# sample.def4: using using simulation. In carolinewei/apsurvival: Total sample size and its allocation for the MRCT

## Description

This function calculates total sample size with and without considering desired conditional assurance probability to claim overall consistency and determines optimal sample size allocation across regions by maximizing conditional assurance probability based on Definition 4 if regional treatment effects are slightly different. (Allocate equal sample size to each region if treatment effects across regions are the same.)

## Usage

 ```1 2``` ```sample.def4(r0, alpha = 0.05, beta = 0.2, lamda, lamda_cen, L, s, u, eps = 0.1, grid = 0.1, n = 1e+05, consistency = 0.8) ```

## Arguments

 `r0` True overall log hazard ratio `alpha` The risk of rejecting the null hypothesis H0:r0>=0 when it is really true `beta` The risk of failing to reject the null hypothesis H0:r0>=0 when it is really false `lamda` The event hazard rate for placebo `lamda_cen` The discontinuation hazard rate `L` The whole study duration of fixed study duration design `s` Number of regions participating in the MRCT `u` A vector presents ratios of true regional log hazard ratios to true overall log hazard ratio r=u*r0 `eps` Significance level of not rejecting H0 in Definition 4 `grid` Grid interval of the grid research `n` Simulation times `consistency` A numeric value is the desired conditional assurance probability to claim overall consistency showing only two decimal places.

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## Examples

 ```1 2 3``` ```set.seed(123) Sampsize4 <- sample.def4(r0=log(0.7), alpha=0.05, beta=0.2, lamda=1, lamda_cen=1, L=2, s=3, u=c(0.9,1,1.1), eps=0.1, grid=0.1, n=1000, consistency=0.8) ```

carolinewei/apsurvival documentation built on Nov. 4, 2019, 8:44 a.m.