GDLRule: Generalized drop-the-loser rule

In grouprar: Group Response Adaptive Randomization for Clinical Trials

Generalized drop-the-loser rule

Description

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

Usage

GDLRule(k, p, ssn, aK, Y0 = NULL, nsim = 2000, alpha = 0.05, test.fun = NULL,
        typeI = FALSE, seed = NULL)

Arguments

k	A positive integer. The number of treatment groups in the trial (k \ge 2).
p	A vector of length k with values between 0 and 1. The true success rates of the treatments, used to generate data for the simulations.
ssn	A positive integer. The total number of participants in each simulated trial.
aK	A positive vector of length k. The number of balls of each treatment type added to the urn when the immigration ball is drawn.
Y0	A vector of length k giving the initial number of treatment balls of each type in the urn. One immigration ball is added automatically. For instance, if Y0 = c(1, 1, 1), the urn starts with one ball of each treatment and one immigration ball. If Y0 is NULL (default), it is set to a vector of k ones.
nsim	A positive integer. The number of simulated trials, with a default value of 2000.
alpha	A number between 0 and 1. The significance level of the two-sided test, with a default value of 0.05.
test.fun	An optional function function(outcome, assignment) that returns the p-value of a test for one simulated trial, where outcome holds the observed responses and assignment the treatment labels (integers 1 to k); missing responses are removed first. The null hypothesis is rejected when the p-value is at most alpha. The default NULL uses the built-in two-sided tests: the t-test for two arms and the Wald chi-squared test of equal means for more than two arms (for binary responses, if some arms have no variability, the variances are computed from (S_k + 1)/(n_k + 2) as in Agresti and Caffo, 2000).
typeI	Logical. If TRUE, the simulation is repeated under the null hypothesis, with every arm's success rate set to the average of p, and the rejection rate is reported as type I error. The default is FALSE.
seed	An optional integer passed to set.seed before simulating, so that the results can be reproduced. The default NULL leaves the random number generator unchanged.

Details

Consider an urn containing balls of K+1 types. Balls of types 1, \ldots, K represent treatments, and balls of type 0 are called immigration balls. When a subject arrives for randomization, a ball is drawn at random. If the ball is of type 0 (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 subject is given treatment k. If the observed response of this subject is a success, the ball is replaced, otherwise it is not replaced.

Value

An object of class "grouprar", a list that is printed as a short summary (see print.grouprar), with the following elements.

method	The name of the procedure.
sample size	The total sample size.
parameter	The true success rates used in the simulations, named pA, pB, ...
propotion	The mean allocation proportion of each arm over the simulations, named treatment A, treatment B, ...
sd of propotion	The standard deviation of the allocation proportion of each arm over the simulations.
failure rate	The mean failure rate over the simulations.
sd of failure rate	The standard deviation of the failure rate (or mean response) over the simulations.
power	The proportion of simulated trials that reject the null hypothesis of equal success rates. Simulations in which the test cannot be computed are dropped.
data: failureRate	The failure rate (or mean response) of each simulated trial.
data: test	The test decision of each simulated trial (1 = reject).
data: assignment	The treatment assignments of the last simulated trial.
data: propotion	A data frame with the allocation proportions of each simulated trial.
data: allocation	An nsim by ssn matrix with the treatment assignments of every simulated trial.
type I error	Only if typeI = TRUE. The rejection rate under the null hypothesis.

References

Zhang, L. X., Chan, W. S., Cheung, S. H. and 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 = 200, aK = c(1, 1, 1), Y0 = NULL, nsim = 100, alpha = 0.05)

## view the output
gdl.res


  ## view all simulation settings
  gdl.res[["method"]]
  gdl.res[["parameter"]]

  ## view the simulation results
  gdl.res[["propotion"]]
  gdl.res[["failure rate"]]
  gdl.res[["power"]]
  gdl.res[["data: assignment"]]
  

grouprar documentation built on Oct. 9, 2026, 9:07 a.m.