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 participant-average treatment effect (pATE) and cluster-average treatment effect (cATE), to address participant 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, (ii.) fixed-effects model, (iii.) exchangeable mixed-effects model, and (iv.) nested-exchangeable mixed-effects model treatment effect estimators in a PB-CRT with continuous outcomes. Overall, we theoretically show that the unweighted and weighted independence estimating equation and fixed-effects model yield consistent estimators for the pATE and cATE estimands. Although mixed-effects models yield inconsistent estimators to these two natural estimands under informative cluster sizes, we empirically demonstrate that the exchangeable mixed-effects model is surprisingly robust to bias. This is in sharp contrast to the corresponding analyses in P-CRTs and the nested-exchangeable mixed-effects model in PB-CRTs, and may carry 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.