Comparison of the risk difference, risk ratio and odds ratio scales for quantifying the unadjusted intervention effect in cluster randomized trials

This paper evaluates methods for unadjusted analyses of binary outcomes in cluster randomized trials (CRTs). Under the generalized estimating equations (GEE) method the identity, log and logit link functions may be specified to make inferences on the risk difference, risk ratio and odds ratio scales, respectively. An alternative, 'cluster-level', method applies the t-test to summary statistics calculated for each cluster, using proportions, log proportions and log odds, to make inferences on the respective scales. Simulation was used to estimate the bias of the unadjusted intervention effect estimates and confidence interval coverage, generating data sets with different combinations of number of clusters, number of participants per cluster, intra-cluster correlation coefficient rho and intervention effect. When the identity link was specified, GEE had little bias and good coverage, performing slightly better than the log and logit link functions. The cluster-level method provided unbiased point estimates when proportions were used to summarize the clusters. When the log proportion and log odds were used, however, the method often had markedly large bias for two reasons: (i) bias in the modified summary statistic used for cluster-level estimation when a cluster has zero cases with the outcome of interest (arising when the number of participants sampled per cluster is small and the outcome prevalence is low) and (ii) asymptotically, the method estimates the ratio of geometric means of the cluster proportions or odds, respectively, between the trial arms rather than the ratio of arithmetic means.