Math @ Duke

Publications [#257926] of David B. Dunson
search arxiv.org.Papers Published
 Chen, Z; Dunson, DB, Bayesian estimation of survival functions under stochastic precedence,
Lifetime Data Analysis, vol. 10 no. 2
(2004),
pp. 159173 [doi]
(last updated on 2018/10/22)
Abstract: When estimating the distributions of two random variables, X and Y; investigators often have prior information that Y tends to be bigger than X. To formalize this prior belief, one could potentially assume stochastic ordering between X and Y, which implies Pr(X ≤ z) ≥ Pr(Y ≥ z) for all z in the domain of X and Y. Stochastic ordering is quite restrictive, though, and this article focuses instead on Bayesian estimation of the distribution functions of X and Y under the weaker stochastic precedence constraint, Pr(X ≤ Y) ≥ 0.5. We consider the case where both X and Y are categorical variables with common support and develop a Gibbs sampling algorithm for posterior computation. The method is then generalized to the case where X and Y are survival times. The proposed approach is illustrated using data on survival after tumor removal for patients with malignant melanoma.


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