A Bayesian approach to the survivor average causal effect in cluster-randomized crossover trials

In cluster-randomized crossover (CRXO) trials, groups of individuals are randomly assigned to two or more sequences of alternating treatments. Since clusters serve as their own control, the CRXO design is typically more statistically efficient than the usual parallel-arm design. CRXO trials are increasingly popular in many areas of health research where the number of available clusters is limited. Further, in trials among severely ill patients, researchers often want to assess the effect of treatments on secondary non-terminal outcomes, but frequently in these studies, there are patients who do not survive to have these measurements fully recorded. In this paper, we provide a causal inference framework and treatment effect estimation methods for addressing truncation by death in the setting of CRXO trials. We target the survivor average causal effect (SACE) estimand, a well-defined subgroup treatment effect obtained via principal stratification. We propose novel structural and standard modeling assumptions that enable estimating the SACE within a Bayesian paradigm. We evaluate the small-sample performance of our proposed Bayesian approach for estimation of the SACE in CRXO trial settings via simulation studies. We apply our methods to a previously conducted two-period cross-sectional CRXO study examining the impact of proton pump inhibitors compared to histamine-2 receptor blockers on length of hospitalization among adults requiring invasive mechanical ventilation.

💡 Research Summary

This paper addresses the problem of “truncation by death” in cluster‑randomized crossover (CRXO) trials, where non‑terminal outcomes (e.g., length of stay) are missing for patients who die before the outcome can be measured. The authors adopt the principal‑stratification framework and target the Survivor Average Causal Effect (SACE), which is the causal contrast of interest among the sub‑population that would survive under either treatment (the “always‑survivors”).

The methodological development proceeds in several steps. First, notation is introduced for the three hierarchical levels of CRXO designs: clusters, cluster‑periods, and individuals. Potential survival status Sᵢⱼₖ(a) and potential non‑terminal outcome Yᵢⱼₖ(a) are defined for each treatment a∈{0,1}. By pairing the two potential survival indicators, four principal strata are formed: always‑survivors (1,1), protected patients (1,0), harmed patients (0,1), and never‑survivors (0,0). The SACE is defined as a function h of the two conditional means E