Testing for a Changepoint in the Cox Survival Regression Model

The Cox regression model is a popular model for analyzing the relationship between a covariate and a survival endpoint. The standard Cox model assumes that the covariate effect is constant across the entire covariate domain. However, in many epidemiological and other applications, there is interest in considering the possibility that the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. In this article, we discuss testing for a threshold effect in the case where the potential threshold value is unknown. We consider a maximum efficiency robust test (MERT) of linear combination form and supremum type tests. We present the relevant theory, present a simulation study comparing the power of various test statistics, and illustrate the use of the tests on data from the Nurses Health Study (NHS) concerning the relationship between chronic exposure to particulate matter of diameter 10 m or less (PM ) and fatal myocardial infarction. We also discuss power calculation for studies aimed at investigating the presence of a threshold effect, and present an illustrative power calculation. The simulation results suggest that the best overall choice of test statistic is either the full supremum statistic or the three-point supremum type statistic. The power calculation methodology will be useful in study planning. Matlab software for performing the tests and power calculation is available by download from the first author's website.