Maximum weighted partial likelihood estimators for the Cox model
New estimators for Cox regression that maximize a weighted version of the partial likelihood are considered. Their asymptotic properties on the model are sketched. Estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency. The results of a small simulation study are included. The estimators are applied to a well-known data set. The possible influence of an outlying observation on the Cox estimator can be of any magnitude. Individuals who survive longest have a high potential of being influential. In analogy with weighted linear rank tests, we introduce estimators of the regression coefficients that maximize a weighted partial likelihood. For instance, by using weights proportional to the number at risk, one obtains a Wilcoxon-type estimator. This estimator has bounded influence (provided the covariate space is compact), and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the Wilcoxon test. Asymptotic prop...