# power_RET: Power related calculations for three-arm clinical trials In ThreeArmedTrials: Design and Analysis of Clinical Non-Inferiority or Superiority Trials with Active and Placebo Control

## Description

Compute power, sample size, or level of significance for Wald-type test for non-inferiority or superiority of the experimental treatment versus reference treatment with respect to placebo.

## Usage

 ```1 2 3``` ```power_RET(experiment, reference, placebo, Delta, sig_level = NULL, power = NULL, n = NULL, allocation = c(1/3, 1/3, 1/3), distribution = NULL, ...) ```

## Arguments

 `experiment` a numeric vector specifying the parameters of the experimental treatment group in the alternative hypothesis `reference` a numeric vector specifying the parameters of the reference treatment group in the alternative hypothesis `placebo` a numeric vector specifying the parameters of the placebo treatment group in the alternative hypothesis `Delta` a numeric value specifying the non-inferiority/superiority margin `sig_level` A numeric value specifying the significance level (type I error probability) `power` A numeric value specifying the target power (1 - type II error probability) `n` The total sample size. Needs to be at least 7. `allocation` A (non-empty) vector specifying the sample size allocation (nExp/n, nRef/n, nPla/n) `distribution` A character specifying the distribution of the endpoints. Must must be either of `"binary"`, `"poisson"`, `"negbin"`, `"exponential"`, `"normal"` `...` Further arguments. See details.

## Details

If the individual group sample sizes, i.e. `n*allocation` are not natural number, the parameters n and allocation will be re-calculated.

The additional parameter `var_estimation` is a character string specifying how the variance for the Wald-type test statistic is estimated in the Poisson and negative binomial model. Must be RML for restricted maximum-likelihood, or ML for unrestricted maximum-likelihood

## Value

A list with class "power.htest" containing the following components:

 `n` The total sample size `power` A numeric value specifying the target power `Delta` A numeric value specifying the non-inferiority or superiority margin. `sig.level` A character string specifying the significance level `type` A character string indicating what type of Wald-type test will be performed `allocation` A vector with the sample size allocation (nExp/n, nRef/n, nPla/n) `sig.level` The significance level (Type I error probability) `nExp` A numeric value specifying the number of sample in the experimental treatment group `nRef` A numeric value specifying the number of sample in the reference treatment group `nPla` A numeric value specifying the number of sample in the placebo treatment group

## Examples

 ```1 2 3 4 5``` ```power_RET(experiment = 15, reference = 17, placebo = 20, Delta = 0.8, sig_level = 0.025, power = 0.8, allocation = c(1, 1, 1) / 3, var_estimation = "RML", distribution = "poisson") ```

### Example output

```     Power calculation for Wald-type test (with restriced variance estimation) in three-arm trial with Poisson endpoints

Rate - Experiment = 15
Rate - Reference = 17
Rate - Placebo = 20
n = 96
sig.level = 0.025
power = 0.8047648
Delta = 0.8
allocation = 0.3333333, 0.3333333, 0.3333333
nExp = 32
nRef = 32
nPla = 32
```

ThreeArmedTrials documentation built on May 2, 2019, 3:28 p.m.