Math @ Duke

Publications [#257918] of David B. Dunson
search www.stat.duke.edu.Papers Published
 Dunson, DB; Neelon, B, Bayesian inference on orderconstrained parameters in generalized linear models,
Biometrics, vol. 59 no. 2
(2003),
pp. 286295 [doi]
(last updated on 2018/08/18)
Abstract: 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 klevel predictor, one typically uses either a k  1 degree of freedom (df) test or a single df trend test, which requires scores for the different 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 efficiency of tests of association. This article proposes a general Bayesian approach for inference on orderconstrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, 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 timetopregnancy study.


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