使用辅助边际分位数的不可忽略缺失数据高斯连接模型
Gaussian Copula Models for Nonignorable Missing Data Using Auxiliary Marginal Quantiles
AI总结：
提出基于高斯连接模型与辅助边际分位数的贝叶斯方法，解决不可忽略缺失数据的建模与插补，证明少量分位数可一致估计相关性，并在铅暴露与学业成绩关联分析中验证其优于传统方法。
摘要：
我们提出了一种建模和插补不可忽略缺失数据的方法。该方法使用贝叶斯数据整合结合两点：(1) 针对所有研究变量和缺失指示符的高斯连接模型，允许任意边际分布、不可忽略缺失及其他依赖关系；(2) 以部分研究变量的边际分位数形式存在的辅助信息。我们证明，只需少量精确指定的分位数即可一致地估计连接相关性。剩余边际分布函数使用高效的MCMC算法非参数化地与连接参数联合推断。我们还刻画了连接模型隐含的（加性）不可忽略缺失机制。模拟证实了该方法在不可忽略缺失数据多元插补中的有效性。我们将该模型应用于分析17万名北卡罗来纳州学生的铅暴露与年级末考试成绩之间的关联。铅暴露存在不可忽略缺失：暴露较高的儿童更可能被测量。我们使用疾病控制与预防中心提供的统计数据获取铅暴露的边际分位数。基于我们模型的多元插补推断支持铅暴露与教育结果之间更强的、更不利的关联，相对于完整病例和随机缺失分析。
英文摘要：
We present an approach for modeling and imputation of nonignorable missing data. Our approach uses Bayesian data integration to combine (1) a Gaussian copula model for all study variables and missingness indicators, which allows arbitrary marginal distributions, nonignorable missingess, and other dependencies, and (2) auxiliary information in the form of marginal quantiles for some study variables. We prove that, remarkably, one only needs a small set of accurately-specified quantiles to estimate the copula correlation consistently. The remaining marginal distribution functions are inferred nonparametrically and jointly with the copula parameters using an efficient MCMC algorithm. We also characterize the (additive) nonignorable missingness mechanism implied by the copula model. Simulations confirm the effectiveness of this approach for multivariate imputation with nonignorable missing data. We apply the model to analyze associations between lead exposure and end-of-grade test scores for 170,000 North Carolina students. Lead exposure has nonignorable missingness: children with higher exposure are more likely to be measured. We elicit marginal quantiles for lead exposure using statistics provided by the Centers for Disease Control and Prevention. Multiple imputation inferences under our model support stronger, more adverse associations between lead exposure and educational outcomes relative to complete case and missing-at-random analyses.
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