alexa Correction of Retransformation Bias in Nonlinear Predic
ISSN: 2155-6180

Journal of Biometrics & Biostatistics
Open Access

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Review Article

Correction of Retransformation Bias in Nonlinear Predictions on Longitudinal Data with Generalized Linear Mixed Models

Liu X1,2*, Freed MC1,2 and McCutchan PK1

1DOD Deployment Health Clinical Center, Defense Centers of Excellence, Walter Reed National Military Medical Center, Silver Spring, Maryland 20910, USA

2Department of Psychiatry, F. Edward Hebert School of Medicine,Uniformed Services University of the Health Sciences, Bethesda, Maryland 20814, USA

*Corresponding Author:
Liu X
Department of Psychiatry
Uniformed Services University of the Health Sciences
4301 Jones Bridge Road
Bethesda, MD 20814, USA
Tel: 301-295-7198
E-mail: [email protected]

Received date: June 04, 2015; Accepted date: June 17, 2015; Published date: June 24, 2015

Citation: Liu X, Freed MC, McCutchan PK (2015) Correction of Retransformation Bias in Nonlinear Predictions on Longitudinal Data with Generalized Linear Mixed Models. J Biomet Biostat 6:235. doi: 10.4172/2155-6180.1000235

Copyright: © 2015 Liu X, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are are credited.



Researchers often encounter discrete response data in longitudinal analysis. Generalized linear mixed models are generally applied to account for potential lack of independence inherent in longitudinally data. When parameter estimates are used to describe longitudinal processes, random effects, both between and within subjects, need to be retransformed in nonlinear predictions on the response data; otherwise, serious retransformation bias can arise to an unanticipated extent. This study attempts to go beyond existing work by developing a retransformation method deriving statistically robust longitudinal trajectory of nonlinear predictions. Variances of population-averaged nonlinear predictions are approximated by the delta method. The empirical illustration uses longitudinal data from the Asset and Health Dynamics among the Oldest Old study. Our analysis compares three sets of nonlinear predictions of death rate at six time points, from the retransformation method, the best linear unbiased predictor, and the fixed-effects approach, respectively. The results demonstrate that failure to retransform the random components in generalized linear mixed models results in severely biased nonlinear predictions, as well as much reduced standard error approximates.


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