Bayesian latent variable models for mixed discrete outcomes.
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.
Dunson
David B
DB
Biostatistics Branch, National Institute of Environmental Health Sciences, MD A3-03, PO Box 12233, Research Triangle Park, NC 27709, USA. dunson1@niehs.nih.gov
Herring
Amy H
AH
D000179:Acrylates / Q000633:toxicity; D000818:Animals; D001499:Bayes Theorem; D003198:Computer Simulation; D008390:Markov Chains; D051379:Mice; D008822:Mice, Transgenic; D008954:Models, Biological; D009010:Monte Carlo Method; D009930:Organic Chemicals / Q000633:toxicity; D010212:Papilloma / Q000139:chemically induced; D016012:Poisson Distribution; D016016:Proportional Hazards Models; D011409:Propylene Glycols / Q000633:toxicity; D012878:Skin Neoplasms / Q000139:chemically induced
D000179:Acrylates; D009930:Organic Chemicals; D011409:Propylene Glycols; C027992:pentaerythrityl triacrylate