The Change-Plane Cox Model.

We propose a projection pursuit technique in survival analysis for finding lower-dimensional projections that exhibit differentiated survival outcome. This idea is formally introduced as the change-plane Cox model, a non-regular Cox model with a change-plane in the covariate space dividing the population into two subgroups whose hazards are proportional. The proposed technique offers a potential framework for principled subgroup discovery. Estimation of the change-plane is accomplished via likelihood maximization over a data-driven sieve constructed using sliced inverse regression. Consistency of the sieve procedure for the change-plane parameters is established. In simulations the sieve estimator demonstrates better classification performance for subgroup identification than alternatives.