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An approximate method for generalized linear and nonlinear mixed effects models with a mechanistic nonlinear covariate measurement error model

Authors
  • Zhang, Hongbin1
  • Wu, Lang2
  • 1 City University of New York, Department of Epidemiology and Biostatistics, Graduate School of Public Health and Health Policy, Institute for Implementation Science in Population Health, 55 West 125th Street, New York, NY, 10027, USA , New York (United States)
  • 2 University of British Columbia, Department of Statistics, Vancouver, V6T 1Z4, Canada , Vancouver (Canada)
Type
Published Article
Journal
Metrika
Publisher
Springer Berlin Heidelberg
Publication Date
Oct 17, 2018
Volume
82
Issue
4
Pages
471–499
Identifiers
DOI: 10.1007/s00184-018-0690-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

The literature on measurement error for time-dependent covariates has mostly focused on empirical models, such as linear mixed effects models. Motivated by an AIDS study, we propose a joint modeling method in which a mechanistic nonlinear model is used to address the time-varying covariate measurement error for a longitudinal outcome that can be either discrete such as binary and count or continuous. We implement an inference procedure that uses first-order Taylor approximation to linearize both the covariate model and the response model. We study the asymptotic properties of the joint model based estimator and provide proof of consistency and normality. We then evaluate the performance of estimation in finite sample size scenario through simulation. Finally, we apply the new method to real data in an HIV/AIDS study.

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