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

Hongbin Zhang; Lang Wu

doi:10.1007/s00184-018-0690-z

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

Hongbin Zhang, Lang Wu

Biostatistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	471-499
Number of pages	29
Journal	Metrika
Volume	82
Issue number	4
DOIs	https://doi.org/10.1007/s00184-018-0690-z
State	Published - May 1 2019

Bibliographical note

Funding Information:
Acknowledgements This work is partially supported by the City University of New York High-Performance Computing Center, College of Staten Island, funded in part by the City and State of New York, City University of New York Research Foundation and National Science Foundation grants CNS-0958379, CNS-0855217, and ACI-112611.

Funding Information:
This work is partially supported by the City University of New York High-Performance Computing Center, College of Staten Island, funded in part by the City and State of New York, City University of New York Research Foundation and National Science Foundation grants CNS-0958379, CNS-0855217, and ACI-112611.

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Asymptotic
First-order Taylor approximation
Longitudinal data
Measurement error
Nonlinear covariate model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1007/s00184-018-0690-z

Cite this

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

UN SDGs

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