Delayed Effect.Design Manual
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Package ‘DelayedEffect.Design’
October 16, 2017
Title Sample Size and Power Calculations using the APPLE, SEPPLE,
APPLE+ and SEPPLE+ Methods
Version 1.0.0
Date 2017-10-16
Author
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
Description Provides sample size and power calculations when the treatment time-lag ef-
fect is present and the lag duration is either homogeneous across the individual sub-
ject, or varies heterogeneously from individual to individual within a certain domain and follow-
ing a specific pattern. The methods used are de-
scribed in Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017) <doi:10.1002/sim.7157>.
Maintainer Bill Wheeler <wheelerb@imsweb.com>
License GPL-2
NeedsCompilation yes
Rtopics documented:
DelayedEffect.Design.................................... 2
HR.APPLE ......................................... 3
HR.APPLE.plus....................................... 4
N.APPLE .......................................... 5
N.APPLE.plus........................................ 6
pow.APPLE......................................... 8
pow.APPLE.plus ...................................... 9
pow.SEPPLE ........................................ 10
pow.SEPPLE.plus...................................... 11
pow.SEPPLE.random.DE.................................. 13
pow.sim.logrk........................................ 14
pow.sim.logrk.random.DE ................................. 16
Index 18
1
2DelayedEffect.Design
DelayedEffect.Design Sample size and power calculations using the APPLE, SEPPLE, AP-
PLE+ and SEPPLE+ methods
Description
An R package for sample size and power calculation when the treatment time-lag effect is present.
The package incorporates two specific lag assumptions:
1. the lag duration is homogeneous across the individual subject;
2. the lag duration varies heterogeneously from individual to individual within a certain domain and
following a specific pattern.
Details
The four new methods in this package for performing the sample size and power calculations are:
1. Analytic Power calculation method based on Piecewise weighted Log-rank tEst (APPLE),
2. Simulation-based Empirical Power calculation method based on Piecewise weighted Log-rank
tEst (SEPPLE),
3. Analytic Power calculation method based on generalized Piecewise weighted Log-rank tEst with
random treatment time-lag effect (APPLE+),
4. Simulation-based Empirical Power calculation method based on generalized Piecewise weighted
Log-rank tEst with random treatment time-lag effect (SEPPLE+).
See the reference for details of these methods. Specifically, APPLE and SEPPLE assume that
the lag duration is homogeneous across the individual subject, whereas APPLE and SEPPLE as-
sume that the lag duration varies heterogeneously from individual to individual or from study
to study within a certain domain and following a specific pattern. The functions for comput-
ing power corresponding to the above methods are pow.APPLE, pow.SEPPLE, pow.APPLE.plus,
pow.SEPPLE.plus and pow.SEPPLE.random.DE. These can be compared to pow.sim.logrk and
pow.sim.logrk.rankdom.DE which compute the power from a simulation-based algorithm using
the regular log-rank test which ignores the existence of lag effects. The package also includes the
function N.APPLE, N.APPLE.plus to back calculate the sample size given the power and hazard
ratio, and the functions HR.APPLE and HR.APPLE.plus to back calculate the hazard ratio given
the power and sample size, respectively, using the close-from APPLE and APPLE+ methods.
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
HR.APPLE 3
HR.APPLE APPLE hazard ratio computation
Description
Perform the post-delay hazard ratio calculation given power and sample size using the close-form
APPLE method based on the piecewise weighted log-rank test when the treatment time-lag effect
is present and the lag duration is homogeneous across the individual subject
Usage
HR.APPLE(lambda1, t1, p, N, tao, A, beta, ap=0.5, alpha=0.05)
Arguments
lambda1 Baseline hazard or NULL (see details)
t1 Delayed duration or NULL (see details)
pProportion of subjects who survive beyond the delayed period or NULL (see
details)
NSample size
tao Total study duration
ATotal enrollment duration
beta Type II error rate; Power=1-beta
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
Details
APPLE is an acronym for:
Analytic Power calculation method based on Piecewise weighted Log-rank tEst. See the reference
for details of this method.
Out of the three input parameters lambda1,t1 and p, only two need to be specified, the remaining
one will be computed internally from the formula lambda1 = -log(p)/t1. If all three are not
NULL, then lambda1 will be set to -log(p)/t1 regardless of the user input value.
Value
The hazard ratio
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
4HR.APPLE.plus
See Also
pow.APPLE,N.APPLE
Examples
lambda1 <- NULL
t1 <- 183
p <- 0.7
N <- 200
tao <- 365*3
A <- 365
beta <- 0.2
HR.APPLE(lambda1, t1, p, N, tao, A, beta)
HR.APPLE.plus APPLE+ hazard ratio computation
Description
Perform the post-delay hazard ratio calculation given power and sample size using the close-form
APPLE+ method based on the generalized piecewise weighted log-rank test when the treatment
time-lag effect is present and the lag duration varies heterogeneously from individual to individual
or from study to study, within a certain domain and following a specific pattern.
Usage
HR.APPLE.plus(lambda1, tl, tu, N, tao, A, beta, ap=0.5, alpha=0.05)
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
NSample size
tao Total study duration
ATotal enrollment duration
beta Type II error rate; Power=1-beta
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
Details
APPLE+ is an acronym for:
Analytic Power calculation method based on generalized Piecewise weighted Log-rank tEst with
random treatment time-lag effect. See the reference for details of this method.
Value
The hazard ratio
N.APPLE 5
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.APPLE.plus,N.APPLE.plus
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
N <- 200
tao <- 365*3
A <- 365
beta <- 0.2
HR.APPLE.plus(lambda1, tl, tu, N, tao, A, beta)
N.APPLE APPLE sample size computation
Description
Perform the sample size calculation given the power and post-delay hazard ratio using the closeform
APPLE method based on the piecewise weighted log-rank test when the treatment time-lag effect
is present and the lag duration is homogeneous across the individual subject
Usage
N.APPLE(lambda1, t1, p, HR, tao, A, beta, ap=0.5, alpha=0.05)
Arguments
lambda1 Baseline hazard or NULL (see details)
t1 Delayed duration or NULL (see details)
pProportion of subjects who survive beyond the delayed period or NULL (see
details)
HR Post-delay hazard ratio, defined as the post-delay hazard rate of the treatment
group compared to that of the control group
tao Total study duration
ATotal enrollment duration
beta Type II error rate; Power=1-beta
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
6N.APPLE.plus
Details
APPLE is an acronym for:
Analytic Power calculation method based on Piecewise weighted Log-rank tEst. See the reference
for details of this method.
Out of the three input parameters lambda1,t1 and p, only two need to be specified, the remaining
one will be computed internally from the formula lambda1 = -log(p)/t1. If all three are not
NULL, then lambda1 will be set to -log(p)/t1 regardless of the user input value.
Value
The sample size
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.APPLE,HR.APPLE
Examples
lambda1 <- NULL
t1 <- 183
p <- 0.7
HR <- 0.55
tao <- 365*3
A <- 365
beta <- 0.2
N.APPLE(lambda1, t1, p, HR, tao, A, beta)
N.APPLE.plus APPLE+ sample size computation
Description
Perform the sample size calculation given the power and post-delay hazard ratio using the close-
form APPLE+ method based on the generalized piecewise weighted log-rank test when the treat-
ment time-lag effect is present and the lag duration varies heterogeneously from individual to indi-
vidual or from study to study, within a certain domain and following a specific pattern.
Usage
N.APPLE.plus(lambda1, tl, tu, HR, tao, A, beta, ap=0.5, alpha=0.05)
N.APPLE.plus 7
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
HR Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the
treatment group compared to that of the control group
tao Total study duration
ATotal enrollment duration
beta Type II error rate; Power=1-beta
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
Details
APPLE+ is an acronym for:
Analytic Power calculation method based on generalized Piecewise weighted Log-rank tEst with
random treatment time-lag effect. See the reference for details of this method.
Value
The sample size
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.APPLE.plus,HR.APPLE.plus
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
HR <- 1.3
tao <- 365*3
A <- 365
beta <- 0.2
N.APPLE.plus(lambda1, tl, tu, HR, tao, A, beta)
8pow.APPLE
pow.APPLE APPLE power computation
Description
Perform the power calculation using the close-form APPLE method based on the piecewise weighted
log-rank test when the treatment time-lag effect is present and the lag duration is homogeneous
across the individual subject
Usage
pow.APPLE(lambda1, t1, p, N, HR, tao, A, ap=0.5, alpha=0.05)
Arguments
lambda1 Baseline hazard or NULL (see details)
t1 Delayed duration or NULL (see details)
pProportion of subjects who survive beyond the delayed period or NULL (see
details)
NSample size
HR Post-delay hazard ratio, defined as the post-delay hazard rate of the treatment
group compared to that of the control group
tao Total study duration
ATotal enrollment duration
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
Details
APPLE is an acronym for:
Analytic Power calculation method based on Piecewise weighted Log-rank tEst. See the reference
for details of this method.
Out of the three input parameters lambda1,t1 and p, only two need to be specified, the remaining
one will be computed internally from the formula lambda1 = -log(p)/t1. If all three are not
NULL, then lambda1 will be set to -log(p)/t1 regardless of the user input value.
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
pow.APPLE.plus 9
See Also
N.APPLE,HR.APPLE,pow.SEPPLE,pow.sim.logrk
Examples
lambda1 <- NULL
t1 <- 183
p <- 0.7
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
pow.APPLE(lambda1, t1, p, N, HR, tao, A)
pow.APPLE.plus APPLE+ power computation
Description
Perform the power calculation using the close-form APPLE+ method based on the generalized
piecewise weighted log-rank test when the treatment time-lag effect is present and the lag duration
varies heterogeneously from individual to individual or from study to study, within a certain domain
and following a specific pattern.
Usage
pow.APPLE.plus(lambda1, tl, tu, N, HR, tao, A, ap=0.5, alpha=0.05)
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
NSample size
HR Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the
treatment group compared to that of the control group
tao Total study duration
ATotal enrollment duration
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
Details
APPLE+ is an acronym for:
Analytic Power calculation method based on generalized Piecewise weighted Log-rank tEst with
random treatment time-lag effect. See the reference for details of this method.
Value
The power
10 pow.SEPPLE
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
N.APPLE.plus,HR.APPLE.plus
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
N <- 200
HR <- 1.3
tao <- 365*3
A <- 365
pow.APPLE.plus(lambda1, tl, tu, N, HR, tao, A)
pow.SEPPLE SEPPLE power computation
Description
Perform the power calculation using the numeric SEPPLE method based on the piecewise weighted
log-rank test when the treatment time-lag effect is present and the lag duration is homogeneous
across the individual subject
Usage
pow.SEPPLE(lambda1, t1, p, N, HR, tao, A, ap=0.5, alpha=0.05, nsim=10000)
Arguments
lambda1 Baseline hazard or NULL (see details)
t1 Delayed duration or NULL (see details)
pProportion of subjects who survive beyond the delayed period or NULL (see
details)
NSample size
HR Post-delay hazard ratio, defined as the post-delay hazard rate of the treatment
group compared to that of the control group
tao Total study duration
ATotal enrollment duration
pow.SEPPLE.plus 11
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
nsim Number of simulations. The default is 10000.
Details
SEPPLE is an acronym for:
Simulation-based Empirical Power calculation method based on Piecewise weighted Log-rank tEst.
See the reference for details of this method.
Out of the three input parameters lambda1,t1 and p, only two need to be specified, the remaining
one will be computed internally from the formula lambda1 = -log(p)/t1. If all three are not
NULL, then lambda1 will be set to -log(p)/t1 regardless of the user input value.
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.APPLE,pow.sim.logrk
Examples
lambda1 <- NULL
t1 <- 183
p <- 0.7
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
pow.SEPPLE(lambda1, t1, p, N, HR, tao, A, nsim=1000)
pow.SEPPLE.plus SEPPLE+ power computation
Description
Perform the power calculation using the numeric SEPPLE+ method based on the generalized piece-
wise weighted log-rank test when the treatment time-lag effect is present and the lag duration varies
heterogeneously from individual to individual or from study to study, within a certain domain and
following a specific pattern.
12 pow.SEPPLE.plus
Usage
pow.SEPPLE.plus(lambda1, tl, tu, N, HR, tao, A, dist="uniform",
shape1=NULL, shape2=NULL, ap=0.5, alpha=0.05, nsim=10000)
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
NSample size
HR Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the
treatment group compared to that of the control group
tao Total study duration
ATotal enrollment duration
dist One of "uniform", "beta" or "gamma", for the lag distribution
shape1 NULL or a positive parameter value for the beta or gamma distribution.
shape2 NULL or a positive parameter value for the beta or gamma distribution.
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
nsim Number of simulations. The default is 10000.
Details
SEPPLE+ is an acronym for:
Simulation-based Empirical Power calculation method based on generalized Piecewise weighted
Log-rank tEst with random treatment time-lag effect. See the reference for details of this method.
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.SEPPLE.random.DE,pow.sim.logrk.random.DE
pow.SEPPLE.random.DE 13
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
shape1 <- 5
shape2 <- 5
pow.SEPPLE.plus(lambda1, tl, tu, N, HR, tao, A, dist="beta",
shape1=shape1, shape2=shape2, nsim=1000)
pow.SEPPLE.random.DE SEPPLE+ power computation
Description
Perform the power calculation using the numeric SEPPLE method based on the piecewise weighted
log-rank test when the treatment time-lag effect is present and the lag duration varies heteroge-
neously from individual to individual or from study to study, within a certain domain and following
a specific pattern. The purpose of this function is to evaluate the property of SEPPLE which assumes
the lag duration is homogeneous across the individual subject, when applied under the random sce-
nario where the lag duration, in fact, varies heterogeneously.
Usage
pow.SEPPLE.random.DE(lambda1, tl, tu, N, HR, tao, A, t.fixed, dist="uniform",
shape1=NULL, shape2=NULL, ap=0.5, alpha=0.05, nsim=10000)
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
NSample size
HR Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the
treatment group compared to that of the control group
tao Total study duration
ATotal enrollment duration
t.fixed Fixed duration in SEPPLE
dist One of "uniform", "beta" or "gamma", for the lag distribution
shape1 NULL or a positive parameter value for the beta or gamma distribution.
shape2 NULL or a positive parameter value for the beta or gamma distribution.
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
nsim Number of simulations. The default is 10000.
14 pow.sim.logrk
Details
SEPPLE+ is an acronym for:
Simulation-based Empirical Power calculation method based on generalized Piecewise weighted
Log-rank tEst with random treatment time-lag effect. See the reference for details of this method.
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.SEPPLE.plus,pow.sim.logrk.random.DE
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
t.fixed <- (tl+tu)/2
shape1 <- 5
shape2 <- 5
pow.SEPPLE.random.DE(lambda1, tl, tu, N, HR, tao, A, t.fixed, dist="beta",
shape1=shape1, shape2=shape2, nsim=1000)
pow.sim.logrk Simulated log-rank power computation
Description
Perform the power calculation using a simulation-based method based on the regular log-rank test
when the treatment time-lag effect is present and the lag duration is homogeneous across the indi-
vidual subject
Usage
pow.sim.logrk(lambda1, t1, p, N, HR, tao, A, ap=0.5, alpha=0.05, nsim=10000)
pow.sim.logrk 15
Arguments
lambda1 Baseline hazard or NULL (see details)
t1 Delayed duration or NULL (see details)
pProportion of subjects who survive beyond the delayed period or NULL (see
details)
NSample size
HR Post-delay hazard ratio, defined as the post-delay hazard rate of the treatment
group compared to that of the control group
tao Total study duration
ATotal enrollment duration
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
nsim Number of simulations. The default is 10000.
Details
Out of the three input parameters lambda1,t1 and p, only two need to be specified, the remaining
one will be computed internally from the formula lambda1 = -log(p)/t1. If all three are not
NULL, then lambda1 will be set to -log(p)/t1 regardless of the user input value.
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
References
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.APPLE,pow.SEPPLE
Examples
lambda1 <- NULL
t1 <- 183
p <- 0.7
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
pow.sim.logrk(lambda1, t1, p, N, HR, tao, A, nsim=1000)
16 pow.sim.logrk.random.DE
pow.sim.logrk.random.DE
Simulated log-rank power computation
Description
Perform the power calculation using a simulation-based method based on the regular log-rank test
when the treatment time-lag effect is present and the lag duration varies heterogeneously from
individual to individual or from study to study, within a certain domain and following a specific
pattern.
Usage
pow.sim.logrk.random.DE(lambda1, tl, tu, N, HR, tao, A, dist="uniform",
shape1=NULL, shape2=NULL, ap=0.5, alpha=0.05, nsim=10000)
Arguments
lambda1 Baseline hazard
tl Lower bound of delayed duration domain
tu Upper bound of delayed duration domain
NSample size
HR Post-delay hazard ratio after tu, defined as the post-delay hazard rate of the
treatment group compared to that of the control group
tao Total study duration
ATotal enrollment duration
dist One of "uniform", "beta" or "gamma", for the lag distribution
shape1 NULL or a positive parameter value for the beta or gamma distribution.
shape2 NULL or a positive parameter value for the beta or gamma distribution.
ap Experimental-control allocation ratio. The default is 0.5.
alpha Type I error rate (two-sided). The default is 0.05.
nsim Number of simulations. The default is 10000.
Details
The regular log-rank test is used here
Value
The power
Author(s)
Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> , Boguang Zhen<Boguang.Zhen@fda.hhs.gov>, Yong-
soek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>
pow.sim.logrk.random.DE 17
References
Xu, Z., Park, Y., Zhen, B. & Zhu, B. (2017). Achieving optimal power of logrank test with random
treatment time-lag effect. Biometrika. Under review.
Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017). Designing therapeutic cancer vaccine trials with
delayed treatment effect. Statistics in medicine, 36(4), 592-605.
See Also
pow.SEPPLE.plus,pow.SEPPLE.random.DE
Examples
lambda1 <- 0.001982
tl <- 30
tu <- 30*11
N <- 200
HR <- 0.55
tao <- 365*3
A <- 365
shape1 <- 5
shape2 <- 5
pow.sim.logrk.random.DE(lambda1, tl, tu, N, HR, tao, A, dist="beta",
shape1=shape1, shape2=shape2, nsim=1000)
Index
∗Topic package
DelayedEffect.Design,2
∗Topic power
HR.APPLE,3
HR.APPLE.plus,4
N.APPLE,5
N.APPLE.plus,6
pow.APPLE,8
pow.APPLE.plus,9
pow.SEPPLE,10
pow.SEPPLE.plus,11
pow.SEPPLE.random.DE,13
pow.sim.logrk,14
pow.sim.logrk.random.DE,16
DelayedEffect.Design,2
HR.APPLE,3,6,9
HR.APPLE.plus,4,7,10
N.APPLE,4,5,9
N.APPLE.plus,5,6,10
pow.APPLE,4,6,8,11,15
pow.APPLE.plus,5,7,9
pow.SEPPLE,9,10,15
pow.SEPPLE.plus,11,14,17
pow.SEPPLE.random.DE,12,13,17
pow.sim.logrk,9,11,14
pow.sim.logrk.random.DE,12,14,16
18
