# PolyaUrn: Randomized Pólya urn procedure In grouprar: Group Response Adaptive Randomization for Clinical Trials

 PolyaUrn R Documentation

## Randomized Pólya urn procedure

### Description

Simulating randomized Pólya urn procedure with two-sided hypothesis testing in a clinical trial context.

### Usage

``````PolyaUrn(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 \ge 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

The randomized Pólya urn (RPU) procedure can be describe as follows: An urn contains at least one ball of each treatment type (totally K treatments) initially. A ball is drawn from the urn with replacement. If a type `i` ball is drawn, `i=1, \ldots, K`, then treatment `i` is assigned to the next patient. If the response is a success, a ball of type `i` is added to the urn. Otherwise the urn remains unchanged.

### 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

Durham, S. D., FlournoY, N. AND LI, W. (1998). Sequential designs for maximizing the probability of a favorable response. Canadian Journal of Statistics, 3, 479-495.

### Examples

``````## a simple use
Polya.res = PolyaUrn(k = 3, p = c(0.6, 0.7, 0.6), ssn = 400, Y0 = NULL, nsim = 200, alpha = 0.05)

## view the output
Polya.res

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

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

``````

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