Baseline adjustments for binary data in repeated cross-sectional cluster randomized trials

Analysis of covariance models, which adjust for a baseline covariate, are often used to compare treatment groups in a controlled trial in which individuals are randomized. Such analysis adjusts for any baseline imbalance and usually increases the precision of the treatment effect estimate. We assess the value of such adjustments in the context of a cluster randomized trial with repeated cross-sectional design and a binary outcome. In such a design, a new sample of individuals is taken from the clusters at each measurement occasion, so that baseline adjustment has to be at the cluster level. Logistic regression models are used to analyse the data, with cluster level random effects to allow for different outcome probabilities in each cluster. We compare the estimated treatment effect and its precision in models that incorporate a covariate measuring the cluster level probabilities at baseline and those that do not. In two data sets, taken from a cluster randomized trial in the treatment of menorrhagia, the value of baseline adjustment is only evident when the number of subjects per cluster is large. We assess the generalizability of these findings by undertaking a simulation study, and find that increased precision of the treatment effect requires both large cluster sizes and substantial heterogeneity between clusters at baseline, but baseline imbalance arising by chance in a randomized study can always be effectively adjusted for.