point, dynamic)

Arguments

Value

Dynamic Heatmap (or Contour Plot) for PPQ Assessment.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

PPQ_pp and PPQ_occurve.

Examples

## Not run: 
mu <- seq(95, 105, 0.1)
sigma <- seq(0.1,1.7,0.1)
PPQ_ggplot(attr.name = "Sterile Concentration Assay", attr.unit = "%", Llim=95, Ulim=105,
mu = mu, sigma = sigma, k=2.373, dynamic = FALSE)
test <- data.frame(mu=c(97,98.3,102.5), sd=c(0.55, 1.5, 0.2))
PPQ_ggplot(attr.name = "Sterile Concentration Assay", attr.unit = "%", Llim=95, Ulim=105,
mu = mu, sigma = sigma, k=2.373, test.point = test)

## End(Not run)

Operating Characteristic (OC) Curves for the CQA PPQ Plan Using General Multiplier.

Description

The function for plotting the OC curve to show the PPQ plan, given lower and upper specification limits.

Usage

PPQ_occurve(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, k, add.reference)

Arguments

Value

OC curves for specification test and PPQ plan.

Author(s)

Yalin Zhu

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

PPQ_pp and rl_pp.

Examples

## Not run: 
PPQ_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%", Llim=95, Ulim=105,
mu=97, sigma=seq(0.1, 10, 0.1), n=10, k=2.373, add.reference=TRUE)
PPQ_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%", Llim=95, Ulim=105,
mu=100, sigma=seq(0.1, 10, 0.1), n=10, k=2.373, add.reference=TRUE)
PPQ_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%", Llim=95, Ulim=105,
mu=seq(95,105,0.1), sigma=1, n=10, k=2.373)
PPQ_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%", Llim=95, Ulim=105,
mu=seq(95,105,0.1), sigma=1, n=10, k=2.373, add.reference=TRUE)

PPQ_occurve(attr.name = "Protein Concentration", attr.unit="%", Llim=90, Ulim=110,
mu=seq(90, 110, 0.1), sigma=1.25, k=2.373)

## Only display referece curves, leave k as NULL by default
PPQ_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%LC", Llim=95, Ulim=105,
mu=98, sigma=seq(0.1, 10, 0.1), n=10, add.reference=TRUE)

## End(Not run)

Probability of Passing PPQ Test Using General Multiplier

Description

The function for calculating the probability of passing critical quality attributes (CQA) PPQ test .

Usage

PPQ_pp(Llim, Ulim, mu, sigma, n, n.batch, k)

Arguments

Value

A numeric value of the passing/acceptance probability

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

rl_pp.

Examples

## Not run: 
PPQ_pp(Llim = 90, Ulim = 110, mu=105, sigma=1.5, n=10, k=3.1034)

# One-sided tolerance interval with k=0.753 (95/67.5 one-sided tolerance interval LTL)
PPQ_pp(sigma=0.03, mu=1.025, n=40, Llim=1, Ulim=Inf, k=0.753)

sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = PPQ_pp, mu=97, n=10, Llim=95, Ulim=105, k=2.373)
sapply(X=seq(0.1,10,0.1), FUN = PPQ_pp, mu=97, n=10, Llim=95, Ulim=105, k=2.373)

sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN =  PPQ_pp, mu=100, n=10, Llim=95, Ulim=105, k=2.373)

sigma <- seq(0.1, 4, 0.1)
pp1 <- sapply(X=sigma, FUN =  PPQ_pp, mu=97, n=10, Llim=95, Ulim=105, k=2.373)
pp2 <- sapply(X=sigma, FUN =  PPQ_pp, mu=98, n=10, Llim=95, Ulim=105, k=2.373)
pp3 <- sapply(X=sigma, FUN =  PPQ_pp, mu=99, n=10, Llim=95, Ulim=105, k=2.373)
pp4 <- sapply(X=sigma, FUN =  PPQ_pp, mu=100, n=10, Llim=95, Ulim=105, k=2.373)
plot(sigma, pp1, xlab="Standard Deviation", main="LSL=95, USL=105, k=2.373, n=10",
ylab="Probability of Passing", type="o", pch=1, col=1, lwd=1, ylim=c(0,1))
lines(sigma, pp2, type="o", pch=2, col=2)
lines(sigma, pp3, type="o", pch=3, col=3)
lines(sigma, pp4, type="o", pch=4, col=4)
legend("topright", legend=paste0(rep("mu=",4),c(97,98,99,100)), bg="white",
col=c(1,2,3,4), pch=c(1,2,3,4), lty=1, cex=0.8)

mu <- seq(95, 105, 0.1)
pp5 <- sapply(X=mu, FUN =  PPQ_pp, sigma=0.5, n=10, Llim=95, Ulim=105, k=2.373)
pp6 <- sapply(X=mu, FUN =  PPQ_pp, sigma=1, n=10, Llim=95, Ulim=105, k=2.373)
pp7 <- sapply(X=mu, FUN =  PPQ_pp, sigma=1.5, n=10, Llim=95, Ulim=105, k=2.373)
pp8 <- sapply(X=mu, FUN =  PPQ_pp, sigma=2, n=10, Llim=95, Ulim=105, k=2.373)
pp9 <- sapply(X=mu, FUN =  PPQ_pp, sigma=2.5, n=10, Llim=95, Ulim=105, k=2.373)
plot(mu, pp5, xlab="Mean Value", main="LSL=95, USL=105, k=2.373, n=10",
ylab="Probability of Passing", type="o", pch=1, col=1, lwd=1, ylim=c(0,1))
lines(mu, pp6, type="o", pch=2, col=2)
lines(mu, pp7, type="o", pch=3, col=3)
lines(mu, pp8, type="o", pch=4, col=4)
lines(mu, pp9, type="o", pch=5, col=5)
legend("topright", legend=paste0(rep("sigma=",5),seq(0.5,2.5,0.5)), bg="white",
col=c(1,2,3,4,5), pch=c(1,2,3,4,5), lty=1, cex=0.8)

## End(Not run)

A General Heatmap for Dynamically Assessing Power of the Sampling Plan Using a General Specification Limit.

Description

The function for dynamically plotting (ggplot) the heatmap to evaluate the sampling plan based on a general lower and/or upper specification limits.

Usage

heatmap_ly(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, test.point, dynamic)

Arguments

Value

A Plain or Dynamic Heatmap for Sampling Plan Assessment.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

pp and PPQ.occurve.

Examples

## Not run: 
heatmap_ly(attr.name = "Thickness", attr.unit = "%",Llim = -0.2, Ulim = 0.2,
mu = seq(-0.2, 0.2, 0.001), sigma = seq(0,0.2, 0.001),
test.point=data.frame(c(0.1,-0.05),c(0.15,0.05)), n=2, dynamic = T)

## End(Not run)

Estimating K-factors for Tolerance Intervals Based on Howe's Method

Description

Estimates k-factors for tolerance intervals based on Howe's method with normality assumption.

Usage

k_factor(n, alpha = 0.05, P = 0.99, side = 1)

Arguments

Value

The estimated k-factor for tolerance intervals assuming normality.

Note

This function is a simplified version of tolerance::K.factor(), only considering Howe's method.

See Also

ti_pp

Examples

k_factor(10, P = 0.95, side = 2)

Heatmap/Contour Plot for Assessing Power of the CQA PPQ Plan Using Prediction Interval.

Description

The function for plotting the heatmap to evaluate the PPQ plan based on the specification test, given lower and upper specification limits.

Usage

pi_ctplot(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, alpha, test.point)

Arguments

Value

Heatmap (or Contour Plot) for PPQ Assessment.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

pi_pp and pi_occurve.

Examples

## Not run: 
## Example verifying simulation resutls in the textbook page 249
mu <- seq(95, 105, 0.1)
sigma <- seq(0.2, 3.5, 0.1)
pi_ctplot(attr.name = "Composite Assay", attr.unit = "%LC",
mu = mu, sigma = sigma, Llim=95, Ulim=105)
mu <- seq(90, 110, 0.5)
pi_ctplot(attr.name = "Composite Assay", attr.unit = "%LC",
mu = mu, sigma = sigma, Llim=90, Ulim=110)

mu <- seq(95,105,0.1)
sigma <- seq(0.1,2.5,0.1)
pi_ctplot(attr.name = "Sterile Concentration Assay", attr.unit = "%",
mu = mu, sigma = sigma, Llim=95, Ulim=105)
test <- data.frame(mean=c(97,98.3,102.5), sd=c(0.55, 1.5, 1.2))
pi_ctplot(attr.name = "Sterile Concentration Assay", attr.unit = "%", Llim=95, Ulim=105,
mu = mu, sigma = sigma, test.point=test)

## End(Not run)

Operating Characteristic (OC) Curves for the CQA PPQ Plan using Prediction Interval.

Description

The function for plotting the OC curves and optimizing the baseline and high performance PPQ plans, given lower and upper specification limits.

Usage

pi_occurve(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, alpha, add.reference)

Arguments

Value

OC curves for specification test and PPQ plan.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

pi_pp and rl_pp.

Examples

## Not run: 
pi_occurve(attr.name = "Total Protein", attr.unit = "mg/mL",
sigma = seq(0.01,1,0.01))
pi_occurve(attr.name = "Total Protein", attr.unit = "mg/mL",
sigma = seq(0.01,1,0.01), n.batch=3)
# Baseline curve
pi_occurve(attr.name = "Total Protein", attr.unit = "mg/mL",
sigma = seq(0.01,1,0.01), alpha = 0.1135434)
# High performance curve
pi_occurve(attr.name = "Total Protein", attr.unit = "mg/mL",
sigma = seq(0.01,1,0.01), alpha = 0.0225518)

# 95% with reference curves
pi_occurve(attr.name = "Total Protein", attr.unit = "mg/mL",
sigma = seq(0.01,1,0.01), add.reference=TRUE)
pi_occurve(attr.name = "Composite Assay", attr.unit = "%",
mu = 100, sigma = seq(0.1,6,0.1), Llim=95, Ulim=105, n.batch=1, add.reference=TRUE)

pi_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%",
mu=97, sigma=seq(0.1, 10, 0.1), Llim=95, Ulim=105, n=10, add.reference=TRUE)

pi_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%",
mu=100, sigma=seq(0.1, 10, 0.1), Llim=95, Ulim=105, n=10, add.reference=TRUE)

pi_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%",
mu=seq(95,105,0.1), sigma=1, Llim=95, Ulim=105, n=10, add.reference=TRUE)

pi_occurve(attr.name = "Protein Concentration", attr.unit="%",
mu=seq(90, 110, 0.1), sigma=1.25, Llim=90, Ulim=110, add.reference=TRUE)

## End(Not run)

Probability of Passing PPQ Test using Prediction Interval

Description

The function for calculating the probability of passing critical quality attributes (CQA) PPQ test .

Usage

pi_pp(Llim, Ulim, mu, sigma, n, n.batch, alpha)

Arguments

Value

A numeric value of the passing/acceptance probability

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

rl_pp.

Examples

## Not run: 
pi_pp(sigma=0.5, mu=2.5, n=10, n.batch=1, Llim=1.5, Ulim=3.5, alpha=0.05)

sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = pi_pp, mu=97, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)
sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = pi_pp, mu=100, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)

## End(Not run)

Probability of Passing General Upper and/or Lower Specification Limit

Description

The function for calculating the probability of passing a general upper and/or lower boundary.

Usage

pp(Llim, Ulim, mu, sigma, n)

Arguments

Value

A numeric value of the passing/acceptance probability

Author(s)

Yalin Zhu

See Also

rl_pp and PPQ_pp.

Probability of Passing Specification Test for a Release Batch

Description

The function for calculating the probability of passing critical quality attributes (CQA) specification test .

Usage

rl_pp(Llim, Ulim, mu, sigma, NV)

Arguments

Value

A numeric value of the passing/acceptance probability

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

PPQ_pp, pi_pp and ti_pp.

Examples

rl_pp(Llim=1.5, Ulim=3.5, mu=2.5, sigma=0.8)

Heatmap/Contour Plot for Assessing Power of the PPQ Plan using Tolerance Interval.

Description

The function for plotting the heatmap to evaluate the PPQ plan based on the specification test, given lower and upper specification limits.

Usage

ti_ctplot(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch,
alpha, coverprob, side, test.point)

Arguments

Value

Heatmap (or Contour Plot) for PPQ Assessment.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

ti_pp and ti_occurve.

Examples

## Not run: 
mu <- seq(95,105,0.1)
sigma <- seq(0.1,2.5,0.1)
ti_ctplot(attr.name = "Sterile Concentration Assay", attr.unit = "%",
mu = mu, sigma = sigma, Llim=95, Ulim=105)

ti_ctplot(attr.name = "Extractable Volume", attr.unit = "% of NV=1mL",
Llim = 100, Ulim = Inf, mu=seq(100, 110, 0.5), sigma=seq(0.2, 15 ,0.5), n=40,
alpha = 0.05, coverprob = 0.675, side=1)

## End(Not run)

Operating Characteristic (OC) Curves for the PPQ Plan using Tolerance Interval.

Description

The function for plotting the OC curve to show the PPQ plan based on the specification test, given lower and upper specification limits.

Usage

ti_occurve(attr.name, attr.unit, Llim, Ulim, mu, sigma, n, n.batch, alpha,
coverprob, side, add.reference, NV)

Arguments

Value

OC curves for specification test and PPQ plan.

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

ti_pp and rl_pp.

Examples

## Not run: 
ti_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%",
mu=97, sigma=seq(0.1, 10, 0.1), Llim=95, Ulim=105, n=10, add.reference=TRUE)

ti_occurve(attr.name = "Sterile Concentration Assay", attr.unit="%",
mu=100, sigma=seq(0.1, 10, 0.1), Llim=95, Ulim=105, n=10, add.reference=TRUE)

ti_occurve(attr.name = "Extractable Volume", attr.unit = "% of NV=3mL",
Llim = 100, Ulim = Inf, mu=102.5, sigma=seq(0.2, 6 ,0.05), n=40,
alpha = 0.05, coverprob = 0.97, side=1, NV=3)

ti_occurve(attr.name = "Extractable Volume", attr.unit = "% of NV=3mL",
Llim = 100, Ulim = Inf, mu=102.5, sigma=seq(0.2, 6 ,0.05), n=40,
alpha = 0.05, coverprob = 0.992, side=1, NV=3)

## End(Not run)

Probability of Passing PPQ Test using Tolerance Interval

Description

The function for calculating the probability of passing critical quality attributes (CQA) PPQ test .

Usage

ti_pp(Llim, Ulim, mu, sigma, n, n.batch, alpha, coverprob, side)

Arguments

Value

A numeric value of the passing/acceptance probability

Author(s)

Yalin Zhu

References

Burdick, R. K., LeBlond, D. J., Pfahler, L. B., Quiroz, J., Sidor, L., Vukovinsky, K., & Zhang, L. (2017). Statistical Applications for Chemistry, Manufacturing and Controls (CMC) in the Pharmaceutical Industry. Springer.

See Also

rl_pp.

Examples

ti_pp(sigma=0.5, mu=2.5, n=10, n.batch=1, Llim=1.5, Ulim=3.5, alpha=0.05)

sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = ti_pp, mu=97, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)
sapply(X=c(0.1,0.5, 1,2,3,4,5,10), FUN = ti_pp, mu=100, n=10, Llim=95, Ulim=105,
n.batch=1, alpha=0.05)