Bayesian hierarchical multiresolution Hazard model for the study of time-dependent failure patterns in early stage breast cancer

Abstract

The multiresolution estimator, developed originally in engineering ap-plications as a wavelet-based method for density estimation, has been recently ex-tended and adapted for estimation of hazard functions (Bouman et al. 2005, 2007). Using the multiresolution hazard (MRH) estimator in the Bayesian framework, we are able to incorporate any a priori desired shape and amount of smoothness in the hazard function. The MRH method's main appeal is in its relatively simple estimation and inference procedures, making it possible to obtain simultaneous condence bands on the hazard function over the entire time span of interest. Moreover, these condence bands properly re ect the multiple sources of uncer-tainty, such as multiple centers or heterogeneity in the patient population. Also, rather than the commonly employed approach of estimating covariate e ects and the hazard function separately, the Bayesian MRH method estimates all of these parameters jointly, thus resulting in properly adjusted inference about any of the quantities. In this paper, we extend the previously proposed MRH methods (Bouman et al. 2005, 2007) into the hierarchical multiresolution hazard setting (HMRH), to ac-commodate the case of separate hazard rate functions within each of several strata as well as some common covariate ects across all strata while accounting for within-stratum correlation. We apply this method to examine patterns of tu-mor recurrence after treatment for early stage breast cancer, using data from two large-scale randomized clinical trials that have substantially in uenced breast cancer treatment standards. We implement the proposed model to estimate the recurrence hazard and explore how the shape diers between patients grouped by a key tumor characteristic (estrogen receptor status) and treatment types, af-ter adjusting for other important patient characteristics such as age, tumor size and progesterone level. We also comment on whether the hazards exhibit non-monotonic patterns consistent with recent hypotheses suggesting multiple hazard change-points at specic time landmarks. © 2007 International Society for Bayesian Analysis.