Confidence interval estimation for treatment effects in cluster randomization trials based on ranks

A cluster randomization trial is one in which clusters of individuals are randomly allocated to different intervention arms. This design has become the standard for the evaluation of health care and educational strategies. To assess treatment effect, many cluster randomization trials involve outcomes that are lack meaningful units, making interpretation difficult. This difficulty may be dealt with by estimating the Mann-Whitney probability, which quantifies the probability that a typical response from one treatment arm is larger (or smaller) than a typical response from the other arm. In this work, we propose procedures for estimating this probability in cluster randomization trials. Primary emphasis is given to confidence interval estimation in trials with a small number of large clusters. The essence of the procedures is to obtain placement values based on overall ranks and arm-specific ranks prior to application of the ratio estimator, cluster-size-weighted means and mixed models for adjusting clustering effects. Nine confidence intervals were developed by applying three interval methods each based on the three variance estimators. The proposed methods can be applied to studies with binary, ordinal or continuous outcomes without making parametric assumptions. Simulation results demonstrated that the three variance estimators performed equally well, with the confidence interval procedures based on logit and inverse hyperbolic sine transformations performing better in terms of coverage and average interval width, even when the numbers of clusters are as small as 3 to 5 clusters per arm. The methods are illustrated using data from three published cluster randomization trials with SAS code provided.