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Biostatistics 2005 6(1):11-25; doi:10.1093/biostatistics/kxh025
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Biostatistics Vol. 6 No. 1 © Oxford University Press 2005; all rights reserved.

Bayesian latent variable models for mixed discrete outcomes

David B. Dunson*

Biostatistics Branch, National Institute of Environmental Health Sciences, MD A3-03, PO Box 12233, Research Triangle Park, NC 27709, USA dunson1{at}niehs.nih.gov

Amy H. Herring

Department of Biostatistics, The University of North Carolina, Chapel Hill, NC, USA

* To whom correspondence should be addressed.

In studies of complex health conditions, mixtures of discrete outcomes (event time, count, binary, ordered categorical) are commonly collected. For example, studies of skin tumorigenesis record latency time prior to the first tumor, increases in the number of tumors at each week, and the occurrence of internal tumors at the time of death. Motivated by this application, we propose a general underlying Poisson variable framework for mixed discrete outcomes, accommodating dependency through an additive gamma frailty model for the Poisson means. The model has log-linear, complementary log-log, and proportional hazards forms for count, binary and discrete event time outcomes, respectively. Simple closed form expressions can be derived for the marginal expectations, variances, and correlations. Following a Bayesian approach to inference, conditionally-conjugate prior distributions are chosen that facilitate posterior computation via an MCMC algorithm. The methods are illustrated using data from a Tg.AC mouse bioassay study.

Keywords: Discrete time survival; Joint model; Latent variables; Multiple binary outcomes; Poisson counts; Proportional hazards; Random effects; Tumor multiplicity


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