Statistica Sinica 24 (2014), 121-146

SEMIPARAMETRIC ESTIMATION OF TREATMENT

EFFECTS IN TWO SAMPLE PROBLEMS

WITH CENSORED DATA

Fangfang Bai$^{1,2}$, Jian Huang$^{3}$ and Yong Zhou$^{2,4}$

$^1$University of International Business and Economics,

$^2$Chinese Academy of Sciences, $^3$University of Iowa

and $^4$Shanghai University of Finance and Economics

Abstract: 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 semiparametric 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.

Key words and phrases: Treatment effect, semiparametric model, estimating equation, censored data, two sample problem.