Abstract
We propose a prior probability model for two distributions that are ordered according to a stochastic precedence constraint, a weaker restriction than the more commonly utilized stochastic order constraint. The modeling approach is based on structured Dirichlet process mixtures of normal distributions. Full inference for functionals of the stochastic precedence constrained mixture distributions is obtained through a Markov chain Monte Carlo posterior simulation method. A motivating application involves study of the discriminatory ability of continuous diagnostic tests in epidemiologic research. Here, stochastic precedence provides a natural restriction for the distributions of test scores corresponding to the non-infected and infected groups. Inference under the model is illustrated with data from a diagnostic test for Johne’s disease in dairy cattle. We also apply the methodology to the comparison of survival distributions associated with two distinct conditions, and illustrate with analysis of data on survival time after bone marrow transplantation for treatment of leukemia.
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Acknowledgements
This work was supported in part by the National Science Foundation under award DEB 0727543. The author thanks two reviewers and the guest editors of the special issue for useful comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Kottas, A. Bayesian semiparametric modeling for stochastic precedence, with applications in epidemiology and survival analysis. Lifetime Data Anal 17, 135–155 (2011). https://doi.org/10.1007/s10985-010-9164-y
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DOI: https://doi.org/10.1007/s10985-010-9164-y