Inclusion of unexposed clusters improves the precision of fixed effects analysis of stepped-wedge cluster randomized trials

Abstract

Stepped-wedge cluster randomized trials (SW-CRTs) are typically analyzed using mixed effects models. The fixed effects model is a useful alternative that controls for all time-invariant cluster-level confounders and has proper control of type I error when the number of clusters is small. In principle, all clusters in SW-CRTs are designed to eventually receive the intervention, but in real-world research, some trials can end with unexposed clusters (clusters that never received the intervention), such as when a trial is terminated early based on interim analysis results. Typically, unexposed clusters are expected to contribute no information to the fixed effects intervention effect estimator and are excluded from fixed effects analyses. In this article we mathematically prove that inclusion of unexposed clusters improves the precision of the fixed effects least squares dummy variable (LSDV) intervention effect estimator, re-analyze data from a recent SW-CRT of a novel palliative care intervention containing an unexposed cluster, and evaluate the methods by simulation. We found that including unexposed clusters improves the precision of the fixed effects LSDV intervention effect estimator in both real and simulated datasets. Our simulations also reveal an increase in power and decrease in root mean square error. These improvements are present even if the assumptions of constant residual variance and period effects are violated. In the case that a SW-CRT concludes with unexposed clusters, these unexposed clusters can be included in the fixed effects LSDV analysis to improve precision, power, and root mean square error.