Erosion of regression effect in a survival study

Lack of persistence, or erosion, of the regression effect is an alternative to proportional hazards of particular interest in many medical applications. Such a departure from proportional hazards is often the most likely direction in which the model may be inadequate. Questions such as, is the effect of treatment only transitory or to what extent does an initially measured prognostic variable maintain its impact, frequently arise. In the context of a simple changepoint model, we propose a test of the null hypothesis of proportional hazards against the specific alternative of erosion of the regression effect. The particular changepoint model used can be viewed as a first approximation to a more complex reality, an approximation that enables us to avoid specifically modeling the functional form that any erosion might take. Practical guidelines for carrying out the test are provided. The approach is illustrated in the context of a study on risk factors for breast cancer survival.