SAS Macro for Constrained Randomization: Balancing covariates in Group Randomized Trials Ashraf Chaudhary, Ph.D. & Larry Moulton, Ph.D. Department of International Health Division of Disease Control and Prevention Johns Hopkins University Bloomberg School of Public Health

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London2 Why Constrained Randomization? In individually randomized designs, larger sample sizes ensure balance on key variables between the trial arms. Group randomized trials are typically small with perhaps only 4-20 groups to be randomized. The groups are usually contiguous and more homogenous relevant to the groups farther apart. Spatial correlation patterns are more difficult to detect in human communities.

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London3 Why Constrained Randomization? Group level randomization may lead to substantial imbalance across the trial arms. Group randomized trials are therefore susceptible to the ill effects of an ‘unlucky’ or ‘bad’ randomization. But the question here is how to randomize a small number of groups so as to avoid an ‘unlucky’ or ‘bad’ randomization.

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London4 Covariate-Based Constrained Randomization Randomizing the groups to, say, ‘intervention’ and ‘control’ study arms so as to achieve a balance on some baseline covariates between the trial arms.

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London5 SAS Macro - Steps Generates all possible randomizations by forming combinations of groups in each stratum. Computes means of covariates for each randomization in each arm and combine the data for the two arms. Shortlists the randomizations that satisfy balancing criteria. Generates a large number of samples, say, 100, by picking one randomization ‘randomly’ from each stratum. Retains only those samples that meet the sample level balancing criteria. As a check, counts the number of times a group appears with another group in the same study arm. Selects one randomization at random from all the short listed samples.

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London6 SAS Macro - Inputs SAS dataset with the following variables s: Stratum ID group: Group ID x1, x2, x3, …: Covariates r: Number to be randomized to, say, study arm 1 SAS Macro parameters Number of covariates Names of covariates Randomization level minimum acceptable differences between treatment arms for each covariate Overall sample level minimum acceptable differences between treatment arms for each covariate Seed for random selection.

July 7-8, 2004 Biostatistics Core Meeting: LSHTM London7