# Conduct the simulation studies of the Adaptive Enrichment Design without early stopping boundary The `AED.sim()` is used to conduct the simulation studies of the Adaptive Enrichment Design without early stopping boundary. The AED design is quite similar with the AED1_SSR design. But, in the AED design, the futility stopping boundary and the Sample Size Re-estimation Procedure are removed. On the contrary, a fixed sample size is used to replace the sample size re-estimated procedure. In addition, an $\epsilon$-rule is also introduced to select the subgroup with larger subgroup-specific test statistic. ```r AED.sim( N1, N2, rho, alpha, beta, theta, theta0, K, Info, epsilon, sigma0, nSim, Seed ) ``` ## Arguments - `N1`: The sample size used at the first stage - `N2`: The sample size used at the second stage - `rho`: The proportion of the subgroup 1 - `alpha`: The overall Type I error rate - `beta`: The (1 - Power) - `theta`: The sizes of treatment effects in subgroups 1 and 2 among the experimental arm - `theta0`: The size of treatment effect in standard arm - `K`: The number of subgroups - `Info`: The observed information - `epsilon`: The threshold of difference between the subgroup-specific test statistics - `sigma0`: The variance of the treatment effect - `nSim`: The number of simulated studies - `Seed`: The random Seed ## Returns A list contains * nTotal The average expected sample size * H00 The probability of rejecting the null hypothesis of $H_{00}$ * H01 The probability of rejecting the null hypothesis of $H_{01}$ * H02 The probability of rejecting the null hypothesis of $H_{02}$ * H0 The probabilities of rejecting at least one of the null hypothesis * Enrich01 The prevalence of adaptive enrichment of subgroup 1 * Enrich02 The prevalence of adaptive enrichment of subgroup 2 ## Examples ```r N1 <- 310 N2 <- 310 rho <- 0.5 alpha <- 0.05 beta <- 0.20 theta <- c(0,0) theta0 <- 0 K <- 2 Info <- 0.5 epsilon <- 0.5 sigma0 <- 1 nSim <- 1000 Seed <- 6 AED.sim(N1 = N1, N2 = N2, rho = rho, alpha = alpha, beta = beta, theta = theta, theta0 = theta0, K = K, Info = Info, epsilon = epsilon, sigma0 = sigma0, nSim = nSim, Seed = Seed) ``` ## References * Lin, R., Yang, Z., Yuan, Y. and Yin, G., 2021. Sample size re-estimation in adaptive enrichment design. Contemporary Clinical Trials, 100, p.106216. \

AED.sim function