SEMIPARAMETRIC ESTIMATION OF TREATMENT EFFECTS IN TWO SAMPLE PROBLEMS WITH CENSORED DATA

The problem of estimating treatment effects with censored two-sample data is of importance in survival analysis and has received much attention in the literature. A common procedure for dealing with censoring is the inverse probability weighted method. However, this method only uses information from uncensored data and can suffer from loss of efficiency. In this paper, we propose a unified semi-parametric estimating equation approach to estimate various types of treatment effects with censored data, including the mean difference between two populations, the difference between two survival times at a given point, the probability that the survival time from one population is greater than that from the other, and the difference in mean residual life times, among others. Our approach uses all the available data, thus it typically leads to gains in efficiency as compared with the existing methods. We study the theoretical properties of the proposed estimator and derive its consistent variance estimator. Our simulation studies demonstrate that the proposed method tends to work better than the existing ones in finite sample settings. We also analyze a data set to illustrate its application.