A simulation study of odds ratio estimation for binary outcomes from cluster randomized trials.

We used simulation to compare accuracy of estimation and confidence interval coverage of several methods for analysing binary outcomes from cluster randomized trials. The following methods were used to estimate the population-averaged intervention effect on the log-odds scale: marginal logistic regression models using generalized estimating equations with information sandwich estimates of standard error (GEE); unweighted cluster-level mean difference (CL/U); weighted cluster-level mean difference (CL/W) and cluster-level random effects linear regression (CL/RE). Methods were compared across trials simulated with different numbers of clusters per trial arm, numbers of subjects per cluster, intraclass correlation coefficients (rho), and intervention versus control arm proportions. Two thousand data sets were generated for each combination of design parameter values. The results showed that the GEE method has generally acceptable properties, including close to nominal levels of confidence interval coverage, when a simple adjustment is made for data with relatively few clusters. CL/U and CL/W have good properties for trials where the number of subjects per cluster is sufficiently large and rho is sufficiently small. CL/RE also has good properties in this situation provided a t-distribution multiplier is used for confidence interval calculation in studies with small numbers of clusters. For studies where the number of subjects per cluster is small and rho is large all cluster-level methods may perform poorly for studies with between 10 and 50 clusters per trial arm.