An Additive–Multiplicative Cox–Aalen Regression Model

Abstract

We propose an additive–multiplicative intensity model that extends the Cox regression model as well as the additive Aalen model. Instead of having a simple baseline intensity the extended model uses an additive Aalen model as its covariate dependent baseline. Approximate maximum likelihood estimators of the baseline intensity functions and the relative risk parameters of the Cox model are suggested by solving the score equations. The derived estimator is efficient. We establish the large sample properties of the estimator. The model provides a simple pragmatic way of including time‐varying covariate effects.