Inference for a hazard rate change point

We discuss inference based on the likelihood ratio process for a hazard rate change point. A random change of time scale transforms the empirical process into a Poisson process which enables us to derive large deviation approximations to the significance level of the likelihood ratio test. We derive approximate confidence regions for the change point and joint confidence regions for the change point and size of change. The effect of censorship is also discussed. The methods are illustrated using Stanford heart transplant data, for which the 70 days following the transplant are found to be most critical.