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.