Goal

This R package implements the power analysis simulation described in the paper: Lee, S.Y. A note on the sample size formula for a win ratio endpoint. Statistics in Medicine (https://doi.org/10.1002/sim.70165).

Install R libaries to install winratiosim

Note: The user needs to install several R libraries in order to set up winratiosim. Ensure that the following libraries are installed.

library(plyr)
library(dplyr)
library(parallel)
library(kableExtra)
library(pbmcapply)
library(foreach)
library(doSNOW)
library(devtools)

Install R package

Note: If there is any error in the installation of winratiosim, it is mainly because the user skipped installing the R libraries listed above or other necessary R libraries.

# devtools::install_github("yain22/winratiosim")
install.packages("winratiosim", repos = c('https://yain22.r-universe.dev', 'https://cloud.r-project.org'))

Load R package

library(winratiosim)

Main R function for the sample size calculation

Note: Once the R package winratiosim has been installed, the user can verify if the main R function can be loaded by checking the following.

# Check
winratiosim
?winratiosim::winratiosim

Implement the power analysis simulation

Note: This simulation is optimized for Windows due to the parallel computing setup.

# Install Library
library(plyr)
library(dplyr)
library(parallel)
library(kableExtra)
library(pbmcapply)
library(foreach)
library(doSNOW)

# Simulation under power scenario
set.seed(20250518)
## Set the data generating parameters
power.design_parameters = list(
      nsim = 10000,
      N = 400, # 100, 200, 300, 400, 500
      Randomization.ratio = c(1, 1),
      alpha.JFM = 0, theta.JFM = 1,
      lambda_trt = 0.13, lambda_ctl = 0.15,
      ann.icr_trt = 0.32, ann.icr_ctl = 0.55,
      xbase_trt = 45, xfinal_trt = 45+7.5, sd.delta.x_trt = 20,
      xbase_ctl = 45, xfinal_ctl = 45, sd.delta.x_ctl = 20,
      censorrate_trt = 0.2, censorrate_ctl = 0.2,
      nc = 10
    )

## Running simulation
power.sim_res = winratiosim(nsim = power.design_parameters$nsim, N = power.design_parameters$N, Randomization.ratio = power.design_parameters$Randomization.ratio,
                                alpha.JFM = power.design_parameters$alpha.JFM, theta.JFM = power.design_parameters$theta.JFM,
                                lambda_trt = power.design_parameters$lambda_trt, lambda_ctl = power.design_parameters$lambda_ctl,
                                ann.icr_trt = power.design_parameters$ann.icr_trt, ann.icr_ctl = power.design_parameters$ann.icr_ctl,
                                xbase_trt = power.design_parameters$xbase_trt, xfinal_trt = power.design_parameters$xfinal_trt,
                                xbase_ctl = power.design_parameters$xbase_ctl, xfinal_ctl = power.design_parameters$xfinal_ctl,
                                sd.delta.x_trt = power.design_parameters$sd.delta.x_trt, sd.delta.x_ctl = power.design_parameters$sd.delta.x_ctl,
                                censorrate_trt = power.design_parameters$censorrate_trt, censorrate_ctl = power.design_parameters$censorrate_ctl,
                                nc = power.design_parameters$nc)

## FS test
Power_one_sided_superiority_FS_Permutation = mean(power.sim_res$df_FS.analysis.summary$p_value_FS < 0.025, na.rm = T)
Power_binom_CI_one_sided_FS_Permutation = binom.conf.exact(x=sum(power.sim_res$df_FS.analysis.summary$p_value_FS < 0.025, na.rm = T), n=nrow(power.sim_res$df_FS.analysis.summary) - sum(is.na(power.sim_res$df_FS.analysis.summary$p_value_FS)))

## YG test
Power_one_sided_superiority_WR_Ron_Yu = mean(power.sim_res$df_WR.analysis.summary$LB_R_w > 1, na.rm = T)
Power_binom_CI_one_sided_WR_Ron_Yu = binom.conf.exact(x=sum(power.sim_res$df_WR.analysis.summary$LB_R_w > 1, na.rm = T), n=nrow(power.sim_res$df_WR.analysis.summary) - sum(is.na(power.sim_res$df_WR.analysis.summary$LB_R_w)))

# Simulation under Type I Error scenario
## Set the data generating parameters
t1e.design_parameters = list(
      nsim = power.design_parameters$nsim,
      N = power.design_parameters$N,
      Randomization.ratio = power.design_parameters$Randomization.ratio,
      alpha.JFM = power.design_parameters$alpha.JFM, theta.JFM = power.design_parameters$theta.JFM,
      lambda_trt = power.design_parameters$lambda_ctl, lambda_ctl = power.design_parameters$lambda_ctl,
      ann.icr_trt = power.design_parameters$ann.icr_ctl, ann.icr_ctl = power.design_parameters$ann.icr_ctl,
      xbase_trt = power.design_parameters$xbase_ctl, xfinal_trt = power.design_parameters$xfinal_ctl, sd.delta.x_trt = power.design_parameters$sd.delta.x_trt,
      xbase_ctl = power.design_parameters$xbase_ctl, xfinal_ctl = power.design_parameters$xfinal_ctl, sd.delta.x_ctl = power.design_parameters$sd.delta.x_ctl,
      censorrate_trt = power.design_parameters$censorrate_trt, censorrate_ctl = power.design_parameters$censorrate_ctl,
      nc = 10)

# Running simulation
t1e.sim_res = winratiosim(nsim = t1e.design_parameters$nsim, N = t1e.design_parameters$N, Randomization.ratio = t1e.design_parameters$Randomization.ratio,
                              alpha.JFM = t1e.design_parameters$alpha.JFM, theta.JFM = t1e.design_parameters$theta.JFM,
                              lambda_trt = t1e.design_parameters$lambda_trt, lambda_ctl = t1e.design_parameters$lambda_ctl,
                              ann.icr_trt = t1e.design_parameters$ann.icr_trt, ann.icr_ctl = t1e.design_parameters$ann.icr_ctl,
                              xbase_trt = t1e.design_parameters$xbase_trt, xfinal_trt = t1e.design_parameters$xfinal_trt,
                              xbase_ctl = t1e.design_parameters$xbase_ctl, xfinal_ctl = t1e.design_parameters$xfinal_ctl,
                              sd.delta.x_trt = t1e.design_parameters$sd.delta.x_trt, sd.delta.x_ctl = t1e.design_parameters$sd.delta.x_ctl,
                              censorrate_trt = t1e.design_parameters$censorrate_trt, censorrate_ctl = t1e.design_parameters$censorrate_trt,
                              nc = t1e.design_parameters$nc)

## FS test
t1e_one_sided_superiority_FS_Permutation = mean(t1e.sim_res$df_FS.analysis.summary$p_value_FS < 0.025, na.rm = T)
t1e_binom_CI_one_sided_FS_Permutation = binom.conf.exact(x=sum(t1e.sim_res$df_FS.analysis.summary$p_value_FS < 0.025, na.rm = T),n=nrow(t1e.sim_res$df_FS.analysis.summary) - sum(is.na(t1e.sim_res$df_FS.analysis.summary$p_value_FS)))

## YG test
t1e_one_sided_superiority_WR_Ron_Yu = mean(t1e.sim_res$df_WR.analysis.summary$LB_R_w > 1, na.rm = T)
t1e_binom_CI_one_sided_WR_Ron_Yu = binom.conf.exact(x=sum(t1e.sim_res$df_WR.analysis.summary$LB_R_w > 1, na.rm = T),n=nrow(t1e.sim_res$df_WR.analysis.summary) - sum(is.na(t1e.sim_res$df_WR.analysis.summary$LB_R_w)))

# Print out results
## Construct compact Power and Type I Error results
  df.power.type1 <- data.frame(
  Method = c("FS test", "YG test"),

  Power = paste(
    round(c(Power_binom_CI_one_sided_FS_Permutation[1], Power_binom_CI_one_sided_WR_Ron_Yu[1]), 3),
    "(",
    round(c(Power_binom_CI_one_sided_FS_Permutation[2], Power_binom_CI_one_sided_WR_Ron_Yu[2]), 3),
    ", ",
    round(c(Power_binom_CI_one_sided_FS_Permutation[3], Power_binom_CI_one_sided_WR_Ron_Yu[3]), 3),
    ")",
    sep = ""
  ),

  Type_I_Error = paste(
    round(c(t1e_binom_CI_one_sided_FS_Permutation[1], t1e_binom_CI_one_sided_WR_Ron_Yu[1]), 3),
    "(",
    round(c(t1e_binom_CI_one_sided_FS_Permutation[2], t1e_binom_CI_one_sided_WR_Ron_Yu[2]), 3),
    ", ",
    round(c(t1e_binom_CI_one_sided_FS_Permutation[3], t1e_binom_CI_one_sided_WR_Ron_Yu[3]), 3),
    ")",
    sep = ""
  )
)

## Median variance values
  df.variance <- data.frame(
    `Median Variance under Power` = c(
      median(power.sim_res$df_WR.analysis.summary$variance_log_R_w_permutation, na.rm = TRUE),
      median(power.sim_res$df_WR.analysis.summary$Var_logR_w, na.rm = TRUE)
    ),
    `Median Variance under Type I Error` = c(
      median(t1e.sim_res$df_WR.analysis.summary$variance_log_R_w_permutation, na.rm = TRUE),
      median(t1e.sim_res$df_WR.analysis.summary$Var_logR_w, na.rm = TRUE)
    )
  )

## Round and combine everything
  df.combined <- cbind(df.power.type1, round(df.variance, 4))

## Generate the summary df.kable
  df_kable_summary <- paste0(
    "Simulation assumptions:\n",
    "  Treatment Arm — Mortality = ", power.design_parameters$lambda_trt,
    ", Annualized HFH = ", power.design_parameters$ann.icr_trt,
    ", ΔKCCQ = ", power.design_parameters$xfinal_trt - power.design_parameters$xbase_trt,
    ", SD(ΔKCCQ) = ", power.design_parameters$sd.delta.x_trt,
    ", Attrition = ", power.design_parameters$censorrate_trt, "\n",

    "  Control Arm — Mortality = ", power.design_parameters$lambda_ctl,
    ", Annualized HFH Rate = ", power.design_parameters$ann.icr_ctl,
    ", ΔKCCQ = ", power.design_parameters$xfinal_ctl - power.design_parameters$xbase_ctl,
    ", SD(ΔKCCQ) = ", power.design_parameters$sd.delta.x_ctl,
    ", Attrition = ", power.design_parameters$censorrate_ctl, "\n",

    "Randomization Ratio (T:C) = ", power.design_parameters$Randomization.ratio[1], ":", power.design_parameters$Randomization.ratio[2], "\n",
    "Sample Size (N) = ", power.design_parameters$N,
    ", Number of simulations = ", power.design_parameters$nsim, "\n",
    "Joint Frailty Model Parameters: alpha = ", power.design_parameters$alpha.JFM,
    ", theta = ", power.design_parameters$theta.JFM
  )

## Final table
df_kable_summary
kable(df.combined, caption = "Simulation Results")
print(paste0("Median value of win ratio is ", round(median(power.sim_res$df_WR.analysis.summary$R_w), 3)))
print(paste0("Median value of probability of tie is ", round(median(power.sim_res$df_Total_probability[, 2]), 3)))

Simulation Results

# Note: Results may slightly differ from those in the paper due to random seed settings.
> df_kable_summary
[1] "Simulation assumptions:\n  Treatment Arm — Mortality = 0.13, Annualized HFH = 0.32, ΔKCCQ = 7.5, SD(ΔKCCQ) = 20, Attrition = 0.2\n  Control Arm — Mortality = 0.15, Annualized HFH Rate = 0.55, ΔKCCQ = 0, SD(ΔKCCQ) = 20, Attrition = 0.2\nRandomization Ratio (T:C) = 1:1\nSample Size (N) = 400, Number of simulations = 10000\nJoint Frailty Model Parameters: alpha = 0, theta = 1"
> kable(df.combined, caption = "Simulation Results")


Table: Simulation Results

|Method  |Power               |Type_I_Error        | Median.Variance.under.Power| Median.Variance.under.Type.I.Error|
|:-------|:-------------------|:-------------------|---------------------------:|----------------------------------:|
|FS test |0.861(0.854, 0.868) |0.025(0.022, 0.028) |                      0.0168|                             0.0161|
|YG test |0.82(0.812, 0.828)  |0.016(0.013, 0.018) |                      0.0197|                             0.0188|
> print(paste0("Median value of win ratio is ", round(median(power.sim_res$df_WR.analysis.summary$R_w), 3)))
[1] "Median value of win ratio is 1.486"
> print(paste0("Median value of probability of tie is ", round(median(power.sim_res$df_Total_probability[, 2]), 3)))
[1] "Median value of probability of tie is 0.191"

References

1. Lee, S.Y. A note on the sample size formula for a win ratio endpoint. Statistics in Medicine (https://doi.org/10.1002/sim.70165)
2. Yu, R. X., & Ganju, J. (2022). Sample size formula for a win ratio endpoint. Statistics in medicine, 41(6), 950-963.
3. Finkelstein, D. M., & Schoenfeld, D. A. (1999). Combining mortality and longitudinal measures in clinical trials. Statistics in medicine, 18(11), 1341-1354.
4. Pocock, S. J., Ariti, C. A., Collier, T. J., & Wang, D. (2012). The win ratio: a new approach to the analysis of composite endpoints in clinical trials based on clinical priorities. European heart journal, 33(2), 176-182.