The need for analysis of multiple responses arises from many applications. In behavioral science, for example, comorbidity is a common phenomenon where multiple disorders occur in the same person. The advantage of jointly analyzing multiple correlated responses has been examined and documented. Due to the difficulties of modeling multiple responses, nonparametric tests such as generalized Kendall's Tau have been developed to assess the association between multiple responses and risk factors. These procedures have been applied to genomewide association studies of multiple complex traits. Unfortunately, those nonparametric tests only provide the significance of the association but not the magnitude. We propose a Gaussian copula model with discrete margins for modeling multivariate binary responses. This model separates marginal effects from between-trait correlations. We use a bootstrapping margins approach to constructing Wald's statistic for the association test. Although our derivation is based on the fully parametric Gaussian copula framework for simplicity, the underlying assumptions to apply our method can be weakened. The bootstrapping margins approach only requires the correct specification of the model margins. Our simulation and real data analysis demonstrate that our proposed method not only increases power over some existing association tests, but also provides further insight into genetic association studies of multivariate traits.

中文翻译：

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通过引导边际对多重反应进行建模并应用于遗传关联测试

许多应用都需要分析多个响应。例如，在行为科学中，合并症是一种常见现象，即同一个人同时出现多种疾病。联合分析多个相关响应的优点已经得到检验和记录。由于对多重响应进行建模的困难，人们开发了非参数检验（例如广义 Kendall's Tau）来评估多重响应与风险因素之间的关联。这些程序已应用于多个复杂性状的全基因组关联研究。不幸的是，这些非参数检验仅提供关联的显着性，而不提供关联的大小。我们提出了一种具有离散边际的高斯关联模型，用于建模多元二元响应。该模型将边际效应与特征间相关性分开。我们使用自举边际方法来构建关联测试的 Wald 统计量。尽管为了简单起见，我们的推导基于全参数高斯关联框架，但应用我们的方法的基本假设可能会被削弱。自举边距方法只需要正确指定模型边距。我们的模拟和真实数据分析表明，我们提出的方法不仅提高了一些现有关联测试的功效，而且还为多变量性状的遗传关联研究提供了进一步的见解。