Bayesian estimation of survival functions under stochastic precedence.
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 < or = z) > or = Pr(Y < or = 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 < or = Y) > or = 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.
Chen
Zhen
Z
Department of Biostatistics and Epidemiology, University of Pennsylvania, 625 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104, USA. zchen@cceb.upenn.edu
Dunson
David B
DB
D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D008545:Melanoma / Q000401:mortality / Q000601:surgery; D015233:Models, Statistical; D018709:Statistics, Nonparametric; D013269:Stochastic Processes; D016019:Survival Analysis; D013995:Time