Empirical-likelihood-based criteria for model selection on marginal analysis of longitudinal data with dropout missingness
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Longitudinal data are common in clinical trials and observational studies, where the outcomes with missing data due to dropouts are always encountered. Under such context with the assumption of missing at random, weighted generalized estimating equations (WGEE) proposed by Robins et al. (1995) is widely adopted for marginal analysis. Of note is that model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest. However, the existing information criteria for WGEE model selection have limitations, such as separate criteria for the selection of marginal mean regression and correlation structures, unsatisfactory selection performance in small-sample set-ups and so on. In particular, there exist few works developing joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into WGEE framework, we propose two innovative information criteria named joint empirical Akaike information criterion (JEAIC) and joint empirical Bayesian information criterion (JEBIC), which can simultaneously select the variables for marginal mean and correlation structures. Through extensive simulation studies, these empirical-likelihood-based criteria exhibit robustness, flexibility, and out-performance compared to other criteria including weighted quasi-likelihood under the independence model criterion (QICW), missing longitudinal information criterion (MLIC) and joint longitudinal information criterion (JLIC). More importantly, we provide rigorous theoretical justification of plug-in estimators in our proposed criteria and assess their asymptotic relationship with empirical likelihood estimators. Lastly, a real data example is presented to further illustrate the application in practice.
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