This paper considers a proportional hazards model, which allows one to
examine the extent to which covariates interact nonlinearly with an exposure
variable, for analysis of lifetime data. A local partial-likelihood technique
is proposed to estimate nonlinear interactions. Asymptotic normality of the
proposed estimator is established. The baseline hazard function, the bias and
the variance of the local likelihood estimator are consistently estimated. In
addition, a one-step local partial-likelihood estimator is presented to
facilitate the computation of the proposed procedure and is demonstrated to be
as efficient as the fully iterated local partial-likelihood estimator.
Furthermore, a penalized local likelihood estimator is proposed to select
important risk variables in the model. Numerical examples are used to
illustrate the effectiveness of the proposed procedures.Comment: Published at http://dx.doi.org/10.1214/009053605000000796 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
