Nonlinear mixed-effects models with misspecified random-effects distribution.

Advanced Search

Reza Drikvandi

Author Information

Reza Drikvandi: Department of Computing and Mathematics, Manchester Metropolitan University, Manchester, UK. ORCID

PMID: 31663263 DOI: 10.1002/pst.1981

Nonlinear mixed-effects models are being widely used for the analysis of longitudinal data, especially from pharmaceutical research. They use random effects which are latent and unobservable variables so the random-effects distribution is subject to misspecification in practice. In this paper, we first study the consequences of misspecifying the random-effects distribution in nonlinear mixed-effects models. Our study is focused on Gauss-Hermite quadrature, which is now the routine method for calculation of the marginal likelihood in mixed models. We then present a formal diagnostic test to check the appropriateness of the assumed random-effects distribution in nonlinear mixed-effects models, which is very useful for real data analysis. Our findings show that the estimates of fixed-effects parameters in nonlinear mixed-effects models are generally robust to deviations from normality of the random-effects distribution, but the estimates of variance components are very sensitive to the distributional assumption of random effects. Furthermore, a misspecified random-effects distribution will either overestimate or underestimate the predictions of random effects. We illustrate the results using a real data application from an intensive pharmacokinetic study.

Gauss-Hermite quadrature diagnostic test longitudinal data nonlinear mixed-effects models prediction random-effects distribution

Dubois A, Gsteiger S, Balser S, Pigeolet E, Steimer JL, Pillai G, Mentré F. Pharmacokinetic similarity of biologics: analysis using nonlinear mixed-effects modeling. Clin Pharmacol Ther. 2012;91(0):234-242.
Drikvandi R. Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution. J Pharmacokinet Pharmacodynamics. 2017;44(0):223-232.
Efendi A, Drikvandi R, Verbeke G, Molenberghs G. A goodness-of-fit test for the random-effects distribution in mixed models. Stat Methods Med Res. 2017;26(0):970-983.
Drikvandi R, Verbeke G, Molenberghs G. Diagnosing misspecification of the random-effects distribution in mixed models. Biometrics. 2017;73(0):63-71.
Verbeke G, Molenberghs G. Linear Mixed Models for Longitudinal Data. New York:Springer Verlag; 2009.
Davidian M, Giltinan DM. Some general estimation methods for nonlinear mixed-effects model. J Biopharmaceutical Stat. 1993;3(0):23-55.
Liu L, Yu Z. A likelihood reformulation method in non-normal random effects models. Stat Med. 2008;27(0):3105-3124.
Harring JR, Liu J. A comparison of estimation methods for nonlinear mixed-effects models under model misspecification and data sparseness: a simulation study. J Modern Appl Stat Methods. 2016;15(0):539-569.
Verbeke G, Lesaffre E. The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Comput Stat Data Anal. 1997;23(0):541-556.
Heagerty PJ, Kurland BF. Misspecified maximum likelihood estimates and generalised linear mixed models. Biometrika. 2001;88(0):973-985.
Agresti A, Caffo B, Ohman-Strickland P. Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies. Comput Stat Data Anal. 2004;47(0):639-653.
Litière S, Alonso A, Molenberghs G. The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models. Stat Med. 2008;27(0):3125-3144.
Alonso A, Litière S, Laenen A. A note on the indeterminacy of the random-effects distribution in hierarchical models. Amer Stat. 2010;64(0):318-324.
Hartford A, Davidian M. Consequences of misspecifying assumptions in nonlinear mixed effects models. Comput Stat Data Anal. 2000;34(0):139-164.
Fitzmaurice G, Davidian M, Verbeke G, Molenberghs G. Longitudinal Data Analysis: A Handbook of Modern Statistical Methods. New York:Chapmann & Hall/CRC; 2008.
Pinheiro JC, Bates DM. Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comput Graphs Stat. 1995;4(0):12-35.
Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Table. New York:Dover; 1964.
Golub GH. Some modified matrix eigenvalue problems. Siam Rev. 1973;15(0):318-334.
Hedeker D, Gibbons RD. MIXOR: a computer program for mixed-effects ordinal regression analysis. Comput Meth Prog Biomedicine. 1996;49(0):157-176.
Lesaffre E, Spiessens B. On the effect of the number of quadrature points in a logistic random effects model: an example. J Royal Stat Soc Ser C (Applied Statistics). 2001;50(0):325-335.
White H. Maximum likelihood estimation of misspecified models. Econometrica. 1982;50(0):1-25.
Verbeke G, Molenberghs G. The gradient function as an exploratory goodness-of-fit assessment of the random-effects distribution in mixed models. Biostatistics. 2013;14(0):477-490.
Boekmann AJ, Sheiner LB, Beal SL. Nonmem user's guide, part V: introductory guide. University of California, San Francisco, 1992.
Davidian M, Giltinan DM. Nonlinear models for repeated measurement data: an overview and update. J Agr Biol Environ Stat. 2003;8(0):387-419.
Drikvandi R, Verbeke G, Khodadadi A, PartoviNia V. Testing multiple variance components in linear mixed-effects models. Biostatistics. 2013;14(0):144-159.
Litière S, Alonso A, Molenberghs G. Type I and type II error under random-effects misspecification in generalized linear mixed models. Biometrics. 2007;63(0):1038-1044.
Woods CM. Likelihood-ratio DIF testing: effects of nonnormality. Appl Psychological Measure. 2008;32(0):511-526.
Sinha SK. Bootstrap tests for variance components in generalized linear mixed models. Can J Stat. 2009;37(0):219-234.
Drikvandi R, AVerbeke K. Testing variance components in balanced linear growth curve models. J Appl Stat. 2012;39(0):563-572.

Administration, Oral

Anti-Asthmatic Agents

Biological Variation, Population

Data Interpretation, Statistical

Humans

Likelihood Functions

Longitudinal Studies

Models, Statistical

Nonlinear Dynamics

Research Design

Theophylline

Time Factors

Anti-Asthmatic Agents

Theophylline

Journal Article

Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution.Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes.Diagnosing misspecification of the random-effects distribution in mixed models.Conditional mixed models with crossed random effects.Assessing robustness of designs for random effects parameters for nonlinear mixed-effects models.Extension of the SAEM algorithm for nonlinear mixed models with 2 levels of random effects.Random effects selection in linear mixed models.Nonlinear Mixed-Effects Models for PET Data.Cross-validation for nonlinear mixed effects models.Maintaining the validity of inference from linear mixed models in stepped-wedge cluster randomized trials under misspecified random-effects structures.

MEGH: A parametric class of general hazard models for clustered survival data.Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses.Evaluation of cerebral hemodynamics by transcranial Doppler ultrasonography and its correlation with intracranial pressure in an animal model of intracranial hypertension.Comparison of empirical and dynamic models for HIV viral load rebound after treatment interruption.

OpenLB
Open Library of Bioscience