Penalized Empirical Likelihood-Based Variable Selection for Longitudinal Data Analysis

Abstract

Longitudinal data with a large number of covariates have become common in many applications such as epidemiology, clinical research, and therapeutic evaluation. The identification of a sub-model that adequately represents the data are necessary for easy interpretation. Existing information theoretic-approaches such as AIC and BIC are useful, but computationally not efficient due to an evaluation of all possible subsets. A new class of penalized likelihood methods such as LASSO, SCAD, etc. are efficient in these situations. All these methods rely on the parametric modeling of the response of interest. The joint likelihood function for longitudinal data is challenging, particularly for correlated discrete outcome data. In such a situation, we propose penalized empirical likelihood (PEL) based on generalized estimating equations (GEE) by which the variable selection and the estimation of the coefficients are carried out simultaneously. We discuss its characteristics and asymptotic properties and present an efficient computational algorithm for optimizing PEL. Simulation studies show that when model assumptions are true, its performance is comparable to that of the existing methods and when the model is misspecified, our method has clear advantages over the existing methods. We have applied the method to two case examples.

KEYWORDS AND PHRASES:

• Adjusted empirical likelihood
• empirical likelihood
• generalized estimating equations
• penalized generalized quasi-likelihood
• penalized likelihood

Acknowledgements

The authors thank the editor and the reviewers for their valuable comments that significantly improved the manuscript.

Additional information

Funding

The authors’ research was supported by grants from Natural Sciences & Engineering Research Council of Canada and the Canadian Institute of Health Research.