Semiparametric estimation in generalized linear mixed models with auxiliary covariates: A pairwise likelihood approach

• Published in: Biometrics Vol. 70; no. 4; pp. 910 - 919
• Main Authors: Liu, Li, Xiang, Liming
• Format: Journal Article
• Language: English
• Published: United States International Biometric Society, etc. 01.12.2014; Blackwell Publishing Ltd; International Biometric Society
• Subjects: Auxiliary; Biomedical research; BIOMETRIC METHODOLOGY; Biometrics; biometry; Biometry - methods; Computer Simulation; Consistent estimators; Data Interpretation, Statistical; Estimation bias; Estimation methods; Estimators; Generalized linear mixed model; Likelihood Functions; Linear Models; Logistic regression; Pairwise likelihood; primary contact; probability; Regression Analysis; Sample Size; Semiparametric; Simulations; Standard error; Urinary tract infections; Auxiliary; Pairwise likelihood; Semiparametric; Generalized linear mixed model
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.12208

Auxiliary covariates are often encountered in biomedical research settings where the primary exposure variable is measured only for a subgroup of study subjects. This article is concerned with generalized linear mixed models in the presence of auxiliary covariate information for clustered data. We propose a novel semiparametric estimation method based on a pairwise likelihood function and develop an estimating equation‐based inference procedure by treating both the error structure and random effects as nuisance parameters. This method is robust against misspecification of either error structure or random‐effects distribution and allows for dependence between random effects and covariates. We show that the resulting estimators are consistent and asymptotically normal. Extensive simulation studies evaluate the finite sample performance of the proposed estimators and demonstrate their advantage over the validation set based method and the existing method. We illustrate the method with two real data examples.