Title: Study Design for Immunotherapy Clinical Trials
Version: 1.0.16
Date: 2024-01-09
Description: Perform sample size, power calculation and subsequent analysis for Immuno-oncology (IO) trials composed of responders and non-responders.
Maintainer: Bill Wheeler <wheelerb@imsweb.com>
Depends: R (≥ 3.5), survival, msm
License: GPL-2
NeedsCompilation: yes
Packaged: 2024-01-09 14:34:07 UTC; wheelerwi
Author: Zhenzhen Xu [aut], Yongsoek Park [aut], Zhu Bin [aut], Bill Wheeler [cre]
Repository: CRAN
Date/Publication: 2024-01-10 14:03:13 UTC

Study design for immunotherapy clinical trials

Description

Perform sample size, power calculation and subsequent analysis for Immuno-oncology (IO) trials composed of responders and nonresponders.

Details

This package is an extension of the Immunotherapy.Design R package but allows for response categories of more than two categories among the treatment population, such as complete responders, partial responders, as well as non-responders.

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

References

Xu, Z., Park, Y., Liu, K. and Zhu, B. Treating non-responders: pitfalls and implications for cancer immunotherapy trial design. Journal of Hematology & Oncology 13, 20 (2020).

Xu, Z., Zhu, B. and Park, Y. Designing immuno-oncology clinical trials composed of responders and nonresponders. Statistics in Medicine. (Under Revision).

EM algorithm

Description

EM algorithm

Usage

 PRIMEplus.EM(data, effect_p, beta0, time.var="X", trt.var="trt", 
        status.var="event_status", id.var="id", t1=1, lambda0=NULL, 
        stopTol=1e-4, maxiter=100000, print=0)

Arguments

data

Data frame or matrix containing a time-to-event variable (time.var), a treatment variable (trt.var), and a censoring variable (status.var).

effect_p

Vector of proportions for groups of responders in the treatment arm at baseline (see details).

beta0

Vector or matrix of initial estimates for the log-hazard ratios (see details).

time.var

Time-to-event variable name in data. The default is "X".

trt.var

Binary treatment variable name in data coded as 0 for controls and 1 for subjects that received treatment.

status.var

Name of the binary censoring variable in data coded as 0 for censored subjects and 1 for subjects that experienced an event.

id.var

NULL or subject id variable in data. The default is "id".

t1

Delayed duration. The default is 1.

lambda0

NULL or vector of initial estimates for the baseline hazards corrsponding to the ordered event times.

stopTol

Stopping tolerance. The default is 1e-4.

maxiter

Maximum number of iterations. The default is 100000.

print

0-2 to print information. Larger values will print more information. The default is 0.

Details

The EM algorithm is sensitive to the initial values of the log-hazard ratios (beta0), so different initial estimates should be tried to ensure the maximum log-likelihood is obtained. Thus, beta0 can be a vector or matrix, where in the case of a matrix, each row corresponds to a different set of intial estimates. Each set of initial estimates must contain distinct non-zero values. The length and order of effect_p must be the same as the columns of beta0. Both of these should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p would be a vector of length two, and beta0 would be a vector of length two or a matrix with two columns.

Value

A list containing the objects:

Name Description
converged TRUE if EM algorithm converged
beta final log(hazard ratio) estimates of responders versus controls
lambda final estimates of baseline hazards
probResponder estimated probability of a subject being a responder
loglike log-likelihood value at the final estimates
loglike.marg marginal log-likelihood value at the final estimates

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

See Also

getHazard, PRIMEplus.LRT

Examples

  data(data, package="PRIMEplus")
  effp  <- c(0.3, 0.3)
  beta0 <- c(log(0.4), log(0.6))
  ret   <- PRIMEplus.EM(data, effp, beta0)
  ret$beta

Likelihood Ratio Test

Description

PRIMEplus likelihood ratio test

Usage

 PRIMEplus.LRT(data, effect_p, beta0, time.var="X", trt.var="trt", 
       status.var="event_status", id.var="id", t1=1, lambda0=NULL, 
       stopTol=1e-4, maxiter=100000, print=0)

Arguments

data

Data frame or matrix containing a time-to-event variable (time.var), a treatment variable (trt.var), and a censoring variable (status.var).

effect_p

Vector of proportions for groups of responders in the treatment arm at baseline (see details).

beta0

Vector or matrix of initial estimates for the log-hazard ratios (see details).

time.var

Time-to-event variable name in data. The default is "X".

trt.var

Binary treatment variable name in data coded as 0 for controls and 1 for subjects that received treatment.

status.var

Name of the binary censoring variable in data coded as 0 for censored subjects and 1 for subjects that experienced an event.

id.var

NULL or subject id variable in data. The default is "id".

t1

Delayed duration. The default is 1.

lambda0

NULL or vector of initial estimates for the baseline hazards corrsponding to the ordered event times.

stopTol

Stopping tolerance. The default is 1e-4.

maxiter

Maximum number of iterations. The default is 100000.

print

0-2 to print information. Larger values will print more information. The default is 0.

Details

The EM algorithm is sensitive to the initial values of the log-hazard ratios (beta0), so different initial estimates should be tried to ensure the maximum log-likelihood is obtained. Thus, beta0 can be a vector or matrix, where in the case of a matrix, each row corresponds to a different set of intial estimates. Each set of initial estimates must contain distinct non-zero values. The length and order of effect_p must be the same as the columns of beta0. Both of these should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p would be a vector of length two, and beta0 would be a vector of length two or a matrix with two columns.

Value

A list containing the objects:

Name Description
converged TRUE if EM algorithm converged
beta final log(hazard ratio) estimates of responders versus controls
lambda final estimates of baseline hazards
probResponder estimated probability of a subject being a responder
loglike log-likelihood value at the final estimates
loglike.marg marginal log-likelihood value at the final estimates
loglike.marg.0 marginal log-likelihood value under the null hypothesis
LRT likelihood-ratio test statistic
pvalue p-value of the likelihood ratio test

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

See Also

PRIMEplus.EM

Examples

  data(data, package="PRIMEplus")
  effp  <- c(0.3, 0.3)
  beta0 <- c(log(0.4), log(0.6))
  ret   <- PRIMEplus.LRT(data, effp, beta0)
  ret$LRT 
  ret$pvalue

Power

Description

Compute the power using LRT Re-randomization test

Usage

 
PRIMEplus.Power(nmax=500, rand_ratio=0.5, effect_p=0.6, 
    enroll_rate=380*0.25/6, lambda1=0.117, HR=0.5, tau=12*5, t1=1, 
    maxiter=100000, stopTol=1e-4, alpha=0.05, num_rand=1000, nsim=10000, 
    print=0, min.sample.size=50, min.n.event=5, min.per.trt=0.25)

Arguments

nmax

Sample size

rand_ratio

Probability of assignment to treatment arm

effect_p

Vector for proportion of responders in the treatment arm at baseline (see details)

enroll_rate

Enrollment rate in subjects per month

lambda1

Baseline hazard in terms of months

HR

Vector of hazard ratios for responders against controls (see details)

tau

Total study duration

t1

Delayed duration in months

maxiter

Maximum number of iterations in the EM algorithm. The default is 100000.

stopTol

Stopping tolerance in the EM algorithm. The default is 1e-4.

alpha

Significance level. The default is 0.05.

num_rand

The number of replications in the re-randomization test. The default is 1000.

nsim

The number of simulations. The default is 1000.

print

0 or 1 to print information. The default is 0.

min.sample.size

Minimum sample size. The default is 50.

min.n.event

Minimum number of events. The default is 5.

min.per.trt

Minimum proportion of controls and treated subjects. The default is 0.25.

Details

The length and order of effect_p must be the same as HR. Both of these vectors should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p and HR would be vectors of length two.

For each simulation, a simulated data set is created from the generate_data function and then an estimated p-value is computed by calling PRIMEplus.ReRand.LRT. The power is calculated as the proportion of iterations whose estimated p-value was less than or equal to alpha.

Value

A list containing the power and the number of simulated datasets used in the calculation.

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

See Also

PRIMEplus.ReRand.LRT

Randomization Test

Description

PRIMEplus randomization likelihood ratio test

Usage

 PRIMEplus.ReRand.LRT(data, effect_p, beta0, time.var="X", trt.var="trt", 
                             status.var="event_status", id.var="id", t1=1, lambda0=NULL, 
                             stopTol=1e-4, maxiter=100000, print=0, num_rand=1000)

Arguments

data

Data frame or matrix containing a time-to-event variable (time.var), a treatment variable (trt.var), and a censoring variable (status.var).

effect_p

Vector of proportions for groups of responders in the treatment arm at baseline (see details).

beta0

Vector or matrix of initial estimates for the log-hazard ratios (see details).

time.var

Time-to-event variable name in data. The default is "X".

trt.var

Binary treatment variable name in data coded as 0 for controls and 1 for subjects that received treatment.

status.var

Name of the binary censoring variable in data coded as 0 for censored subjects and 1 for subjects that experienced an event.

id.var

NULL or subject id variable in data. The default is "id".

t1

Delayed duration. The default is 1.

lambda0

NULL or vector of initial estimates for the baseline hazards corrsponding to the ordered event times.

stopTol

Stopping tolerance. The default is 1e-4.

maxiter

Maximum number of iterations. The default is 100000.

print

0-2 to print information. Larger values will print more information. The default is 0.

num_rand

The number of randomizations. The default is 1000.

Details

The EM algorithm is sensitive to the initial values of the log-hazard ratios (beta0), so different initial estimates should be tried to ensure the maximum log-likelihood is obtained. Thus, beta0 can be a vector or matrix, where in the case of a matrix, each row corresponds to a different set of intial estimates. Each set of initial estimates must contain distinct non-zero values. The length and order of effect_p must be the same as the columns of beta0. Both of these should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p would be a vector of length two, and beta0 would be a vector of length two or a matrix with two columns. The initial values are only used for the observed data; each randomization uses the MLE estimates as initial estimates.

Value

A list containing the objects:

Name Description
pvalue.LRT p-value of the randomization test based on the likelihood ratio test
pvalue.loglike.marg p-value of the randomization test based on the marginal likelihood
n.randomizations the number of randomizations that the p-values are based on

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

See Also

PRIMEplus.LRT

Examples

  data(data, package="PRIMEplus")
  effp  <- c(0.3, 0.3)
  beta0 <- c(log(0.4), log(0.6))
  ret   <- PRIMEplus.ReRand.LRT(data, effp, beta0, num_rand=100)
  ret

Sample Size

Description

Compute the sample size for a given power

Usage

 
PRIMEplus.SampleSize(power=0.8, rand_ratio=0.5, effect_p=0.6, enroll_rate=380*0.25/6, 
              lambda1=0.117, HR=0.5, tau=12*5, t1=1, maxiter=100000, stopTol=1e-4,
              alpha=0.05, num_rand=1000, nsim=10000, min.N=100, max.N=700,
              tol.power=0.01, tol.N=1, print=1,
              min.sample.size=50, min.n.event=5, min.per.trt=0.25)

Arguments

power

The desired power. The default is 0.8.

rand_ratio

Allocation ratio

effect_p

Vector for proportion of responders in the treatment arm at baseline (see details)

enroll_rate

Enrollment rate in subjects per month

lambda1

Baseline hazard in terms of months

HR

Vector of hazard ratios for responders against controls (see details)

tau

Total study duration

t1

Delayed duration

maxiter

Maximum number of iterations in the EM algorithm. The default is 100000.

stopTol

Stopping tolerance in the EM algorithm. The default is 1e-4.

alpha

Significance level. The default is 0.05.

num_rand

Number of replications in the re-randomization test. The default is 1000.

nsim

Number of simulations in computing power (see Details). The default is 10000.

min.N

Lower bound for the sample size. The default is 100.

max.N

Upper bound for the sample size. The default is 700.

tol.power

Stopping tolerance for the power. The default is 0.01.

tol.N

Stopping tolerance for the sample size. The default is 1.

print

0 or 1 to print information. The default is 1.

min.sample.size

Minimum sample size. The default is 50.

min.n.event

Minimum number of events. The default is 5.

min.per.trt

Minimum proportion of controls and treated subjects. The default is 0.25.

Details

The length and order of effect_p must be the same as HR. Both of these vectors should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p and HR would be vectors of length two.

This uses a bisection method to estimate the sample size. At each iteration, the estimated power power_est is computed using PRIMEplus.Power for a given sample size holding all other parameters fixed. The algorithm terminates when abs(power - power_est) <= tol.power or when the length of the estimated interval containing the sample size is less than or equal to tol.N.

NOTE:
It is important to note that the power for a given sample size is estimated by running a simulation. Thus, by setting a different seed, a different result may be returned. Therefore, to ensure a more precise estimated sample size, set the option nsim to a large value and/or run this function several times by setting different seeds and examine the distribution of returned sample sizes.

Value

A list containing the sample size and power.

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

See Also

PRIMEplus.Power

Data for examples

Description

Data for examples.

Details

A data frame used in the examples.

Examples


 data(data, package="PRIMEplus")

 # Display some of the data
 data[1:5, ]

Simulated data

Description

Generate simulated data

Usage

 
generate_data(N=500, rand_ratio=0.5, effect_p=0.6, enroll_rate=380*0.25/6, 
              lambda1=0.117, HR=0.5, tau=12*5, t1=1)

Arguments

N

Maximum sample size

rand_ratio

Allocation ratio

effect_p

Vector for proportion of responders in the treatment arm at baseline (see details)

enroll_rate

Enrollment rate in subjects per month

lambda1

Baseline hazard in terms of months

HR

Vector of hazard ratios for responders against controls (see details)

tau

Total study duration

t1

Delayed duration

Details

The length and order of effect_p must be the same as HR. Both of these vectors should contain information only for the groups of responders. For example, if there are full responders and partial responders, then effect_p and HR would be vectors of length two.

Value

A data frame with columns:

Name Description
id id variable
trt treatment allocation: 1 = treatment arm
D1 patient's response status for group 1
D2 patient's response status for group 2
Dm patient's response status for non-responders
tau total study duration
enroll_time patients' enrollment times
time_to_event patients' event times
event_status censoring indicator
X observational time
t1 delayed duration

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov>, Yongsoek Park <yongpark@pitt.edu> and Bin Zhu <bin.zhu@nih.gov>

Examples

  data <- generate_data()
  data[1:5, ]

Compute initial estimates for the baseline hazard

Description

Calls the coxph function to compute initial estimates for the baseline hazard

Usage

 getHazard(time, treatment, event_status, t.fail.o=NULL)

Arguments

time

Vector of times.

treatment

Binary vector of treatments (1=subject received treatment).

event_status

Binary vector of event status (1=subject experienced an event).

t.fail.o

NULL or vector of event times.

Value

List containing the baseline hazards ordered by the event times.

Author(s)

Zhenzhen Xu <Zhenzhen.Xu@fda.hhs.gov> and Bin Zhu <bin.zhu@nih.gov>

See Also

PRIMEplus.EM

Examples

  data(data, package="PRIMEplus")
  lambda0 <- getHazard(data[, "X"], data[, "trt"], data[, "event_status"])$hazard
  lambda0[1:10]