Maximum Likelihood Estimation for Cox Proportional Hazards Model with a Change Hyperplane

We propose a Cox proportional hazards model with a change hyperplane to allow the effect of risk factors to differ depending on whether a linear combination of baseline covariates exceeds a threshold. The proposed model is a natural extension of the change-point hazards model. We maximize the partial likelihood function for estimation and suggest an m-out-of-n bootstrapping procedure for inference. We establish the asymptotic distribution of the estimators and show that the estimators for the change hyperplane converge in distribution to an integrated composite Poisson process defined on a multidimensional space. Finally, the numerical performance of the proposed approach is demonstrated using simulation studies and an analysis of the Cardiovascular Health Study.