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Biostatistics Advance Access originally published online on January 8, 2009
Biostatistics 2009 10(2):374-389; doi:10.1093/biostatistics/kxn044
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© 2009 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Bias in 2-part mixed models for longitudinal semicontinuous data

Li Su*, Brian D. M. Tom and Vernon T. Farewell

Medical Research Council, Biostatistics Unit, Robinson Way, Cambridge CB2 0SR, UK li.su{at}mrc-bsu.cam.ac.uk

* To whom correspondence should be addressed.

Semicontinuous data in the form of a mixture of zeros and continuously distributed positive values frequently arise in biomedical research. Two-part mixed models with correlated random effects are an attractive approach to characterize the complex structure of longitudinal semicontinuous data. In practice, however, an independence assumption about random effects in these models may often be made for convenience and computational feasibility. In this article, we show that bias can be induced for regression coefficients when random effects are truly correlated but misspecified as independent in a 2-part mixed model. Paralleling work on bias under nonignorable missingness within a shared parameter model, we derive and investigate the asymptotic bias in selected settings for misspecified 2-part mixed models. The performance of these models in practice is further evaluated using Monte Carlo simulations. Additionally, the potential bias is investigated when artificial zeros, due to left censoring from some detection or measuring limit, are incorporated. To illustrate, we fit different 2-part mixed models to the data from the University of Toronto Psoriatic Arthritis Clinic, the aim being to examine whether there are differential effects of disease activity and damage on physical functioning as measured by the health assessment questionnaire scores over the course of psoriatic arthritis. Some practical issues on variance component estimation revealed through this data analysis are considered.

Keywords: Correlated random effects; Excess zeros; Outcome-dependent sampling; Repeated measures

Received February 25, 2008; revised October 7, 2008; revised October 10, 2008; revised October 27, 2008; accepted for publication November 21, 2008.


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