Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data
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Semiparametric efficient estimation for additive hazards regression with case II interval-censored survival data Baihua He1 · Yanyan Liu1 · Yuanshan Wu2 · Xingqiu Zhao3 Received: 15 November 2018 / Accepted: 2 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Interval-censored data often arise naturally in medical, biological, and demographical studies. As a matter of routine, the Cox proportional hazards regression is employed to fit such censored data. The related work in the framework of additive hazards regression, which is always considered as a promising alternative, remains to be investigated. We propose a sieve maximum likelihood method for estimating regression parameters in the additive hazards regression with case II interval-censored data, which consists of right-, left- and interval-censored observations. We establish the consistency and the asymptotic normality of the proposed estimator and show that it attains the semiparametric efficiency bound. The finite-sample performance of the proposed method is assessed via comprehensive simulation studies, which is further illustrated by a real clinical example for patients with hemophilia. Keywords Survival analysis · Interval-censored data · Additive hazards · Sieve maximum likelihood estimator · Semiparametric efficiency bound · Empirical process
1 Introduction Interval-censoring is encountered in studies when the event of interest cannot be observed and is only known to occur within a time interval. For example, the event time to human immunodeficiency virus (HIV) positive status for transfusion-related
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Yanyan Liu [email protected] Xingqiu Zhao [email protected]
1
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
2
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430072, Hubei, China
3
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
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B. He et al.
acquired immune deficiency syndrome (AIDS) patients can never be known exactly, while the only observed information is the change of status among some monitoring times. When only one monitoring time is applied and each subject experiences the event either before or after the monitoring time, this type of data is referred to as current status or case I interval-censored data (Huang 1996; Li and Zhang 1998). When each subject is known to experience the event between a time interval, or before the first point of the time interval, or after the last point of the time interval, the resulting data are referred to as case II interval-censored data. The analysis of case II interval-censored data are more challenging than that of right censored data due to the more complicated data structure. The counting process and martingale theory which are commonly used for the analysis of right-censored data do not directly apply to interval-censored data. There have been a rich literature for the regression analysis of current status data and case II inter
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