In multisite trials, statistical goals often include obtaining individual site-specific treatment effects, determining their rankings, and examining their distribution across multiple sites. This paper explores two strategies for improving inferences related to site-specific effects: (a) semiparametric modeling of the prior distribution using Dirichlet process mixture (DPM) models to relax the normality assumption, and (b) using estimators other than the posterior mean, such as the constrained Bayes or triple-goal estimators, to summarize the posterior. We conduct a large-scale simulation study, calibrated to multisite trials common in education research. We then explore the conditions and degrees to which these strategies and their combinations succeed or falter in the limited data environments. We found that the average reliability of within-site effect estimates is crucial for determining effective estimation strategies. In settings with low-to-moderate data informativeness, flexible DPM models perform no better than the simple parametric Gaussian model coupled with a posterior summary method tailored to a specific inferential goal. DPM models outperform Gaussian models only in select high-information settings, indicating considerable sensitivity to the level of cross-site information available in the data. We discuss the implications of our findings for balancing trade-offs associated with shrinkage for the design and analysis of future multisite randomized experiments.

翻译：在多中心试验中，统计目标常包括获取每个场所的特定处理效应、确定其排序，以及考察其在多个场所间的分布。本文探讨了两种改进场所特定效应推断的策略：(a) 使用狄利克雷过程混合（DPM）模型对先验分布进行半参数建模，以放宽正态性假设；(b) 使用后验均值以外的估计量（如约束贝叶斯或三重目标估计量）来汇总后验分布。我们开展了一项大规模模拟研究，并针对教育研究中常见的多中心试验进行了校准。进而，我们探讨了在有限数据环境下，这些策略及其组合成功或失败的条件与程度。研究发现，场所内效应估计的平均可靠性是决定有效估计策略的关键。在数据信息量较低至中等的情况下，灵活的DPM模型并不优于简单的参数高斯模型与针对特定推断目标定制的后验汇总方法的结合。仅在高信息量的特定环境下，DPM模型才优于高斯模型，这表明其对数据中可用跨场所信息水平高度敏感。我们讨论了这些发现对未来多中心随机试验设计中平衡收缩相关权衡的启示。