# WeiUrn: Randomized Play-the-winner rule with multiple arms (k > 2) In grouprar: Group Response Adaptive Randomization for Clinical Trials

 WeiUrn R Documentation

## Randomized Play-the-winner rule with multiple arms (`k > 2`)

### Description

Simulating randomized play-the-winner rule (multiple arms) with two-sided hypothesis testing in a clinical trial context.

### Usage

``````  WeiUrn(k, p, ssn, Y0 = NULL, nsim = 2000, alpha = 0.05)
``````

### Arguments

 `k` a positive integer. The value specifies the number of treatment groups involved in a clinical trial. (`k > 2`) `p` a positive vector of length equals to `k`. The values specify the true success rates for the various treatments, and these rates are used to generate data for simulations. `ssn` a positive integer. The value specifies the total number of participants involved in each round of the simulation. `Y0` A vector of length `k`, specifying the initial probability of allocating a patient to each group. For instance, if `Y0 = c(1, 1, 1)`, the initial probabilities are calculated as `Y0 / sum(Y0)`. When `Y0` is `NULL`, the initial urn will be set as If `Y0` is `NULL`, then `Y0` is set to a vector of length `k`, with all values equal to 1 by default. `nsim` a positive integer. The value specifies the total number of simulations, with a default value of 2000. `alpha` A number between 0 and 1. The value represents the predetermined level of significance that defines the probability threshold for rejecting the null hypothesis, with a default value of 0.05.

### Details

Wei's urn procedure is obtained by extending the randomized play the winner rule (Wei1978) from the case `k = 2` to `k > 2`. Hence, It enables to conduct multi-arm clinical trials, and offers a greater range of applications.

### Value

 `name` The name of procedure. `parameter` The true parameters used to do the simulations. `assignment` The randomization sequence. `propotion` Average allocation porpotion for each of treatment groups. `failRate` The proportion of individuals who do not achieve the expected outcome in each simulation, on average. `pwClac` The probability of the study to detect a significant difference or effect if it truly exists. `k` Number of arms involved in the trial.

### References

LJ Wei (1979). The generalized polya’s urn design for sequential medical trials. The Annals of Statistics, 7(2):291–296, 19

### Examples

``````## a simple use
wei.res = WeiUrn(k = 3, p = c(0.7, 0.8, 0.7), ssn = 400, Y0 = NULL, nsim = 200, alpha = 0.05)

## view the output
wei.res

## view all simulation settings
wei.res\$name
wei.res\$parameter
wei.res\$k

## View the simulations results
wei.res\$propotion
wei.res\$failRate
wei.res\$pwCalc
wei.res\$assignment

``````

grouprar documentation built on June 22, 2024, 7:18 p.m.