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

TL;DR

This paper tackles truncation by death in cluster-randomized crossover trials by defining and estimating the survivor average causal effect (SACE) within a principal-stratification framework. It develops a Bayesian model that jointly handles non-mortal outcomes and principal-stratum membership, using data augmentation and Polya-Gamma methods to obtain a tractable Gibbs sampler. Simulation study shows the proposed full model provides low bias and near-nominal coverage across realistic CRXO settings, while analyses reveal the importance of including cluster and cluster-period random effects in the correct parts of the model. The PEPTIC trial application demonstrates a causal interpretation for differences and ratios of non-mortality outcomes among always-survivors, offering practical guidance for causal inference in critical-care contexts with truncation by death. Overall, the approach enables robust, interpretable SACE assessment in CRXO designs and highlights avenues for sensitivity analyses and methodological extensions.

Abstract

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.

Figures (2)

• Figure 1: Illustration of a two-period cluster-randomized crossover (CRXO) design. Shaded cells indicate treatment condition and unshaded cells indicate the control condition. The first and second clusters have been randomized to the treatment sequence $A_1=(0,1)$ and $A_2=(1,0)$, respectively. The remaining clusters may be randomly assigned to either sequence. For each individual, the observed data shown are treatment, survival status $S_{ijk}$, and non-mortality outcome $Y_{ijk}$. For illustration purposes we include all $Y_{ijk}$, but we note that $Y_{ijk}$ is only fully observed when $S_{ijk}=1$, and $Y_{ijk}$ is truncated in the data when $S_{ijk}=0$.
• Figure 1: Trace plots to assess mixing of key parameters for data application PEPTIC, a two-period cross-sectional CRXO trial. 4 chains with 10,000 iterations with 2,500 burn-ins with random initials are plotted. Run time was about 2.7 hours, parallelized over 4 chains.