Bayesian Variable Selection in Generalized Linear Models with Missing Varibles

描述（由申请人提供）：在进行医学研究，特别是行为和社会问题，统计数据分析的挑战来自缺失值引入的问题。缺失值可能是由主观因素（例如，无应答和辍学）和技术原因（例如，在量化级之上/之下删失）。广义线性模型（GLM）广泛应用于生物医学数据分析，其中一个基本任务是通过潜在解释变量的子集来解释或预测结果变量。在数据不完整的情况下，从业人员经常采取删除案例的策略，如果个人错过了分析的任何变量，他们就被排除在考虑之外。这是许多软件包中使用的默认选项。然而，病例删除不仅可能牺牲有用的信息，而且会导致有偏估计，因为它需要对缺失机制进行强假设。缺失数据问题的一个更令人满意的解决方案涉及多重插补，即为同一组缺失值创建多个插补。插补之间的差异反映了缺失导致的不确定性。然而，在多重插补数据集上，传统的变量选择方法（基于显著性检验或各种标准）通常会导致模型具有不同的选定预测因子，从而提出了将模型组合以进行最终推断的问题。在这个R 01的建议与3年的研究计划，我们的目标是制定两个替代战略的变量选择GLM与缺失值的贝叶斯框架。一种方法，我们称之为“插补，然后选择”（ITS）涉及最初执行多重插补，然后将贝叶斯变量选择应用于多重插补数据集。第二种策略-“同时估算和选择”（SIAS）-是在一个马尔可夫链蒙特卡罗（MCMC）过程中同时进行贝叶斯变量选择和缺失数据估算。ITS和SIAS提供了两个通用的框架，在其中可以实现各种贝叶斯变量选择算法和缺失数据填补算法。这两种策略将被开发、评估并实施到R库中，用于正态回归、二项式回归和其他具有分类和/或连续解释变量的GLM。将利用关于药物滥用和儿童孤独症的几项研究的实际数据集来探讨拟议战略的有效性和灵活性。这些程序的开发和软件对统计人员和医学研究人员的贡献将大大提高重要和临床相关数据的评价质量。

DESCRIPTION (provided by applicant): In conducting medical research, especially with behavioral and social problems, a challenge for statistical data analysis comes from the problems introduced by missing values. Missing values may be caused by subjective (e.g., nonresponse and dropout) and technical reasons (e.g., censoring over/below quantization level). Generalized linear models (GLMs) are popularly applied in biomedical data analysis where a fundamental task is to interpret or predict an outcome variable by a subset of potentially explanatory variables. Given an incomplete data set, practitioners frequently resort to the strategy of case-deletion where individuals are excluded from consideration if they miss any of the variables targeted for analysis. This is the default option used in many software packages. Yet, case-deletion may not only sacrifice useful information, but also give rise to biased estimates because it requires strong assumptions on the missingness mechanisms. A more satisfactory solution for missing data problems involves multiple imputation, where several imputations are created for the same set of missing values. The variance between imputations reflects the uncertainty due to missingness. Across multiply imputed data sets, however, traditional variable selection methods (based on significance tests or various criteria) often result in models with different selected predictors, thus presenting a problem of combining the models to make final inferences. In this R01 proposal with a 3-year research plan, we aim to develop two alternative strategies of variable selection for GLMs with missing values by drawing on a Bayesian framework. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. The second strategy - "simultaneously impute and select" (SIAS) - is to conduct Bayesian variable selection and missing data imputation simultaneously within one Markov Chain Monte Carlo (MCMC) process. ITS and SIAS offer two generic frameworks within which various Bayesian variable selection algorithms and missing data imputation algorithms can be implemented. Both strategies will be developed, evaluated, and implemented into an R library for normal regression, binomial regression, and other GLMs with categorical and/or continuous explanatory variables. Practical data sets from several studies on substances abuse and childhood autism will be used to address the effectiveness and flexibility of the proposed strategies. Development of these procedures and contribution of the software to statisticians and researchers in medical research would significantly improve the quality of evaluation of important and clinically relevant data.