Conditional Second-Order Generalized Estimating Equations for Generalized Linear and Nonlinear Mixed-Effects Models

• Published in: Journal of the American Statistical Association Vol. 97; no. 457; pp. 271 - 283
• Main Authors: Vonesh, Edward F, Wang, Hao, Nie, Lei, Majumdar, Dibyen
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.03.2002; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Approximation; Asymptotics; Consistent estimators; Covariance; Covariance matrices; Estimation; Estimators; Exact sciences and technology; First-order linearization; Gaussian random effects; Laplace approximation; Least squares method; Linear inference, regression; Linear models; Mathematical models; Mathematics; Maximum likelihood estimation; Medical sciences; Modeling; Multilevel models; Non-linear models; Nonparametric inference; Parametric inference; Parametric models; Penalized extended least squares; Probability and statistics; Quadratic exponential family; Random variables; Sciences and techniques of general use; Statistical analysis; Statistical methods; Statistical variance; Statistics; Theory and Methods; Second order equation; Generalized linear model; Statistical analysis; First order linearization; Covariance analysis; Epilepsy; Gaussian distribution; Variance analysis; Penalty method; Least squares method; Mixed model; Non linear model; Generalized equation; Exponential family; Numerical simulation; Laplace transformation; Asymptotic approximation; Quadratic estimation
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214502753479400

Generalized linear and nonlinear mixed-effects models are used extensively in health care research, including applications in pharmacokinetics, clinical trials, and epidemiology. Because the underlying model may be nonlinear in the random effects, there will generally be no closed-form expression for the marginal likelihood or indeed for the marginal moments. Consequently, estimation is often carried out either using numerical integration techniques or by approximating the marginal likelihood and/or marginal moments using first-order expansion methods. An advantage of the first-order methods is that they do not necessarily require specification of a conditional like-lihood to estimate the regression parameters of interest. However, in many cases they may not take full advantage of the fact that the conditional variance depends on both fixed and random effects. In this article we propose using conditional second-order generalized estimating equations (CGEE2) to estimate both fixed- and random-effects parameters. Under mild regularity conditions, the CGEE2 estimator is shown to be consistent and asymptotically efficient with a rate of convergence depending on both the number of subjects and the number of observations per subject. We compare the CGEE2 estimator against alternative estimators using limited simulation and demonstrate its utility with a numerical example.