Functional ANOVA Modeling for Proportional Hazards Regression
by Jianhua Z. Huang, Charles Kooperberg, Charles J. Stone and Young K. Truong
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.
Key words and phrases. Convergence rates, Cox model, partial likelihood,
splines, tensor product.