Additive hazards model with auxiliary subgroup survival information

The semiparametric additive hazards model is an important way for studying the effect of potential risk factors for right-censored time-to-event data. In this paper, we study the additive hazards model in the presence of auxiliary subgroup t∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t^*$$\end{document}-year survival information. We formulate the known auxiliary information in the form of estimating equations, and combine them with the conventional score-type estimating equations for the estimation of the regression parameters based on the maximum empirical likelihood method. We prove that the new estimator of the regression coefficients follows asymptotically a multivariate normal distribution with a sandwich-type covariance matrix that can be consistently estimated, and is strictly more efficient, in an asymptotic sense, than the conventional one without incorporation of the available auxiliary information. Simulation studies show that the new proposal has substantial advantages over the conventional one in terms of standard errors, and with the accommodation of more informative information, the proposed estimator becomes more competing. An AIDS data example is used for illustration.