# compRand: Compare Different Randomization Procedures via Tables and... In carat: Covariate-Adaptive Randomization for Clinical Trials

## Description

Compares randomization procedures based on several different quantities of imbalances. Among all included randomization procedures of class "careval", two or more procedures can be compared in this function.

## Usage

 1 compRand(...)

## Arguments

 ... objects of class "careval".

## Details

The primary goal of using covariate-adaptive randomization in practice is to achieve balance with respect to the key covariates. We choose four rules to measure the absolute imbalances at overall, within-covariate-margin, and within-stratum levels, which are maximal, 95%quantile, median and mean of the absolute imbalances at different aspects. The Monte Carlo method is used to calculate the four types of imbalances. Let D_{n,i}(\cdot) be the final difference at the corresponding level for ith iteration, i=1,…, N, and N is the number of iterations.

(1) Maximal

\max_{i = 1, …, N}|D_{n,i}(\cdot)|.

(2) 95% quantile

|D_{n,\lceil0.95N\rceil}(\cdot)|.

(3) Median

|D_{n,(N+1)/2}(\cdot)|

for N is odd, and

\frac{1}{2}(|D_{(N/2)}(\cdot)|+|D_{(N/2+1)}(\cdot)|)

for N is even.

(4) Mean

\frac{1}{N}∑_{i = 1}^{N}|D_{n, i}(\cdot)|.

## Value

It returns an object of class "carcomp".

An object of class "carcomp" is a list containing the following components:

 Overall Imbalances a matrix containing the maximum, 95%-quantile, median, and mean of the absolute overall imbalances for the randomization method(s) to be evaluated. Within-covariate-margin Imbalances Imbalances a matrix containing the maximum, 95%-quantile, median, and mean of the absolute within-covariate-margin imbalances for the randomization method(s) to be evaluated. Within-stratum Imbalances a matrix containing the maximum, 95%-quantile, median, and mean of the absolute within-stratum imbalances for the randomization method(s) to be evaluated. dfmm a data frame containing the mean absolute imbalances at the overall, within-stratum, and within-covariate-margin levels for the randomization method(s) to be evaluated. df_abm a data frame containing the absolute imbalances at the overall, within-stratum, and within-covariate-margin levels. mechanism a character string giving the randomization method(s) to be evaluated. n the number of patients. iteration the number of iterations. cov_num the number of covariates. level_num a vector of level numbers for each covariate. Data Type a character string giving the data type, Real or Simulated. DataGeneration a bool vector indicating whether the data used for all the iterations is the same for the randomization method(s) to be evaluated.

## References

Atkinson A C. Optimum biased coin designs for sequential clinical trials with prognostic factors[J]. Biometrika, 1982, 69(1): 61-67.

Baldi Antognini A, Zagoraiou M. The covariate-adaptive biased coin design for balancing clinical trials in the presence of prognostic factors[J]. Biometrika, 2011, 98(3): 519-535.

Hu Y, Hu F. Asymptotic properties of covariate-adaptive randomization[J]. The Annals of Statistics, 2012, 40(3): 1794-1815.

Pocock S J, Simon R. Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial[J]. Biometrics, 1975: 103-115.

Shao J, Yu X, Zhong B. A theory for testing hypotheses under covariate-adaptive randomization[J]. Biometrika, 2010, 97(2): 347-360.

Zelen M. The randomization and stratification of patients to clinical trials[J]. Journal of chronic diseases, 1974, 27(7): 365-375.