Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing

We propose Bayesian inference in hazard regression models where the baseline hazard is unknown, covariate e¤ects are possibly agevarying (non-proportional), and there is multiplicative frailty with arbitrary distribution. Our framework incorporates a wide variety of order restrictions on covariate dependence and duration dependence (ageing). We propose estimation and evaluation of age-varying covariate e¤ects when covariate dependence is monotone rather than proportional. In particular, we consider situations where the lifetime conditional on a higher value of the covariate ages faster or slower than that conditional on a lower value; this kind of situation is common in Corresponding Author: M. Bhattacharjee, Department of Mathematics and Statistics, Fylde College Building, Floor B, Lancaster University, Lancaster LA1 4YF, UK. Tel: +44 1524 593066. e-mail: [email protected] The authors thanks Ananda Sen, Debasis Sengupta, and participants at the IISA Joint Statistical Meeting and International Conference (Cochin, India, Jan. 2007) for their valuable comments and suggestions.