Bayesian isotonic regression and trend analysis

1 SUMMARY. In many applications, the mean of a response variable can be assumed to be a non-decreasing function of a continuous predictor, controlling for covariates. In such cases, interest often focuses on estimating the regression function, while also assessing evidence of an association. This article proposes a new framework for Bayesian isotonic regression and order restricted inference based on a constrained piecewise linear model with unknown knot locations, corresponding to thresholds in the regression function. The non-decreasing constraint is incorporated through a prior distribution consisting of a product mixture of point masses (accounting for flat regions) and truncated autoregressive normal densities. An MCMC algorithm is used to obtain a smooth estimate of the regression function and posterior probabilities of an association for different regions of the predictor. Generalizations to categorical outcomes and multiple predictors are described, and the approach is applied to data from a study of pesticide exposure and birth weight