Exact Percentage Points of the Likelihood-Ratio Test for a Change-Point Hazard-Rate Model

Abstract

We wish to test that the hazard rate of survival or failure-time data is constant against the alternative of a change in hazard after an unspecified time. The likelihood ratio is unbounded but the exact null distribution of a restricted likelihood-ratio test statistic is found. This distribution is not affected by Type II censoring but it does depend very strongly on the interval in which the unknown change-point is assumed to lie. Some exact percentage points are given which are much larger than simulated points that have been reported in the literature.