Causal mediation analysis, pleiotropy analysis, and replication analysis are three highly popular genetic study designs. Although these analyses address different scientific questions, the underlying inference problems all involve large-scale testing of composite null hypotheses. The goal is to determine whether all null hypotheses - as opposed to at least one - in a set of individual tests should simultaneously be rejected. Various recent methodology has been proposed for the aforementioned situations, and an appealing empirical Bayes strategy is to apply the popular two-group model, calculating local false discovery rates (lfdr) for each set of hypotheses. However, such a strategy is difficult due to the need for multivariate density estimation. Furthermore, the multiple testing rules for the empirical Bayes lfdr approach and conventional frequentist z-statistics can disagree, which is troubling for a field that ubiquitously utilizes summary statistics. This work proposes a framework to unify two-group testing in genetic association composite null settings, the conditionally symmetric multidimensional Gaussian mixture model (csmGmm). The csmGmm is shown to demonstrate more robust operating characteristics than recently-proposed alternatives. Crucially, the csmGmm also offers strong interpretability guarantees by harmonizing lfdr and z-statistic testing rules. We extend the base csmGmm to cover each of the mediation, pleiotropy, and replication settings, and we prove that the lfdr z-statistic agreement holds in each situation. We apply the model to a collection of translational lung cancer genetic association studies that motivated this work.

翻译：因果中介分析、多效性分析和复制分析是三种广受欢迎的遗传学研究设计。尽管这些研究针对不同的科学问题，其背后的推断问题均涉及对复合零假设的大规模检验。其目标是判断一组独立检验中的所有零假设（而非至少一个）是否应被同时拒绝。近年来，针对上述场景已提出多种方法论，其中一种有吸引力的经验贝叶斯策略是应用经典的两组模型，计算每组假设的局部错误发现率（lfdr）。然而，该策略因需要多元密度估计而难以实现。此外，经验贝叶斯lfdr方法与常规频率学派z统计量的多重检验规则可能不一致，这对于普遍使用汇总统计的领域而言是一个问题。为此，本研究提出一个框架，以统一遗传关联复合零假设场景中的两组检验，即条件对称多维高斯混合模型（csmGmm）。结果表明，csmGmm相比近期提出的替代方法具有更稳健的运行特性。关键在于，csmGmm通过协调lfdr与z统计量检验规则，提供了强的可解释性保证。我们将基础csmGmm扩展至涵盖中介分析、多效性分析和复制分析场景，并证明每种情况下lfdr与z统计量的一致性均成立。我们将该模型应用于一组推动本研究的转化肺癌遗传关联研究。