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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 
Description Provides sample size and power calculations when the treatment time-lag effect is present and the lag duration is either homogeneous across the individual subject, or varies heterogeneously from individual to individual within a certain domain and following a specific pattern. The methods used are described in Xu, Z., Zhen, B., Park, Y., & Zhu, B. (2017) .
Maintainer Bill Wheeler 
License GPL-2
NeedsCompilation yes

R topics documented:
DelayedEffect.Design . . .
HR.APPLE . . . . . . . .
HR.APPLE.plus . . . . . .
N.APPLE . . . . . . . . .
N.APPLE.plus . . . . . . .
pow.APPLE . . . . . . . .
pow.APPLE.plus . . . . .
pow.SEPPLE . . . . . . .
pow.SEPPLE.plus . . . . .
pow.SEPPLE.random.DE .
pow.sim.logrk . . . . . . .
pow.sim.logrk.random.DE

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18

1

2

DelayedEffect.Design

DelayedEffect.Design

Sample size and power calculations using the APPLE, SEPPLE, APPLE+ 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 assume 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 computing 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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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

HR.APPLE

3

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)

p

Proportion of subjects who survive beyond the delayed period or NULL (see
details)

N

Sample size

tao

Total study duration

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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.

4

HR.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

N

Sample size

tao

Total study duration

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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
t1
p
HR
tao
A
beta
ap
alpha

Baseline hazard or NULL (see details)
Delayed duration or NULL (see details)
Proportion of subjects who survive beyond the delayed period or NULL (see
details)
Post-delay hazard ratio, defined as the post-delay hazard rate of the treatment
group compared to that of the control group
Total study duration
Total enrollment duration
Type II error rate; Power=1-beta
Experimental-control allocation ratio. The default is 0.5.
Type I error rate (two-sided). The default is 0.05.

6

N.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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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 closeform 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
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

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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)

8

pow.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)

p

Proportion of subjects who survive beyond the delayed period or NULL (see
details)

N

Sample 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

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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

N

Sample 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

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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)

p

Proportion of subjects who survive beyond the delayed period or NULL (see
details)

N

Sample 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

A

Total 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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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 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.

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

N

Sample 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

A

Total 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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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 heterogeneously 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 scenario 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

N

Sample 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

A

Total 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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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 individual 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)

p

Proportion of subjects who survive beyond the delayed period or NULL (see
details)

N

Sample 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

A

Total 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 , Boguang Zhen, Yongsoek Park  and Bin Zhu 
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

N

Sample 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

A

Total 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  , Boguang Zhen, Yongsoek Park  and Bin Zhu 

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



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