He Jie, Li Hui, Zhang Shumei, Duan Xiaogang
School of Mathematics, Beijing Normal University, Beijing, 100875, People's Republic of China.
Department of Statistics, Beijing Normal University, Beijing, 100875, People's Republic of China.
Lifetime Data Anal. 2019 Jan;25(1):128-149. doi: 10.1007/s10985-018-9426-7. Epub 2018 Feb 22.
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 [Formula: see text]-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.
半参数加法风险模型是研究右删失事件发生时间数据潜在风险因素影响的重要方法。本文研究了存在辅助亚组[公式：见正文]年生存信息情况下的加法风险模型。我们将已知的辅助信息以估计方程的形式进行表述，并基于最大经验似然法将它们与用于估计回归参数的传统得分型估计方程相结合。我们证明回归系数的新估计量渐近地服从具有可一致估计的三明治型协方差矩阵的多元正态分布，并且在渐近意义上比未纳入可用辅助信息的传统估计量严格更有效。模拟研究表明，新方法在标准误差方面比传统方法具有显著优势，并且随着纳入更多信息，所提出的估计量更具竞争力。通过一个艾滋病数据实例进行说明。
