Inference in Regression Models with Missing Covariates

描述：（改编自研究者摘要）本项目将研究两类常用回归模型在缺少协变量数据的情况下对回归参数进行推断的新方法。特别地，我们检查了一类广义线性模型的一般类型的反应数据和Cox模型的生存数据。该方法解决了慢性疾病（包括癌症和艾滋病）临床调查中经常出现的问题。该项目的具体目标是：1)在缺少协变量数据的情况下，开发和研究广义线性模型（GLM）类的经典和贝叶斯推理方法。特别是，我们将i)检查估计回归参数的方法，当缺失的协变量是分类或连续的，缺失的数据机制是可以忽略的。此外，协变量分布的参数模型将被检查。估计方法将着重于蒙特卡罗版本的EM算法（Wei and Tanner, 1990）和其他相关的迭代算法。Gibbs采样器（Gelfand and Smith, 1990）以及Gilks and Wild（1992）的自适应拒绝算法将被用于从给定观测数据的缺失协变量的条件分布中采样。Ii)检验在缺失协变量为分类或连续且缺失数据机制不可忽略的情况下估计回归参数的方法。缺失数据机制的模型将被研究。iii)开发和研究存在协变量缺失数据时的贝叶斯推理方法，当缺失的协变量是分类的或连续的，并且缺失的数据机制是可以忽略的。提出了回归系数的参数先验分布。我们将研究回归系数后验分布的性质。该方法将使用类似于Tanner和Wong（1987）的马尔可夫链蒙特卡罗方法来实现。iv)当协变量是分类或连续且缺失数据机制不可忽略时，研究贝叶斯方法。将研究缺失数据机制的多项模型。我们将研究多项参数的Dirichlet先验分布。2)在缺少协变量的情况下，发展和研究Cox模型的经典和贝叶斯推理方法。具体而言，我们将i)开发和研究在存在缺失协变量的情况下生存结果的Cox模型的估计方法。本文将研究缺失协变量为分类或连续时的回归参数估计方法。估计方法将侧重于类似于Wei和Tanner（1990）的EM型算法。Ii)研究缺失协变量为分类或连续且缺失数据机制不可忽略时回归参数的估计。缺失数据机制的模型将被研究。将研究类似于1-iii)和-iv)的贝叶斯方法。将实现使用1-iii)中描述的蒙特卡罗方法的计算技术。

DESCRIPTION: (Adapted from investigator's abstract) This project will examine new methodology for making inference about the regression parameters in the presence of missing covariate data for two commonly used classes of regression models. In particular, we examine the class of generalized linear models for general types of response data and the Cox model for survival data. The methodology addresses problems occurring frequently in clinical investigations for chronic disease, including cancer and AIDS. The specific objectives of the project are to: 1) develop and study classical and Bayesian methods of inference for the class of generalized linear models (GLM's) in the presence of missing covariate data. In particular, we will i) examine methods for estimating the regression parameters when the missing covariates are either categorical or continuous and the missing data mechanism is ignorable. Also, parametric models for the covariate distribution will be examined. The methods of estimation will focus on the Monte Carlo version of the EM algorithm (Wei and Tanner, 1990) and other related iterative algorithms. The Gibbs sampler (Gelfand and Smith, 1990) along with the adaptive rejection algorithm of Gilks and Wild (1992) will be used to sample from the conditional distribution of the missing covariates given the observed data. ii) examine estimating the regression parameters when the missing covariates are either categorical or continuous and the missing data mechanism is nonignorable. Models for the missing data mechanism will be studied. iii) develop and study Bayesian methods of inference in the presence of missing covariate data when the missing covariates are either categorical or continuous and the missing data mechanism is ignorable. Parametric prior distributions for the regression coefficients are proposed. Properties of the posterior distributions of the regression coefficients will be studied. The methodology will be implemented using Markov Chain Monte Carlo methods similar to those of Tanner and Wong (1987). iv) investigate Bayesian methods when the covariates are either categorical or continuous and the missing data mechanism is nonignorable. Multinomial models for the missing data mechanism will be studied. Dirichlet prior distributions for the multinomial parameters will be investigated. 2) develop and study classical and Bayesian methods of inference for the Cox model for survival outcomes in the presence of missing covariates. Specifically, we will i) develop and study estimation methods for the Cox model for survival outcomes in the presence of missing covariates. Methods for estimating the regression parameters when the missing covariates are either categorical or continuous will be studied. The methods of estimation will focus on an EM type algorithm similar to that of Wei and Tanner (1990). ii) study estimation of the regression parameters when the missing covariates are either categorical or continuous and the missing data mechanisms nonignorable. Models for the missing data mechanism will be studied. Bayesian methods similar to those of 1-iii) and -iv) will be investigated. Computational techniques using the Monte Carlo methods described in 1-iii) will be implemented.