In biomedical studies, there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable, adjusting for covariates. For a k-level predictor, one typically uses either a k-1 degree of freedom (df) test or a single df trend test, which requires scores for the di erent levels of the predictor. In the absence of knowledge of a parametric form for the response function, one can incorporate monotonicity constraints to improve the e ciency of tests of association. This article proposes a general Bayesian approach for inference on order constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational di culties, we propose to map draws from an unconstrained posterior density using an isotonic regression transformation. This approach allows flat regions over which increases in the level of a predictor have no effect. Bayes factors for assessing ordered trends can be computed based on the output from a Gibbs sampling algorithm. Results from a simulation study are presented and the approach is applied to data from a time to pregnancy study.

Keywords: Bayes factor; Constrained estimation; Categorical covariates; Gibbs sampling; Isotonic regression; Monotonicity; Simple ordering; Trend test

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