Approximate Conditional Likelihood for Generalized Linear Models with General Missing Data Mechanism  

作　　者：ZHAO Jiwei SHAO Jun 

机构地区：[1]Department of Biostatistics,State University of New York at Buffalo [2]School of Statistics,East China Normal University

出　　处：《Journal of Systems Science & Complexity》2017年第1期139-153,共15页系统科学与复杂性学报（英文版）

基　　金：supported by the Chinese 111 Project B14019;the US National Science Foundation under Grant Nos.DMS-1305474 and DMS-1612873;the US National Institutes of Health Award UL1TR001412

摘　　要：The generalized linear model is an indispensable tool for analyzing non-Gaussian response data, with both canonical and non-canonical link functions comprehensively used. When missing values are present, many existing methods in the literature heavily depend on an unverifiable assumption of the missing data mechanism, and they fail when the assumption is violated. This paper proposes a missing data mechanism that is as generally applicable as possible, which includes both ignorable and nonignorable missing data cases, as well as both scenarios of missing values in response and covariate.Under this general missing data mechanism, the authors adopt an approximate conditional likelihood method to estimate unknown parameters. The authors rigorously establish the regularity conditions under which the unknown parameters are identifiable under the approximate conditional likelihood approach. For parameters that are identifiable, the authors prove the asymptotic normality of the estimators obtained by maximizing the approximate conditional likelihood. Some simulation studies are conducted to evaluate finite sample performance of the proposed estimators as well as estimators from some existing methods. Finally, the authors present a biomarker analysis in prostate cancer study to illustrate the proposed method.

关 键 词：Asymptotic normality generalized linear model IDENTIFIABILITY missing data mechanism non-canonical link function nonignorable missingness. 

分 类 号：O212[理学—概率论与数理统计] O326[理学—数学]