PolyaUrn {grouprar}

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