The Cox proportional hazards model with change point: an epidemiologic application

In this paper, we develop the Cox proportional hazards model with special structured time-dependent covariates in the context of prospective epidemiologic studies. Our model possesses the following two features: (i) different relative risk parameters are allowed for early versus late onset of the disease of interest; (ii) an additional parameter is introduced so that specification is not required for the time (age) at which a change of the magnitude of the relative risks takes place, the so-called change point. Some difficulties with statistical inference for the proposed model are briefly discussed, and the large-sample distribution of a test for no change point is derived. As an illustration, we apply the model to a set of data gathered on a group of white male medical students of The Johns Hopkins Medical School enrolled between 1948 and 1964. We examine the hypothesis that the effect of reactivity to the cold pressor test may vary with early versus late onset of hypertension.