Bayesian Isotonic Regression and Trend Analysis

• Activity Number: 290
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section*
• Author(s): Brian Neelon*+ and David Dunson
• Affiliation(s): University of North Carolina and National Institute of Environmental Health Sciences
• Keywords: Constrained Estimation ; Isotonic Regression ; Monotonicity ; Order Restriction ; Piecewise Linear ; Trend Test

Abstract

In many applications, the mean of a response variable is known to be a non-increasing (or non-decreasing) function of a predictor (e.g., dose), and interest focuses on assessing evidence of no trend and estimating the mean response function. This paper proposes a new framework for Bayesian isotonic regression based on a constrained piecewise linear model with unknown knot locations. The non-increasing constraint is incorporated through a prior distribution, which is parameterized according to the prior probability of no trend and the prior expectation of the regression coefficients. The prior is formulated within an underlying normal framework, which results in efficient posterior computation using a Metropolis-Hastings algorithm. The approach is easily generalizable to multiple predictors and non-Gaussian outcomes in the exponential family. The methods are illustrated through application to binary response data from a bioassay study.