NDLI: Mixed Effects versus Fixed Effects Modelling of Binary Data with Inter-subject Variability

Content Provider	Springer Nature Link
Author	Murphy, Valda Dunne, Adrian
Copyright Year	2005
Abstract	The question of whether or not a mixed effects model is required when modelling binary data with inter-subject variability and within subject correlation was reported in this journal by Yano et al. (J. Pharmacokin. Pharmacodyn. 28:389–412 [2001]). That report used simulation experiments to demonstrate that, under certain circumstances, the use of a fixed effects model produced more accurate estimates of the fixed effect parameters than those produced by a mixed effects model. The Laplace approximation to the likelihood was used when fitting the mixed effects model. This paper repeats one of those simulation experiments, with two binary observations recorded for every subject, and uses both the Laplace and the adaptive Gaussian quadrature approximations to the likelihood when fitting the mixed effects model. The results show that the estimates produced using the Laplace approximation include a small number of extreme outliers. This was not the case when using the adaptive Gaussian quadrature approximation. Further examination of these outliers shows that they arise in situations in which the Laplace approximation seriously overestimates the likelihood in an extreme region of the parameter space. It is also demonstrated that when the number of observations per subject is increased from two to three, the estimates based on the Laplace approximation no longer include any extreme outliers. The root mean squared error is a combination of the bias and the variability of the estimates. Increasing the sample size is known to reduce the variability of an estimator with a consequent reduction in its root mean squared error. The estimates based on the fixed effects model are inherently biased and this bias acts as a lower bound for the root mean squared error of these estimates. Consequently, it might be expected that for data sets with a greater number of subjects the estimates based on the mixed effects model would be more accurate than those based on the fixed effects model. This is borne out by the results of a further simulation experiment with an increased number of subjects in each set of data. The difference in the interpretation of the parameters of the fixed and mixed effects models is discussed. It is demonstrated that the mixed effects model and parameter estimates can be used to estimate the parameters of the fixed effects model but not vice versa.
Starting Page	245
Ending Page	260
Page Count	16
File Format	PDF
ISSN	1567567X
Journal	Journal of Pharmacokinetics and Pharmacodynamics
Volume Number	32
Issue Number	2
e-ISSN	15738744
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	2005-11-07
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	binary fixed effects mixed effects bias precision accuracy Laplace approximation Gaussian quadrature Pharmacology/Toxicology Pharmacy Veterinary Medicine Biochemistry Biomedical Engineering
Content Type	Text
Resource Type	Article
Subject	Pharmacology

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