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Adaptive grid search for critical value using RMST (Simple or Sculpted (parallel))

adp_grid_src.Rd

This is the function for adaptive grid search of RMST two-stage design with one searching parameters gamma. The grid search make use of the conditional distribution (Normal) of E | D, which is illustrated in paper. When power is not given, the function finds the critical values that control the overall type I error < alpha while maximizing the empirical power. When power is given, it searches for valid critical values such that the empirical power is greater than the specified power. If power is given, int_n and fin_n are required

Usage

adp_grid_src(
  rmst_data,
  mu_cov_h0,
  mu_cov_h1,
  int_n,
  fin_n,
  sim_size,
  method,
  alpha,
  power = NULL
)

Arguments

rmst_data

Combined RMST data generated by the RMST_sim_cal function.

mu_cov_h0

Variance-covariance matrix of (E1-C1, E1, E2-C2, E2) under the null hypothesis (H0), obtained from the mu_cov_mc function.

mu_cov_h1

Variance-covariance matrix of (E1-C1, E1, E2-C2, E2) under the alternative hypothesis (H1), obtained from the mu_cov_mc function.

int_n

Interim sample size (n).

fin_n

Total sample size (N).

sim_size

Number of simulations to perform in the grid search.

method

Method used for the RMST design. "Simple" indicates a Simple RMST with the rejection region (D1 > m1 & D2 > m2), where D = E - C is the RMST difference between groups. "Complex" indicates a Sculpted RMST with the rejection region (D1 > m1 & E1 > q1 & D2 > m2 & E2 > q2), where E is the RMST in the experimental group.

alpha

Stated type I error level.

power

Desired power of the test (optional).

Value

A data frame with the following columns:

m1

Critical value for RMST difference at the first stage

m2

Critical value for RMST difference at the second stage

q1

Critical value for Experiment group RMST at the first stage

q2

Critical value for Experiment group RMST at the second stage

PET0

Probability of early termination under H0.

PET1

Probability of early termination under H1.

alpha

Empirical overall type I error rate.

power

Empirical power of the test.

PET

Probability of early termination (PET0+PET1)/2.

EN0

Expected sample size under H0.

EN1

Expected sample size under H1.

EN

Average expected sample size.

If no valid critical values are found, the function returns a data frame with m1 = 0, m2 = 0, q1 = 0, q2 = 0, PET0 = 0, PET1 = 0, alpha = 0, power = 0, PET = 0, EN0 = NA, EN1 = NA, EN = NA.

Examples

# Example usage of adp_grid_src function
sim_size <- 5000 
N <- 100
r <- 60
acc_time <- N / r
cen_time <- 1
lambda_H1 <- 0.9
HR <- 1.7
lambda_H0 <- 0.9 * 1.7
change_time <- 1
interim <- 0.6 * acc_time
n <- ceiling(N / 2)
alpha <- 0.05
tau_f <- 2.5

# Generate data for control arm (C) and experimental arm (E) under H0 and H1
data_C <- expo_gen_2stages(N = n * sim_size, acc_time = acc_time, 
                           lambda = lambda_H0, dist = 'exp', 
                           cen_time = cen_time, arm = 0, interim = interim)
data_E_H0 <- expo_gen_2stages(N = n * sim_size, acc_time = acc_time, 
                           lambda = lambda_H0, dist = 'exp',
                           cen_time = cen_time, arm = 1, interim = interim)
data_E_H1 <- expo_gen_2stages(N = n * sim_size, acc_time = acc_time, 
                           lambda = lambda_H1, dist = 'exp', 
                           cen_time = cen_time, arm = 1, interim = interim)

# Calculate RMST data for interim and final stages under H0 and H1
rmst_h0_int <- RMST_sim_cal(n = n, data_E = data_E_H0[ , c(2,3,1)], 
               data_C = data_C[ , c(2,3,1)], tau = interim, sim_size = sim_size)
#> Error in makeCluster(n_cores): could not find function "makeCluster"
rmst_h0_fin <- RMST_sim_cal(n = n, data_E = data_E_H0[ , c(4,5,1)], 
               data_C = data_C[ , c(4,5,1)], tau = tau_f, sim_size = sim_size)
#> Error in makeCluster(n_cores): could not find function "makeCluster"
rmst_h1_int <- RMST_sim_cal(n = n, data_E = data_E_H1[ , c(2,3,1)], 
               data_C = data_C[ , c(2,3,1)], tau = interim, sim_size = sim_size)
#> Error in makeCluster(n_cores): could not find function "makeCluster"
rmst_h1_fin <- RMST_sim_cal(n = n, data_E = data_E_H1[ , c(4,5,1)], 
               data_C = data_C[ , c(4,5,1)], tau = tau_f, sim_size = sim_size)
#> Error in makeCluster(n_cores): could not find function "makeCluster"

# Combine RMST data
rmst_data <- rbind(rmst_h0_int, rmst_h1_int, rmst_h0_fin, rmst_h1_fin)
#> Error: object 'rmst_h0_int' not found

# Calculate variance-covariance matrices under H0 and H1
mu_cov_h0 <- mu_cov_mc(rmst_int = rmst_h0_int, rmst_fin = rmst_h0_fin, sim_size = sim_size)
#> Error: object 'rmst_h0_int' not found
mu_cov_h1 <- mu_cov_mc(rmst_int = rmst_h1_int, rmst_fin = rmst_h1_fin, sim_size = sim_size)
#> Error: object 'rmst_h1_int' not found

# Perform adaptive grid search for the best RMST design
best_RMST <- adp_grid_src(rmst_data = rmst_data, mu_cov_h0 = mu_cov_h0, 
               mu_cov_h1 = mu_cov_h1, int_n = interim * r, fin_n = 2 * n, 
               alpha = 0.05, sim_size = sim_size, method = 'Complex')
#> Error in makeCluster(n_cores): could not find function "makeCluster"