Alternatives to Logistic Regression Models when Analyzing Cluster Randomized Trials with Binary Outcomes

Binary outcomes are often encountered when analyzing cluster randomized trials (CRTs). A common approach to obtaining the average treatment effect of an intervention may involve using a logistic regression model. We outline some interpretive and statistical challenges associated with using logistic regression and discuss two alternative/supplementary approaches for analyzing clustered data with binary outcomes: the linear probability model (LPM) and the modified Poisson regression model. In our simulation and applied example, all models use a standard error adjustment that is effective even if a low number of clusters is present. Simulation results show that both the LPM and modified Poisson regression models can provide unbiased point estimates with acceptable coverage and type I error rates even with as little as 20 clusters.