README.md

In lilywang1988/GSMC: Group Sequential Design for Maxcombo tests

R package GSMC: a simulation-free group sequential design with max-combo tests in the presence of non-proportional hazards ================ Lili Wang 2021-03-08

Purpose

This R package is to implement the proposed simulation-free method for group sequential design with maxcombo tests(GS-MC). The goal here is to improve the detection power of the weighted log-rank tests (WLRTs) when the non-proportional hazards are present. Moreover, the method is simulation-free, and allows multiple checks (interims) before ending the study.

For details about the calculation of the information and covariance using estimation (data-driven) and prediction methods please find another R package [IAfrac][1]. The recent version (>= 0.2.1) has all the functions in package IAfrac imported already so there is no need to attach it separately.

We hope this package will be improved gradually. Please let us know your feedback.

Preparation

To install and use this R package from Github, please uncomment the codes.

# install.packages("devtools")
# library(devtools)
# 
# Optional: to obtain the expected errors spent at each stage
# install.packages("gsDesign")
library(gsDesign) 

# Install the R package
# install_github("lilywang1988/GSMC")
library(GSMC) 

Sample size and threshold prediction for three tests and 4 stages (3 interim and 1 final)

The detailed difference between the two prediction approaches can be found in the methodology paper:

1. The exact method is faster.

2. The exact approach is limited to piece-wise exponential distribution.

3. When the number of subintervals at each time unit (or value b) is large in stochastic approach, both methods produce very comparable results.

Stochastic prediction approach

We consider three different Fleming Harrington type weighted log-rank tests, and the first one must be the standard log-rank test. We will use the event number ratios (surrogate information fractions in the Hasegawa 2016 paper) to monitor the stopping time points.

### Parameters
# The first pair of FHweight parameters must be a standard log-rank test
FHweights <- list(
  c(0,0), # must be c(0,0)
  c(0,1),
  c(1,0)
)
n_FHweights <- length(FHweights)

# stop when what proportions of the events have been observed.
interim_ratio <- c(0.6, 0.7, 0.8, 1)
n_stage <- length(interim_ratio)

# treatment assignment
p <- 1/2 
# end of the study, chronological, assuming it's on the alternative arm
tau <- 18
# end of the accrual period, chronological
R <- 14 
# minimum potential follow-up time
omega <- (tau-R) 
# waiting time before the delayed effect starts
eps <- 2
# event hazard of the control arm.
lambda <- log(2)/6 
# hazard ratio after the change point eps under the alternative hypothesis. 
theta <- 0.6 
# event hazard for the treatment arm under the alternative hypothesis and after the change point eps.
lambda.trt <- lambda * theta  
# cumulative type I error under the control.
alpha <- 0.025 
# cumulative type II error under the alternative. 
beta <- 0.1 

# Obtain the cumulative errors spent at each stage following O\'Brien-Fleming
x <- gsDesign(
  k = n_stage, 
  test.type = 1, 
  timing = interim_ratio[-n_stage], 
  sfu = "OF", 
  alpha = alpha, 
  beta = beta, 
  delta = -log(theta)
)
# obtain the cumulative errors spent at each stage
error_spend <- cumsum(x$upper$prob[,1])
# correct the last entry
error_spend[length(error_spend)] <- alpha 


# number of subintervals for a time unit, the larger the finer 
# and more accurate; 30 should be good enough for most cases
b <- 30

# Obtain the settings from stochastic prediction
setting_stoch <- GSMC_design(
  FHweights,
  interim_ratio,
  error_spend,
  eps, 
  p, 
  b, 
  tau, 
  omega,
  lambda,
  lambda.trt,
  rho, 
  gamma,
  beta,
  stoch = T
)
# Boundaries at each stage
setting_stoch$z_alpha_pred
#> [1] 2.856776 2.692030 2.558120 2.314972
# Event numbers to pause/stop
setting_stoch$d_fixed
#> [1] 189 221 252 315

# Boundary if only consider the last stage (without interim stages)
setting_stoch$z_final_alpha_pred
#> [1] 2.136161

# Predicted type I error at each stages
sapply(1:n_stage, function(stage){
   1-Maxcombo.beta.n(
     setting_stoch$Sigma0[1:(n_FHweights * (stage)), 
                          1:(n_FHweights * (stage))],
     0, # mean is 0 under null
     setting_stoch$z_alpha_vec_pred[1:(n_FHweights * (stage))],
     rep(
       unlist(setting_stoch$interim_pred0), 
       each = n_FHweights)[1:(n_FHweights * (stage))],
     R,
     setting_stoch$n_FH)
   })
#> [1] 0.004256047 0.008361410 0.013283999 0.024973707
# vs. the designed errors spent at each stage
error_spend
#> [1] 0.004035615 0.008187950 0.013471082 0.025000000
# Predicted power at each stage
sapply(1:length(interim_ratio), function(stage){
   1-Maxcombo.beta.n(
     setting_stoch$Sigma1[1:(n_FHweights * (stage)), 
                          1:(n_FHweights * (stage))],
     setting_stoch$mu1[1:(n_FHweights * (stage))],
     setting_stoch$z_alpha_vec_pred[1:(n_FHweights * (stage))],
     rep(
       unlist(setting_stoch$interim_pred1), 
       each = n_FHweights)[1:(n_FHweights * (stage))],
     R,
     setting_stoch$n_FH)
   })
#> [1] 0.2931478 0.5042741 0.6768744 0.9002630

Exact prediction approach

# Obtain the settings from exact prediction
setting_exact <- GSMC_design(
  FHweights,
  interim_ratio,
  error_spend,
  eps, 
  p, 
  b, 
  tau, 
  omega,
  lambda,
  lambda.trt,
  rho, 
  gamma,
  beta,
  stoch = F # disable stochastic approach
)
# Boundaries at each stage
setting_exact$z_alpha_pred
#> [1] 2.857449 2.699048 2.550232 2.315363
# Event numbers to pause/stop
setting_exact$d_fixed
#> [1] 189 220 252 314

# Boundary if only consider the last stage (without interim stages)
setting_exact$z_final_alpha_pred
#> [1] 2.135569

# Predicted type I error at each stage
sapply(1:length(interim_ratio), function(stage){
   1-Maxcombo.beta.n(
     setting_exact$Sigma0[1:(n_FHweights * (stage)), 
                          1:(n_FHweights * (stage))],
     0, # mean is 0 under null
     setting_exact$z_alpha_vec_pred[1:(n_FHweights * (stage))],
     rep(
       unlist(setting_exact$interim_pred0), 
       each = n_FHweights)[1:(n_FHweights * (stage))],
     R,
     setting_exact$n_FH)
   })
#> [1] 0.004044344 0.008035714 0.013416979 0.025059931
# vs. the designed errors spent at each stage
error_spend
#> [1] 0.004035615 0.008187950 0.013471082 0.025000000
# Predicted power at each stage
sapply(1:length(interim_ratio), function(stage){
   1-Maxcombo.beta.n(
     setting_exact$Sigma1[1:(n_FHweights * (stage)), 
                          1:(n_FHweights * (stage))],
     setting_exact$mu1[1:(n_FHweights * (stage))],
     setting_exact$z_alpha_vec_pred[1:(n_FHweights * (stage))],
     rep(
       unlist(setting_exact$interim_pred1), 
       each = n_FHweights)[1:(n_FHweights * (stage))],
     R,
     setting_exact$n_FH)
   })
#> [1] 0.2940379 0.5044077 0.6790195 0.9002245

References

1. Lakatos, E. (1988). Sample sizes based on the log-rank statistic in complex clinical trials. Biometrics, 229-241.

2. Hasegawa, T. (2014). Sample size determination for the weighted log‐rank test with the Fleming–Harrington class of weights in cancer vaccine studies. Pharmaceutical statistics, 13(2), 128-135.

3. Hasegawa, T. (2016). Group sequential monitoring based on the weighted log‐rank test statistic with the Fleming–Harrington class of weights in cancer vaccine studies. Pharmaceutical statistics, 15(5), 412-419.

4. Luo, X., Mao, X., Chen, X., Qiu, J., Bai, S., & Quan, H. (2019). Design and monitoring of survival trials in complex scenarios. Statistics in medicine, 38(2), 192-209.

5. Wang, L., Luo, X., & Zheng, C. (2021). A Simulation-free Group Sequential Design with Max-combo Tests in the Presence of Non-proportional Hazards. Pharmaceutical Statistics.

Other relevant R packages:

1. https://github.com/lilywang1988/IAfrac
2. https://github.com/keaven/nphsim
3. https://cran.r-project.org/web/packages/mvtnorm/index.html

lilywang1988/GSMC documentation built on March 9, 2021, 5:25 p.m.