Inference in Regression Models with Missing Covariates

描述：(改编自研究人员的摘要)本项目将研究两类常用回归模型在存在缺失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，我们研究了一般类型的响应数据的广义线性模型和生存数据的Cox模型。该方法解决了包括癌症和艾滋病在内的慢性疾病临床调查中经常出现的问题。该项目的具体目标是：1)在存在缺失协变量数据的情况下，发展和研究广义线性模型(GLM)的经典和贝叶斯推断方法。特别是，当缺失协变量是分类的或连续的，并且缺失数据机制可以忽略时，我们将研究用于估计回归参数的方法。此外，还将研究协变量分布的参数模型。估计方法将集中在EM算法的蒙特卡罗版本(魏和Tanner，1990)和其他相关的迭代算法上。Gibbs采样器(Gelfand and Smith，1990)和Gilks and Wild(1992)的自适应拒绝算法将被用来从给定观测数据的缺失协变量的条件分布中进行采样。Ii)当缺失协变量是分类的或连续的，并且缺失数据机制是不可忽略的时，检查回归参数的估计。将研究缺失数据机制的模型。Iii)发展和研究在缺失协变量存在的情况下的贝叶斯推理方法，当缺失协变量是范畴的或连续的，并且缺失数据的机制是可以忽略的。给出了回归系数的参数先验分布。将研究回归系数的后验分布的性质。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施。Iv)研究协变量为范畴变量或连续变量且丢失数据机制不可忽略时的贝叶斯方法。我们将研究缺失数据机制的多项式模型。我们将研究多项式参数的Dirichlet先验分布。2)发展和研究经典的和贝叶斯的方法来推断存在缺失协变量的Cox模型的生存结果。具体地说，我们将发展和研究存在缺失协变量的Cox模型的生存结果估计方法。当缺失的协变量是分类的或连续的时，将研究估计回归参数的方法。估计的方法将集中在EM型算法上，类似于魏和Tanner(1990)的算法。Ii)当缺失协变量是范畴变量或连续变量，且缺失数据机制不可忽略时，回归参数的估计。将研究缺失数据机制的模型。将研究类似于1-III)和-IV)的贝叶斯方法。将实施使用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.