Nonparametric and semiparametric estimators of restricted mean survival time under length-biased sampling
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Nonparametric and semiparametric estimators of restricted mean survival time under length-biased sampling Yifan He1 · Yong Zhou2 Received: 9 September 2018 / Accepted: 30 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Restricted mean survival time is often of direct interest in epidemiologic studies involving censored survival time. In this article, we propose the nonparametric and semiparametric estimators of the mean restricted to the preassigned interval with censored length-biased data. Based on the peculiarity of length-biased data, the auxiliary information that truncation time and residual time have the same distribution is taken into account for improving estimation efficiency. For two-sample comparison, we construct two tests which are easy to implement. We also derive the asymptotic properties for the proposed estimators and test statistics. In simulation studies, some simulations are conducted to compare the performances of several approaches to estimate restricted mean and to assess the test statistics. In addition, our methods are applied to a real data example and some interesting results are presented. Keywords Restricted mean survival time · Length-biased sampling · Right-censored data · Truncated and residual time · Treatment effect
1 Introduction A central problem in medical studies is comparing the survival outcomes of different treatments. One desirable approach on this matter is to compare the average survival time of all treatment groups. In practice, the treatments are assigned to patients
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Yong Zhou [email protected] Yifan He [email protected]
1
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
2
Key Laboratory of Advanced Theory and Application in Statistics and Data Science, Ministry of Education and Academy of Statistics and Interdisciplinary Sciences and School of Statistics, East China Normal University, Shanghai 200062, China
123
Y. He, Y. Zhou
non-randomly and many lifetimes are censored. As a result, it is not appropriate to use simple sample average. If we choose mean lifetime, many estimators of survival function which need to be integrand are not defined beyond the largest observation. Its integral interval could cause problems. Neither approach seems satisfactory. One available solution to this problem is to estimate the mean restricted to some preassigned intervals, where the upper limit can be the longest observed time or preassigned by the investigator. In addition to its statistical meaning, the restricted mean lifetime is also a very meaningful quantity in the research about solid organ transplant setting (Zhang and Schaubel 2012). Much work had been done on estimating the restricted mean lifetime, most of which focused on the adjusted survival function associated with confounding variables. Karrison (1987) incorporated covariates into the estimator of restricted mean and built piecewise exponential models. Zucker (1998) described a simplified procedure for imple
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