Testing for a Change in the Hazard Rate with Staggered Entry

Abstract

We develop a likelihood-ratio based procedure for testing for a change in the hazard rate of the patients' survival distribution when the patients enter the trial at random times. We show that the profile log-likelihood ratio process converges weakly to a non-stationary Gaussian process and obtain the upper percentiles of the supremum of the limiting process using an approximation for the tail distribution of the supremum of the Ornstein–Uhlenbeck process. We also discuss the power of the test.

Key Words:

• Change-point
• Likelihood ratio test
• Gaussianprocesses
• Monte Carlo simulation
• Poisson process

Acknowledgments

The research of the first two authors was supported by the National Science Foundation and US Army Research Office.