# Compare Different Randomization Procedures via Tables and Plots 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. ```r 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 $i$th iteration, $i=1,\ldots$, `N`, and `N` is the number of iterations. (1) Maximal $$ \max_{i = 1, \dots, N}|D_{n,i}(\cdot)|. $$ (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 $$ \frac{1}{N}\sum_{i = 1}^{N}|D_{n, i}(\cdot)|. $$ ## Returns 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. ## See Also See `evalRand` or `evalRand.sim` to evaluate a specific randomization procedure. ## 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. Ma W, Ye X, Tu F, Hu F. **carat: Covariate-Adaptive Randomization for Clinical Trials**[J]. Journal of Statistical Software, 2023, 107(2): 1-47. 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. ## Examples ```r ## Compare stratified permuted block randomization and Hu and Hu's general CAR cov_num <- 2 level_num <- c(2, 2) pr <- rep(0.5, 4) n <- 500 N <- 20 # <

compRand function