Robust statistical inference for longitudinal data with nonignorable dropouts

• Published in: Statistics (Berlin, DDR) Vol. 56; no. 5; pp. 1072 - 1094
• Main Authors: Shao, Yujing, Ma, Wei, Wang, Lei
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.09.2022; Taylor & Francis Ltd
• Subjects: Algorithms; Asymptotic methods; Asymptotic properties; Dropout propensity; Dropouts; empirical likelihood; Estimators; Feature selection; Generalized linear models; Generalized method of moments; Method of moments; missing not at random; nonresponse instrument; Outliers (statistics); quadratic inference function; Robustness; Statistical analysis; Statistical inference; Statistical models; variable selection
• ISSN: 0233-1888; 1029-4910
• DOI: 10.1080/02331888.2022.2110250

In this paper, we propose robust statistical inference and variable selection method for generalized linear models that accommodate the outliers, nonignorable dropouts and within-subject correlations. The purpose of our study is threefold. First, we construct the robust and bias-corrected generalized estimating equations (GEEs) by combining the Mallows-type weights, Huber's score function and inverse probability weighting approaches to against the influence of outliers and account for nonignorable dropouts. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Second, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function and hybrid-GEE to obtain the improved empirical likelihood procedures. The asymptotic properties of the proposed estimators and their confidence regions are derived. Third, the robust variable selection and algorithm are investigated. We evaluate the performance of proposed estimators through simulation and illustrate our method in an application to HIV-CD4 data.