Functional ANOVA modeling for proportional hazards regression

Abstract

The logarithm of the relative risk function in a proportional hazards model involving one or more possibly time-dependent covariates is treated as a specified sum of a constant term, main effects, and selected interaction terms. Maximum partial likelihood estimation is used, where the maximization is taken over a suitably chosen finite-dimensional estimation space, whose dimension increases with the sample size and which is constructed from linear spaces of functions of one covariate and their tensor products. The $L_2$ rate of convergence for the estimate and its ANOVA components is obtained. An adaptive numerical implementation is discussed, whose performance is compared to (full likelihood) hazard regression both with and without the restriction to proportional hazards.