Compare the effects of sample size on the log-rank test

simulation_logrank_test.R

library(survival)

# Function to generate survival data
generate_data <- function(sample_size, event_rate_group1, event_rate_group2) {
  group <- c(rep(1, sample_size), rep(0, sample_size))
  event_times <- c(rexp(sample_size, rate = event_rate_group1),
                   rexp(sample_size, rate = event_rate_group2))
  observed <- rep(1, sample_size * 2)  # Assuming all events are observed
  data <- data.frame(group = group, event_times = event_times, observed = observed)
  return(data)
}

# Function to perform the log-rank test
perform_log_rank_test <- function(data) {
  surv_object <- Surv(data$event_times, data$observed)
  fit <- survdiff(surv_object ~ data$group)
  return(1 - pchisq(fit$chisq, df = 1))
}

sample_sizes <- c(10, 30, 50, 100, 200)
p_values <- numeric(length(sample_sizes))

# Simulate and perform the log-rank test for different sample sizes
set.seed(1)
for (i in 1:length(sample_sizes)) {
  data <- generate_data(sample_sizes[i], event_rate_group1 = 0.1, event_rate_group2 = 0.2)
  p_values[i] <- perform_log_rank_test(data)
  print(paste("Sample size:", sample_sizes[i] * 2, ", p-value:", round(p_values[i], 5)))
}

# [1] "Sample size: 20 , p-value: 0.42122"
# [1] "Sample size: 60 , p-value: 0.20008"
# [1] "Sample size: 100 , p-value: 0.0033"
# [1] "Sample size: 200 , p-value: 0"
# [1] "Sample size: 400 , p-value: 0"

# Plotting the results
plot(sample_sizes, p_values, type = "b", pch = 19, col = "blue",
     xlab = "Sample Size per Group", ylab = "p-value",
     main = "Effect of Sample Size on Log-Rank Test")
abline(h = 0.05, col = "red", lty = 2)

set.seed(1234)
for (i in 1:length(sample_sizes)) {
  data <- generate_data(sample_sizes[i], event_rate_group1 = 0.1, event_rate_group2 = 0.2)
  p_values[i] <- perform_log_rank_test(data)
  print(paste("Sample size:", sample_sizes[i] * 2, ", p-value:", round(p_values[i], 5)))
}
# [1] "Sample size: 20 , p-value: 0.89394"
# [1] "Sample size: 60 , p-value: 0.0937"
# [1] "Sample size: 100 , p-value: 0.27181"
# [1] "Sample size: 200 , p-value: 1e-05"
# [1] "Sample size: 400 , p-value: 0"