A Semiparametric Bayesian Approach to Dropout in Longitudinal Studies With Auxiliary Covariates

We develop a semiparametric Bayesian approach to missing outcome data in longitudinal studies in the presence of auxiliary covariates. We consider a joint model for the full data response, missingness, and auxiliary covariates. We include auxiliary covariates to “move” the missingness “closer” to missing at random. In particular, we specify a semiparametric Bayesian model for the observed data via Gaussian process priors and Bayesian additive regression trees. These model specifications allow us to capture nonlinear and nonadditive effects, in contrast to existing parametric methods. We then separately specify the conditional distribution of the missing data response given the observed data response, missingness, and auxiliary covariates (i.e., the extrapolation distribution) using identifying restrictions. We introduce meaningful sensitivity parameters that allow for a simple sensitivity analysis. Informative priors on those sensitivity parameters can be elicited from subject-matter experts. We use Monte Carlo integration to compute the full data estimands. Performance of our approach is assessed using simulated datasets. Our methodology is motivated by, and applied to, data from a clinical trial on treatments for schizophrenia. Supplementary materials for this article are available online.

我们针对存在辅助协变量的纵向研究中的缺失结局数据，提出了一种半参数贝叶斯方法（semiparametric Bayesian approach）。我们针对完整数据的响应、缺失机制与辅助协变量构建了联合模型。引入辅助协变量可使缺失机制更趋近于随机缺失（missing at random）。具体而言，我们通过高斯过程先验（Gaussian process priors）与贝叶斯加法回归树（Bayesian additive regression trees）为观测数据构建半参数贝叶斯模型。与现有参数化方法不同，此类模型设定能够捕捉非线性与非可加效应。随后，我们利用识别约束，分别针对给定观测数据响应、缺失机制与辅助协变量的缺失数据响应的条件分布（即外推分布）进行设定。我们引入了具有实际意义的敏感性参数，可用于开展简便的敏感性分析。可从领域专家处获取针对这些敏感性参数的信息性先验分布。我们采用蒙特卡洛积分（Monte Carlo integration）计算完整数据的待估量。我们通过模拟数据集评估了所提方法的性能。本研究的方法学灵感源于一项针对精神分裂症治疗的临床试验数据，并将其应用于该数据集。本文的补充材料可在线获取。