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Biostatistics Advance Access originally published online on June 22, 2009
Biostatistics 2009 10(4):640-658; doi:10.1093/biostatistics/kxp019
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© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

A semiparametric 2-part mixed-effects heteroscedastic transformation model for correlated right-skewed semicontinuous data

Huazhen Lin

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People Republic of China

Xiao-Hua Zhou*

HSR&D Center of Excellence, VA Puget Sound Health Care System, Seattle, WA 98108, USA and Department of Biostatistics, University of Washington, Seattle, WA 98195, USA azhou{at}u.washington.edu

* To whom correspondence should be addressed.

In longitudinal or hierarchical structure studies, we often encounter a semicontinuous variable that has a certain proportion of a single value and a continuous and skewed distribution among the rest of values. In this paper, we propose a new semiparametric 2-part mixed-effects transformation model to fit correlated skewed semicontinuous data. In our model, we allow the transformation to be nonparametric. Fitting the proposed model faces computational challenges due to intractable numerical integrations. We derive the estimates for the parameter and the transformation function based on an approximate likelihood, which has high-order accuracy but less computational burden. We also propose an estimator for the expected value of the semicontinuous outcome on the original scale. Finally, we apply the proposed methods to a clinical study on effectiveness of a collaborative care treatment on late-life depression on health care costs.

Keywords: Laplace approximation; Mixed effects; Right skewed; Semicontinuous; Semiparametric; Transformation model

Received August 25, 2008; revised April 28, 2009; accepted for publication May 20, 2009.


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