Estimating the Relative Risk with Censored Data

Abstract

We investigate a class of nonparametric estimators of relative risk in the two-sample case of the proportional hazards model for censored data. The asymptotic distribution of these estimators is derived using influence functions. The optimal estimator in this class has the same influence functions and the same asymptotic distribution as the maximum partial likelihood estimator of Cox (1972). The behavior of the influence functions is discussed briefly, and the last section presents two examples from the literature.

Key Words:

• Relative risk
• Proportional hazards model
• Censored data
• Two-sample problem
• Influence function