# Stratified Permuted Block Randomization Allocates patients to one of two treatments using stratified permuted block randomization proposed by Zelen M (1974) . ```r StrPBR(data, bsize = 4) ``` ## Arguments - `data`: a data frame. A row of the dataframe corresponds to the covariate profile of a patient. - `bsize`: the block size for stratified randomization. It is required to be a multiple of 2. The default is `4`. ## Details Different covariate profiles are defined to be strata, and then permuted block randomization is applied to each stratum. It works efficiently when the number of strata is small. However, when the number of strata increases, the stratified permuted block randomization fails to obtain balance between two treatments. Permuted block randomization, or blocking, is used to balance treatments within a block so that there are the same number of subjects in each treatment. A block contains the same number of each treatment and blocks of different sizes are combined to make up the randomization list. Details of the procedure can be found in Zelen M (1974). ## Returns It returns an object of `class` `"carandom"`. An object of class `"carandom"` is a list containing the following components: - **datanumeric**: a bool indicating whether the data is a numeric data frame. - **covariates**: a character string giving the name(s) of the included covariates. - **strt_num**: the number of strata. - **cov_num**: the number of covariates. - **level_num**: a vector of level numbers for each covariate. - **n**: the number of patients. - **Cov_Assig**: a `(cov_num + 1) * n` matrix containing covariate profiles for all patients and the corresponding assignments. The $i$th column represents the $i$th patient. The first `cov_num` rows include patients' covariate profiles, and the last row contains the assignments. - **assignments**: the randomization sequence. - **All strata**: a matrix containing all strata involved. - **Diff**: a matrix with only one column. There are final differences at the overall, within-stratum, and within-covariate-margin levels. - **method**: a character string describing the randomization procedure to be used. - **Data Type**: a character string giving the data type, `Real` or `Simulated`. - **framework**: the framework of the used randomization procedure: stratified randomization, or model-based method. - **data**: the data frame. - **bsize**: the block size. - **numbers of pats for each stratum**: a vector giving the numbers of patients for each stratum. ## See Also See `StrPBR.sim` for allocating patients with covariate data generating mechanism. See `StrPBR.ui` for the command-line user interface. ## References 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. Zelen M. **The randomization and stratification of patients to clinical trials**[J]. Journal of chronic diseases, 1974, 27(7): 365-375. ## Examples ```r # a simple use ## Real Data ## creat a dataframe df <- data.frame("gender" = sample(c("female", "male"), 100, TRUE, c(1 / 3, 2 / 3)), "age" = sample(c("0-30", "30-50", ">50"), 100, TRUE), "jobs" = sample(c("stu.", "teac.", "others"), 100, TRUE), stringsAsFactors = TRUE) Res <- StrPBR(data = df, bsize = 4) ## view the output Res ## view all patients' profile and assignments Res$Cov_Assig ## Simulated data cov_num <- 3 level_num <- c(2, 3, 3) pr <- c(0.4, 0.6, 0.3, 0.4, 0.3, 0.4, 0.3, 0.3) Res.sim <- StrPBR.sim(n = 100, cov_num, level_num, pr) ## view the output Res.sim ## view the detials of difference Res.sim$Diff N <- 5 n <- 1000 cov_num <- 3 level_num <- c(2, 3, 5) # Set pr to follow two tips: #(1) length of pr should be sum(level_num); #(2)sum of probabilities for each margin should be 1. pr <- c(0.4, 0.6, 0.3, 0.4, 0.3, rep(0.2, times = 5)) omega <- c(0.2, 0.2, rep(0.6 / cov_num, times = cov_num)) # Set block size for stratified randomization bsize <- 4 ## generate a container to contain Diff DS <- matrix(NA, ncol = N, nrow = 1 + prod(level_num) + sum(level_num)) for(i in 1 : N){ rtS <- StrPBR.sim(n, cov_num, level_num, pr, bsize) DS[ , i] <- rtS$Diff } ## do some analysis require(dplyr) ## analyze the overall imbalance Ana_O <- matrix(NA, nrow = 1, ncol = 3) rownames(Ana_O) <- c("Str.R") colnames(Ana_O) <- c("mean", "median", "95%quantile") tempS <- DS[1, ] %>% abs Ana_O[1, ] <- c((tempS %>% mean), (tempS %>% median), (tempS %>% quantile(0.95))) ## analyze the within-stratum imbalances tempWS <- DS[2 : 1 + prod(level_num), ] %>% abs Ana_W <- matrix(NA, nrow = 1, ncol = 3) rownames(Ana_W) <- c("Str.R") colnames(Ana_W) <- c("mean", "median", "95%quantile") Ana_W[1, ] = c((tempWS %>% apply(1, mean) %>% mean), (tempWS %>% apply(1, median) %>% mean), (tempWS %>% apply(1, mean) %>% quantile(0.95))) ## analyze the marginal imbalance tempMS <- DS[(1 + prod(level_num) + 1) : (1 + prod(level_num) + sum(level_num)), ] %>% abs Ana_M <- matrix(NA, nrow = 1, ncol = 3) rownames(Ana_M) <- c("Str.R"); colnames(Ana_M) <- c("mean", "median", "95%quantile") Ana_M[1, ] = c((tempMS %>% apply(1, mean) %>% mean), (tempMS %>% apply(1, median) %>% mean), (tempMS %>% apply(1, mean) %>% quantile(0.95))) AnaHP <- list(Ana_O, Ana_M, Ana_W) names(AnaHP) <- c("Overall", "Marginal", "Within-stratum") AnaHP ```

StrPBR function