Generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits

Research output: Contribution to journalArticle

Abstract

Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95% confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points; while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women.

Original languageEnglish (US)
Pages (from-to)119-136
Number of pages18
JournalStatistics in Medicine
Volume37
Issue number1
DOIs
StatePublished - Jan 15 2018

Fingerprint

Binary Outcomes
Generalized Linear Mixed Model
Newton-Raphson method
Detection Limit
Measurement Error
Monte Carlo method
Limit of Detection
Covariates
Linear Models
Maximum Likelihood Method
Biomarkers
Quadrature
Left Censoring
Delta Method
Longitudinal Study
Imputation
Coverage Probability
Risk Factors
Standard error
Likelihood Function

Keywords

  • detection limit
  • generalized linear mixed model
  • longitudinal data
  • measurement error
  • Monte Carlo Newton-Raphson

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability

Cite this

@article{b9b9c4364ba1427d99fbb8e003f588eb,
title = "Generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits",
abstract = "Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95{\%} confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points; while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women.",
keywords = "detection limit, generalized linear mixed model, longitudinal data, measurement error, Monte Carlo Newton-Raphson",
author = "Xianhong Xie and Xue, {Xiaonan (Nan)} and Howard Strickler",
year = "2018",
month = "1",
day = "15",
doi = "10.1002/sim.7509",
language = "English (US)",
volume = "37",
pages = "119--136",
journal = "Statistics in Medicine",
issn = "0277-6715",
publisher = "John Wiley and Sons Ltd",
number = "1",

}

TY - JOUR

T1 - Generalized linear mixed model for binary outcomes when covariates are subject to measurement errors and detection limits

AU - Xie, Xianhong

AU - Xue, Xiaonan (Nan)

AU - Strickler, Howard

PY - 2018/1/15

Y1 - 2018/1/15

N2 - Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95% confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points; while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women.

AB - Longitudinal measurement of biomarkers is important in determining risk factors for binary endpoints such as infection or disease. However, biomarkers are subject to measurement error, and some are also subject to left-censoring due to a lower limit of detection. Statistical methods to address these issues are few. We herein propose a generalized linear mixed model and estimate the model parameters using the Monte Carlo Newton-Raphson (MCNR) method. Inferences regarding the parameters are made by applying Louis's method and the delta method. Simulation studies were conducted to compare the proposed MCNR method with existing methods including the maximum likelihood (ML) method and the ad hoc approach of replacing the left-censored values with half of the detection limit (HDL). The results showed that the performance of the MCNR method is superior to ML and HDL with respect to the empirical standard error, as well as the coverage probability for the 95% confidence interval. The HDL method uses an incorrect imputation method, and the computation is constrained by the number of quadrature points; while the ML method also suffers from the constrain for the number of quadrature points, the MCNR method does not have this limitation and approximates the likelihood function better than the other methods. The improvement of the MCNR method is further illustrated with real-world data from a longitudinal study of local cervicovaginal HIV viral load and its effects on oncogenic HPV detection in HIV-positive women.

KW - detection limit

KW - generalized linear mixed model

KW - longitudinal data

KW - measurement error

KW - Monte Carlo Newton-Raphson

UR - http://www.scopus.com/inward/record.url?scp=85037653190&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037653190&partnerID=8YFLogxK

U2 - 10.1002/sim.7509

DO - 10.1002/sim.7509

M3 - Article

VL - 37

SP - 119

EP - 136

JO - Statistics in Medicine

JF - Statistics in Medicine

SN - 0277-6715

IS - 1

ER -