Cluster‐Level Analyses to Estimate a Risk Difference in a Cluster Randomized Trial With Confounding Individual‐Level Covariates: A Simulation Study

Cluster randomized trials (CRTs) may be analyzed using cluster-level analyses. For binary outcomes, proportions are estimated for each cluster, and a risk difference can be estimated. The confidence interval is estimated using a Student distribution. However, in doing so, individual-level characteristics are not adjusted for even though CRTs are known to be prone to recruitment/identification bias, possibly implying individual-level confounders. With a simulation study, we compared cluster-level analyses to estimate a risk difference for a two-arm parallel CRT with individual-level confounders and cluster-level covariates. We considered the unadjusted (UN) method, two two-stage procedure (TSP) methods considering a binomial or a Gaussian distribution, G-computation (GC), and targeted maximum likelihood estimation (TMLE) methods. As expected, the UN method was biased. TSP methods were also biased for scenarios with a treatment effect when the number of clusters per arm was small. GC and TMLE methods were unbiased. For these latter methods, adjustment on only individual-level covariates led to better performance measures (type I error rate, coverage rate and relative error of the standard error) than adjustment on both individual- and cluster-level covariates. TSP, GC and TMLE had very similar results except in scenarios with a small number of clusters: Biased results for TSP methods and convergence problems for GC methods. In this case, TMLE should be preferred.