grouprar (version 0.1.0)

WeiUrn: 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)

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.

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.

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
# \donttest{

  ## 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
  # }