Improving efficiency in the stepped-wedge trial design via Bayesian modeling with an informative prior for the time...

In a cross-sectional stepped-wedge cluster randomized trial comparing usual care to a new intervention, treatment allocation and time are correlated by design because participants enrolled early in the trial predominantly receive usual care while those enrolled late in the trial predominantly receive the new intervention. Current guidelines recommend adjustment for time effects when analyzing stepped-wedge cluster randomized trials to remove the confounding bias induced by this correlation. However, adjustment for time effects impacts study power. Within the Frequentist framework, adopting a sample size calculation that includes time effects would ensure the trial having adequate power regardless of the magnitude of the effect of time on the outcome. But if in fact time effects were negligible, this would overestimate the required sample size and could lead to the trial being deemed infeasible due to cost or unavailability of the required numbers of clusters or participants. In this study, we explore the use of prior information on time effects to potentially reduce the required sample size of the trial.

We applied a Bayesian approach to incorporate the prior information on the time effects into cluster-level statistical models (for continuous, binary, or count outcomes) for the stepped-wedge cluster randomized trial. We conducted simulations to illustrate how the bias in the intervention effect estimate and the trial power vary as a function of the prior precision and the mis-specification of the prior means of the time effects in an example scenario.

When a nearly flat prior for the time effects was used, the power or sample size calculated using the Bayesian approach matched the result obtained using the Frequentist approach with time effects included. When a highly precise prior for the time effects (with accurately specified prior means) was used, the Bayesian result matched the Frequentist result obtained with time effects excluded. When the prior means of the time effects were nearly correctly specified, including this information improved the efficiency of the trial with little bias introduced into the intervention effect estimate. When the prior means of the time effects were greatly mis-specified and a precise prior was used, this bias was substantial.

Including prior information on time effects using a Bayesian approach may substantially reduce the required sample size. When the prior can be justified, results from applying this approach could support the conduct of a trial, which would be deemed infeasible if based on the larger sample size obtained using a Frequentist calculation. Caution is warranted as biased intervention effect estimates may arise when the prior distribution for the time effects is concentrated far from their true values.