Restricted randomization of ZAMSTAR: a 2 x 2 factorial cluster randomized trial

Abstract

Background: A small number of clusters and substantial variation between clusters increase the chance of unbalanced randomization in cluster randomized trials. Baseline imbalances between groups may distort intervention effects. When adjusting for imbalances in the cluster-level analysis, this results in loss of degrees of freedom. Variance reduction that can be achieved through stratification and blocking is limited. Restricted randomization is an alternative approach that ensures balanced allocation.

Purpose: We present the randomization scheme used in the ZAMSTAR trial of tuberculosis control interventions in Southern Africa.

Methods: We used stratification and restriction to randomize 24 clusters (16 Zambian, 8 South African) into four intervention groups in a 2 x 2 factorial design. Stratification was by country and tuberculous infection prevalence and restriction by tuberculous infection prevalence, HIV prevalence, urban/rural, social context, and geographical location. Balance was defined in terms of covariate-specific tolerance thresholds for the measure of imbalance. For binary (0/1) covariates we defined imbalance = max(S(i)) - min(S(i)), where, S(i) was the number of 1s in group i = 1,2,3,4. For continuous covariates we defined imbalance = (max(M(i)) - min(M(i)))/ min(M(i) ), where, M( i) was the average in group i = 1,2,3,4.We used simulation to estimate the restriction factor (proportion of unacceptable allocations) both for individual covariates and overall. Simulation was also used to investigate the validity of the restricted randomization design, with the use of the validity matrix, by monitoring the probability that any given pair of clusters is allocated to the same intervention group.

Results: There were 3 657 930 400 possible ways of allocating the 24 clusters to the four groups after stratification. With a combined restriction factor of 0.998 this still left 7 million acceptable allocations. The final allocation was selected at a public ceremony from a randomly-generated list of acceptable allocations. The design of the allocation process was observed to be valid.

Limitations: The restricted randomization scheme significantly decreased the total number of available allocations of clusters into intervention groups.

Conclusion: Our restricted randomization was successful in that it achieved good balance while preserving the impartiality and validity of the trial.