Estimating Marginal Odds Ratios for Cluster Randomized Trials: The Cluster-Level GLM

Methods for estimating marginal effects in cluster randomized trials are limited. We describe and evaluate a cluster-level generalized linear model (CL-GLM) that applies a GLM to cluster-level summaries (means, proportions, or rates) and can estimate differences, ratios, or odds ratios. We focus on odds ratios.

We conducted a simulation study with 10-50 clusters, intracluster correlation coefficients of 0.05 or 0.15, and a mean cluster size of 120, either fixed or variable. Informative cluster size, where the intervention effect varies with cluster size, was also considered. Control arm prevalence was set to 50%. We compared cluster-level GLMs with normal and gamma distributions and logit link to generalized estimating equations (GEE) and independence estimating equations (IEEs). Weighted and unweighted analyses were examined to target cluster-average and individual-average estimands.

CL-GLM with a normal distribution produced unbiased marginal cluster-average odds ratios with appropriate confidence interval coverage. CL-GLM with a gamma distribution resulted in over-coverage. Unweighted IEE produced unbiased marginal individual-average odds ratios with correct coverage. GEE was unbiased when cluster size was uninformative but biased under informative cluster size. Weighted CL-GLM led to under-coverage, whereas weighted IEE resulted in over-coverage. The CL-GLM had similar power to GEE and unweighted IEE.

The cluster-level GLM with a normal distribution provides a robust alternative to estimating equation approaches for marginal odds ratios in cluster randomized trials, with good performance under both informative and uninformative cluster size and no loss of power. We recommend the cluster-level GLM with a normal distribution when the marginal cluster-average estimand is of interest, and unweighted IEEs when the marginal individual-average estimand is of interest.