Empirical-likelihood-based criteria for model selection on marginal analysis of longitudinal data with dropout missingness

TL;DR

This paper introduces new empirical-likelihood-based criteria, JEAIC and JEBIC, for joint selection of marginal mean variables and correlation structures in longitudinal data with dropout missingness, improving model selection accuracy.

Contribution

It develops the first joint empirical likelihood criteria for simultaneous selection of mean and correlation models in longitudinal data analysis with missing outcomes.

Findings

JEAIC and JEBIC outperform existing criteria in simulations.

The proposed criteria are robust and flexible across different sample sizes.

Theoretical justification supports their validity.

Abstract

Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equations (WGEE) approach is widely adopted for marginal analysis. 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 and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate criteria for the selection of marginal mean and correlation structures, unsatisfactory selection performance in small-sample set-ups and so on. In particular, there are few studies to develop joint information criteria for selection of both marginal mean and correlation structures. In this work, by embedding empirical likelihood into the WGEE framework, we propose two innovative information criteria named a joint empirical Akaike information criterion (JEAIC) and a joint empirical Bayesian information criterion (JEBIC), which can simultaneously select the variables for marginal mean regression and also correlation structure. Through extensive simulation studies, these empirical-likelihood-based criteria exhibit robustness, flexibility, and outperformance compared to the other criteria including the weighted quasi-likelihood under the independence model criterion, the missing longitudinal information criterion and the joint longitudinal information criterion. In addition, we provide a theoretical justification of our proposed criteria, and present two real data examples in practice for further illustration.