Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
Stat Med. 2023 May 20;42(11):1722-1740. doi: 10.1002/sim.9696. Epub 2023 Mar 17.
There has been increased interest in the design and analysis of studies consisting of multiple response variables of mixed types. For example, in clinical trials, it is desirable to establish efficacy for a treatment effect in primary and secondary outcomes. In this article, we develop Bayesian approaches for hypothesis testing and study planning for data consisting of multiple response variables of mixed types with covariates. We assume that the responses are correlated via a Gaussian copula, and that the model for each response is, marginally, a generalized linear model (GLM). Taking a fully Bayesian approach, the proposed method enables inference based on the joint posterior distribution of the parameters. Under some mild conditions, we show that the joint distribution of the posterior probabilities under any Bayesian analysis converges to a Gaussian copula distribution as the sample size tends to infinity. Using this result, we develop an approach to control the type I error rate under multiple testing. Simulation results indicate that the method is more powerful than conducting marginal regression models and correcting for multiplicity using the Bonferroni-Holm Method. We also develop a Bayesian approach to sample size determination in the presence of response variables of mixed types, extending the concept of probability of success (POS) to multiple response variables of mixed types.
人们对由混合类型的多个响应变量组成的研究的设计和分析越来越感兴趣。例如，在临床试验中，人们希望在主要和次要结果中确定治疗效果的疗效。在本文中，我们针对包含协变量的混合类型的多个响应变量的数据，开发了用于假设检验和研究计划的贝叶斯方法。我们假设响应通过高斯 Copula 相关联，并且每个响应的模型在边缘上是广义线性模型（GLM）。采用完全贝叶斯方法，所提出的方法可以根据参数的联合后验分布进行推断。在一些温和的条件下，我们证明了任何贝叶斯分析下的后验概率的联合分布在样本量趋于无穷大时收敛于高斯 Copula 分布。利用这一结果，我们开发了一种在多重检验下控制误报率的方法。模拟结果表明，该方法比进行边际回归模型更有效，并使用 Bonferroni-Holm 方法纠正多重性。我们还针对混合类型的响应变量的存在开发了一种贝叶斯样本量确定方法，将成功概率（POS）的概念扩展到了混合类型的多个响应变量。
