Global Partial Likelihood for Nonparametric Proportional Hazards Models

As an alternative to the local partial likelihood method of Tibshirani and Hastie and Fan, Gijbels, and King. a global partial likelihood method is proposed to estimate the covariate effect in a nonparametric proportional hazards model, lambda(t vertical bar x) = exp{psi(x)}lambda(0)(t). The estimator, (psi) over cap (x), reduces to the Cox partial likelihood estimator if the covariate is discrete. The estimator is shown to be consistent and semiparametrically efficient for linear functionals of psi(x). Moreover, Breslow-type estimation of the cumulative baseline hazard function, using the proposed estimator (psi) over cap (x), is proved to be efficient. The asymptotic bias and variance are derived under regularity conditions. Computation of the estimator involves an iterative but simple algorithm. Extensive simulation studies provide evidence supporting the theory. The method is illustrated with the Stanford heart transplant data set. The proposed global approach is also extended to a partially linear proportional hazards model and found to provide efficient estimation of the slope parameter. This article has the supplementary materials online.