Bayesian Variable Selection in Generalized Linear Models with Missing Varibles

描述(申请人提供)：在进行医学研究，特别是在行为和社会问题方面，统计数据分析的挑战来自于缺失值带来的问题。遗漏的值可能是由主观原因(例如，无响应和丢弃)和技术原因(例如，在量化水平之上/之下进行审查)造成的。广义线性模型被广泛应用于生物医学数据分析中，其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。由于数据集不完整，从业者经常采取病例删除策略，即如果个人错过了任何目标分析变量，就会被排除在考虑范围之外。这是许多软件包中使用的默认选项。然而，删除案例不仅可能牺牲有用的信息，而且还会引起有偏见的估计，因为这需要对缺失机制做出强有力的假设。对于丢失数据问题，更令人满意的解决方案涉及多个补偿，其中为相同的缺失值集合创建多个补偿。推算之间的差异反映了由于遗漏而产生的不确定性。然而，在多重推定的数据集上，传统的变量选择方法(基于显著性检验或各种标准)往往会导致选择不同预测因子的模型，因此出现了组合模型以做出最终推断的问题。在这份包含三年研究计划的R01提案中，我们的目标是通过借鉴贝叶斯框架，为缺失数值的GLMS开发两种变量选择的替代策略。一种方法，我们称之为“输入，然后选择”(ITS)，涉及最初执行多个输入，然后将贝叶斯变量选择应用于多个输入的数据集。第二种策略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填充。ITS和SIAS提供了两个通用框架，可以在其中实现各种贝叶斯变量选择算法和缺失数据补偿算法。这两种策略都将被开发、评估并实施到R库中，用于正态回归、二项回归和其他具有分类和/或连续解释变量的GLMS。将使用关于药物滥用和儿童自闭症的几项研究的实际数据集来说明拟议战略的有效性和灵活性。这些程序的开发和该软件对医学研究中的统计学家和研究人员的贡献将显著提高重要和临床相关数据的评估质量。

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.