How Should Parallel Cluster Randomized Trials With a Baseline Period be Analyzed?-A Survey of Estimands and Common Estimators.

The parallel cluster randomized trial with baseline (PB-CRT) is a common variant of the standard parallel cluster randomized trial (P-CRT). We define two natural estimands in the context of PB-CRTs with informative cluster sizes, the individual-average treatment effect (iATE) and cluster-average treatment effect (cATE), to address individual and cluster-level hypotheses. In this work, we theoretically derive the convergence of the unweighted and inverse cluster-period size weighted (i) independence estimating equation (IEE), (ii) fixed-effects (FE) model, (iii) exchangeable mixed-effects (EME) model, and (iv) nested-exchangeable mixed-effects (NEME) model treatment effect estimators in a PB-CRT with informative cluster sizes and continuous outcomes. Overall, we theoretically show that the unweighted and weighted IEE and FE models yield consistent estimators for the iATE and cATE estimands. Although mixed-effects models yield inconsistent estimators to these two natural estimands under informative cluster sizes, we empirically demonstrate that the EME model is surprisingly robust to bias. This is in sharp contrast to the corresponding analyses in P-CRTs and the NEME model in PB-CRTs when informative cluster sizes are present, carrying implications for practice. We report a simulation study and conclude with a re-analysis of a PB-CRT examining the effects of community youth teams on improving mental health among adolescent girls in rural eastern India.