# GDLRule: Generalized drop-the-loser rule In grouprar: Group Response Adaptive Randomization for Clinical Trials

 GDLRule R Documentation

## 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

``````

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