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.
Department of Biostatistics and Epidemiology, University of Pennsylvania, 625 Blockley Hall, 423 Guardian Drive, Philadelphia, PA 19104, USA. zchen@cceb.upenn.edu
Zhen
Z
Chen
David B
DB
Dunson
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