# Bayesian estimation of survival functions under stochastic precedence.

Journal Article (Journal Article)

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.

### Full Text

### Duke Authors

### Cited Authors

- Chen, Z; Dunson, DB

### Published Date

- June 2004

### Published In

### Volume / Issue

- 10 / 2

### Start / End Page

- 159 - 173

### PubMed ID

- 15293630

### Electronic International Standard Serial Number (EISSN)

- 1572-9249

### International Standard Serial Number (ISSN)

- 1380-7870

### Digital Object Identifier (DOI)

- 10.1023/b:lida.0000030201.12943.13

### Language

- eng