Zhou Tianjian, Daniels Michael J, Müller Peter
Department of Public Health Sciences, The University of Chicago.
Department of Statistics, University of Florida.
J Comput Graph Stat. 2020;29(1):1-12. doi: 10.1080/10618600.2019.1617159. Epub 2019 Jul 2.
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 (MAR). 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 non-linear and non-additive 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.
我们开发了一种半参数贝叶斯方法，用于处理纵向研究中存在辅助协变量时的缺失结局数据。我们考虑了一个针对完整数据响应、缺失情况和辅助协变量的联合模型。我们纳入辅助协变量，以使缺失情况“更接近”随机缺失（MAR）。具体而言，我们通过高斯过程先验和贝叶斯加法回归树为观测数据指定一个半参数贝叶斯模型。与现有的参数方法相比，这些模型规范使我们能够捕捉非线性和非加性效应。然后，我们利用识别性限制分别指定给定观测数据响应、缺失情况和辅助协变量时缺失数据响应的条件分布（即外推分布）。我们引入了有意义的敏感性参数，以便进行简单的敏感性分析。这些敏感性参数的信息性先验可以从主题专家那里获取。我们使用蒙特卡罗积分来计算完整数据的估计量。我们通过模拟数据集评估了我们方法的性能。我们的方法是受一项关于精神分裂症治疗的临床试验数据启发，并应用于该数据。
