GDLRule {grouprar}

Generalized drop-the-loser rule

Description

Simulating generalized drop-the-loser rule procedure (number of arms > 2) with two-sided hypothesis testing in a clinical trial context.

Usage

GDLRule(k, p, ssn, aK, 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.

aK

a positive vector of length equals to k. The values specifies when the immigration ball is drawn, the number of each treatment ball added to the urn.

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

Consider an urn containing balls of K+1 types. Balls of types $1, ..., K$ represent treatments, balls of type 0 will be called immigration balls. When the subject arrived for randomizition, a ball is drawn at random. If the ball is of type 0 (i.e, an immigration ball), no subject is treated, and the ball is returned to the urn together with A=a_1+\cdots+a_K additional balls, a_k of treatment type k, k=1, \ldots, K. If a treatment ball is drawn (say, of type k, for some k=1, \ldots, K) the next subject is given treatment k and the ball is not replaced. If the observed response of this subject is a success, then the ball is replaced, otherwise not replaced.

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

Zhang, L. X., Chan, W. S., Cheung, S. H., & Hu, F. (2007). A generalized drop-the-loser urn for clinical trials with delayed responses. Statistica Sinica, 17(1), 387-409.

Examples

## a simple use
gdl.res = GDLRule(k = 3, p = c(0.6, 0.7, 0.6),
                  ssn = 400, aK = c(1, 1, 1), Y0 = NULL, nsim = 200, alpha = 0.05)

## view the output
gdl.res


  ## view all simulation settings
  gdl.res$name
  gdl.res$parameter
  gdl.res$k

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