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Biostatistics Advance Access published online on June 12, 2007
Biostatistics, doi:10.1093/biostatistics/kxm018
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Published by Oxford University Press 2007.

Combining assays for estimating prevalence of human herpesvirus 8 infection using multivariate mixture models

Ruth M. Pfeiffer*

Biostatistics Branch, National Cancer Institute, Division of Cancer Epidemiology and Genetics, 6120 Executive Blvd, EPS/8030, Bethesda, MD 20892-7244, USA pfeiffer{at}mail.nih.gov

Raymond J. Carroll

Department of Statistics, Texas A&M University, College Station, TX 77843-3141, USA

William Wheeler

Information Management Services Inc., Rockville, MD 20852, USA

Denise Whitby and Sam Mbulaiteye

Viral Epidemiology Branch, National Cancer Institute, DCEG, 6120 Executive Blvd, Bethesda, MD 20892-7244, USA

* To whom correspondence should be addressed.

For many diseases, it is difficult or impossible to establish a definitive diagnosis because a perfect "gold standard" may not exist or may be too costly to obtain. In this paper, we propose a method to use continuous test results to estimate prevalence of disease in a given population and to estimate the effects of factors that may influence prevalence. Motivated by a study of human herpesvirus 8 among children with sickle-cell anemia in Uganda, where 2 enzyme immunoassays were used to assess infection status, we fit 2-component multivariate mixture models. We model the component densities using parametric densities that include data transformation as well as flexible transformed models. In addition, we model the mixing proportion, the probability of a latent variable corresponding to the true unknown infection status, via a logistic regression to incorporate covariates. This model includes mixtures of multivariate normal densities as a special case and is able to accommodate unusual shapes and skewness in the data. We assess model performance in simulations and present results from applying various parameterizations of the model to the Ugandan study.

Keywords: Diagnostic tests; Mixture models; Semi-nonparametric densities; Semiparametrics; Sensitivity; Specificity; Transformations

Received August 18, 2006; revised January 17, 2007; revised March 22, 2007; accepted for publication April 17, 2007.


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