September 2005
In biomedical studies that collect event time data, it is often appropriate to assume non-decreasing hazards across dose groups, though dose effects may vary with time. Motivated by this application, we propose a Bayesian approach for order restricted inference using an additive hazard model with time-varying coefficients. In order to make inferences on equalities versus increases in hazard functions, a prior is chosen for the time-varying coefficients that assigns positive probability to no dose effect while restricting coefficients to be non-negative. By using a high-dimensional piecewise constant model and smoothing the functions by coupling Markov beta and gamma processes, we obtain a flexible and computationally tractable approach for identifying sets of dose and age values at which hazards are increased. This approach can also be used to estimate dose response and survival curves. The methods are illustrated through application to data from a toxicology study.
Keywords: Additive hazards; Bayesian hypothesis testing; Bioassay; Gibbs sampler; Markov prior process; Order restricted inference; Point mass; Survival analysis.
The manuscript is available in PDF formats.