Non-parametric and semiparametric models for missing covariates in parametric regression Abstracts

s Robustness of covariate modeling for the missing covariate problem in parametric regression is studied under the MAR assumption. For a simple missing covariate pattern, non-parametric likelihood is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter. Total robustness is achieved in this situation. For more general missing covariate patterns, novel semiparametric models are proposed for modeling missing covariates. In this modeling approach, the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing data patterns and the conditional distributions are then represented in the general odds ratio form. The general odds ratios are modeled parametrically and the other components of the covariate distribution are modeled nonparametrically. Maximum semiparametric likelihood is proposed to find the parameter estimates. The proposed method yields a consistent estimator for the regression parameter when the odds ratios are modeled correctly. In general, the semiparametric covariate modeling strategy increases the robustness against covariate model misspecification when compared with the parametric modeling strategy proposed by Lipsitz and Ibrahim. The new covariate modeling approach can also be incorporated into the doubly robust procedure of Robins et al to increase protection against misspecification of the missing data mechanism. Furthermore, the proposed modeling strategy avoids the usually intractable integrations that are involved in the maximization of the incomplete data likelihood with parametric covariate models. The proposed method can be applied to solve missing covariate problems in many regression models frequently used in practice. Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorably Missing Data Abstracts Missing data, measurement error and misclassification are three important problems in many research fields, such as epidemiological studies. It is well known that missing data and measurement error in covariates may lead to biased estimation. Misclassification may be considered as a special type of measurement error, for categorical data. Nevertheless, we treat misclassification as a different problem from measurement error since statistical models for them are different. Indeed, in the literature, methods for these three problems were proposed separately given that statistical modeling for them are very different. The problem is more challenging in a longitudinal study when data are missing nonignorably. In this paper, we consider estimation in generalized linear models under these three incomplete data models. We propose a general approach based on expected estimating equations to solving these three incomplete data problems in a unified fashion. Bias analysis for naive estimation is conducted for some specific models. This expected estimating equation approach can be easily implemented and its asymptotic covariance can be obtained by sandwich estimation. Intensive simulation studies are performed under various incomplete data settings. The proposed method is applied to a longitudinal study of oral bone density in relation to body bone density.