Likelihood-based testing and model selection for hazard functions with unknown change-points

Abstract

The focus of this work is the development of testing procedures for the existence of change-points in parametric hazard models of various types. Hazard functions and the related survival functions are common units of analysis for survival and reliability modeling. We develop a methodology to test for the alternative of a two-piece hazard against a simpler one-piece hazard. The location of the change is unknown and the tests are irregular due to the presence of the change-point only under the alternative hypothesis. Our approach is to consider the profile log-likelihood ratio test statistic as a process with respect to the unknown change-point. We then derive its limiting process and find the supremum distribution of the limiting process to obtain critical values for the test statistic. We first reexamine existing work based on Taylor Series expansions for abrupt changes in exponential data. We generalize these results to include Weibull data with known shape parameter. We then develop new tests for two-piece continuous hazard functions using local asymptotic normality (LAN). Finally we generalize our earlier results for abrupt changes to include covariate information using the LAN techniques. While we focus on the cases of no censoring, simple right censoring, and censoring generated by staggered-entry; our derivations reveal that our framework should apply to much broader censoring scenarios.