Time-varying treatment effect models in stepped-wedge cluster-randomized trials with multiple interventions

The traditional model specification of stepped-wedge cluster-randomized trials assumes a homogeneous treatment effect across time while adjusting for fixed-time effects. However, when treatment effects vary over time, the constant effect estimator may be biased. In the general setting of stepped-wedge cluster-randomized trials with multiple interventions, we derive the expected value of the constant effect estimator when the true treatment effects depend on exposure time periods. Applying this result to concurrent and factorial stepped wedge designs, we show that the estimator represents a weighted average of exposure-time-specific treatment effects, with weights that are not necessarily uniform across exposure periods. Extensive simulation studies reveal that ignoring time heterogeneity can result in biased estimates and poor coverage of the average treatment effect. In this study, we examine two models designed to accommodate multiple interventions with time-varying treatment effects: (1) a time-varying fixed treatment effect model, which allows treatment effects to vary by exposure time but remain fixed for each time point, and (2) a random treatment effect model, where the time-varying treatment effects are modeled as random deviations from an overall mean. In the simulations considered in this study, concurrent designs generally achieve higher power than factorial designs under a time-varying fixed treatment effect model, though the differences are modest. Finally, we apply the constant effect model and both time-varying treatment effect models to data from the Prognosticating Outcomes and Nudging Decisions in the Electronic Health Record (PONDER) trial. All three models indicate a lack of treatment effect for either intervention, though they differ in the precision of their estimates, likely due to variations in modeling assumptions.