TESTING FOR A TIME-DEPENDENT COEFFICIENT IN COX REGRESSION-MODEL

This paper discusses a commonly used test to detect a nonproportional hazard. The test can be viewed as an example of the method of sieves a pproach to hypothesis testing. In this framework the test can be shown to be consistent against a wide class of alternatives to proportional hazards. However there is a price exacted for such consistency. This price is that the test can not detect local alternatives of order one over the square root of the sample size.