Bayesian Variable Selection in Generalized Linear Models with Missing Varibles

描述（由申请人提供）：申请人寻求解决缺失值问题，生物医学研究的主要挑战来自缺失值问题，缺失值问题可能由主观原因（例如，无反应和辍学）和技术原因（例如，审查超过/低于量化水平）引起。广义线性模型（GLMs）和广义线性混合模型（glmm）广泛应用于生物医学数据分析，其基本任务是识别自变量的子集（例如，遗传，蛋白质组学，行为或环境因素）来解释或预测因变量（例如，治疗有效性和安全性）。给定一个不完整的数据集，从业者可能不必要地求助于病例删除策略，如果个人错过了任何用于分析的变量，则将其排除在考虑之外。这种方法不仅会牺牲有用的信息，而且还会产生有偏差的估计，因为它需要强有力的假设来接受缺失机制。对于缺失数据问题，一个更令人满意的解决方案涉及多个输入，其中为同一组缺失值创建多个输入。然而，在多个输入数据集中，传统的变量选择方法（基于显著性检验或似然标准）往往导致模型具有不同的选择预测因子，从而提出了将模型组合起来进行最终推断的问题。在本R01提案中，我们的目标是通过借鉴贝叶斯框架，为缺失值的glm开发变量选择的替代策略。一种称为“先输入后选择”（ITS）的方法涉及首先执行多个输入，然后对多个输入数据集应用贝叶斯变量选择。第二种策略-“同时输入和选择”(SIAS) -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输入。ITS和SIAS提供了两个通用框架，其中可以实现各种贝叶斯变量选择算法和缺失数据输入算法。这些策略将被扩展到处理复杂的数据集，例如那些具有多层次设计结构和/或大量变量的数据集。这些策略将被开发、评估并实现到一个R库中，用于正态、二项/多项和泊松回归模型，这些模型具有混合分类和连续解释变量。来自儿童自闭症和药物依赖研究的模拟和实际数据集将用于解决拟议策略的有效性和灵活性。

DESCRIPTION (provided by applicant): The applicant seeks to address the problem of missing values A major challenge for biomedical research comes from the problems of missing values, which may be caused by subjective (e.g., nonresponse and dropout) and technical reasons (e.g., censoring over/below quantization level). Generalized linear models (GLMs) and Generalized Linear Mixed Models (GLMMs) are popularly applied in biomedical data analysis where a fundamental task is to identify a subset of independent variables (e.g., genetic, proteomic, behavioral, or environmental factors) to interpret or predict a dependent variable (e.g., therapeutic effectiveness and safety). Given an incomplete data set, practitioners may needlessly resort to the strategy of case-deletion where individuals are excluded from consideration if they miss any of the variables targeted for analysis. This method would not only sacrifice useful information, but also give rise to biased estimates because it requires strong assumptions to accept 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. Across multiply imputed data sets, however, traditional variable selection methods (based on significance tests or likelihood 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, we aim to develop alternative strategies of variable selection for GLMs with missing values by drawing on a Bayesian framework. One approach called "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) - conducts 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. The strategies will be extended to handle complex data sets such as those with multi-level design structures and/or large number of variables. The strategies will be developed, evaluated, and implemented into an R library for normal, binomial/multinomial, and Poisson regression models with mixed categorical and continuous explanatory variables. Simulated and practical data sets from studies on childhood autism and drug dependence will be used to address the effectiveness and flexibility of the proposed strategies.