Shrinkage priors for isotonic probability vectors and binary data modeling, with applications to dose-response modeling.

ABSTRACT: Motivated by the need to model dose-response or dose-toxicity curves in clinical trials, we develop a new horseshoe-based prior for Bayesian isotonic regression modeling a binary outcome against an ordered categorical predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The set of differences between outcome probabilities in consecutive categories of the predictor is equipped with a multivariate prior having support over simplex. The Dirichlet distribution, which can be derived from a normalized sum of independent gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that the resulting posterior is prone to underflow and other numerical instabilities, even

SUBMITTER: Boonstra PS 

PROVIDER: S-EPMC11737611 | biostudies-literature | 2024 Jul-Aug

REPOSITORIES: biostudies-literature