A robust joint modeling approach for longitudinal data with informative dropouts
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A robust joint modeling approach for longitudinal data with informative dropouts Weiping Zhang1
· Feiyue Xie1 · Jiaxin Tan1
Received: 10 December 2018 / Accepted: 28 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This article proposes a robust method for analysing longitudinal continuous responses with informative dropouts and potential outliers by using the multivariate tdistribution. We specify a dropout mechanism and a missing covariate distribution and incorporate them into the complete data log-likelihood. Unlike the existing approaches which mainly focus on the inference of regression mean and dropouts process, our approach aims to reveal the dynamics in the location function, marginal scale function and association by joint parsimonious modeling the location and dependence structure. A parametric fractional imputation algorithm is developed to speed up the computation associated with the EM algorithm for maximum likelihood estimation with missing data. The resulting estimators are shown to be consistent and asymptotically normally distributed. Data examples and simulations demonstrate the effectiveness of the proposed approach. Keywords Robust estimation · EM algorithm · Joint modeling
1 Introduction A typical characteristic of longitudinal studies is that study subjects are measured over repeated time intervals. Thus, observations for the same subject are intrinsically correlated, it is fundamentally important to account for within-subject correlation in analyzing such data. Regression models on the mean and variance functions for understanding longitudinal data have been extensively studied in the literature. Diggle (2002) gave an excellent overview of various approaches in this filed. To understand the
This work is supported by the National Key Research and Development Plan (No. 2016YFC0800100) and the NSFC of China (Nos. 11671374, 71771203, 71631006).
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Weiping Zhang [email protected] Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China
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dynamics in the mean function and covariance structure, a class of mean–variance– correlation modeling framework has been explored; see, for example, Pourahmadi (1999, 2000, 2007), Pan and Mackenzie (2003), Ye and Pan (2006), Leng et al. (2010), Zhang and Leng (2012) and Zhang et al. (2015). These methods perform well under certain assumptions, but are not resistant to outliers and are applicable to some types of missing data. Furthermore, researchers are frequently confronted with dropout in longitudinal study, that is, some participants leave the study and their outcome measurements are missing. The resulting data are then unbalanced with unequal numbers of measures for each subject and may contain missing covariates. There are two types of dropout patterns being generally considered in statistical literature (Ibrahim and Molenberghs 2009). The first type is called intermittently missing or non-monotone dropout, where a subject ma
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