Nonparametric Method of Estimating Survival Functions Containing Right-censored and Interval-censored Data_Journal of Biomedical Engineering

Authors：

 XUYonghong ¹ , GAOXiaohuan ¹ , WANGZhengxi ²

1. Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China;
2. Institute of information science and Engineering, Yanshan University, Qinhuangdao 066004, China;

Corresponding author：

XUYonghong, Email: xyh@ysu.edu.cn

Keywords：

SC(self-consistent) algorithm; interval-censored data; right-censored data; single imputation method; empirical distribution function

DOI：

10.7507/1001-5515.20140050

Video：

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Abstract Full text Figures/Tables Video References Cited by

Missing data represent a general problem in many scientific fields, especially in medical survival analysis. Dealing with censored data, interpolation method is one of important methods. However, most of the interpolation methods replace the censored data with the exact data, which will distort the real distribution of the censored data and reduce the probability of the real data falling into the interpolation data. In order to solve this problem, we in this paper propose a nonparametric method of estimating the survival function of right-censored and interval-censored data and compare its performance to SC (self-consistent) algorithm. Comparing to the average interpolation and the nearest neighbor interpolation method, the proposed method in this paper replaces the right-censored data with the interval-censored data, and greatly improves the probability of the real data falling into imputation interval. Then it bases on the empirical distribution theory to estimate the survival function of right-censored and interval-censored data. The results of numerical examples and a real breast cancer data set demonstrated that the proposed method had higher accuracy and better robustness for the different proportion of the censored data. This paper provides a good method to compare the clinical treatments performance with estimation of the survival data of the patients. This provides some help to the medical survival data analysis.

Citation： XUYonghong, GAOXiaohuan, WANGZhengxi. Nonparametric Method of Estimating Survival Functions Containing Right-censored and Interval-censored Data. Journal of Biomedical Engineering, 2014, 31(2): 267-272. doi: 10.7507/1001-5515.20140050 Copy

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1. 彭非,王伟.生存分析[M].北京:中国人民大学出版社,2004:40-42.
2. PETO R.Experimental survival curves for interval-censored data[J].J Roy Stat Soc Ser C-Appl Stat,1973,22(1):86-91.
3. TURNBULL B W.The empirical distribution function with arbitrary grouped,censored and truncated data[J].J Roy Statist Soc Ser B-STAT MET,1976,38(3):290-295.
4. GU G M,ZHANG C H.Asymptotic properties of self-consistent estimators based on doubly censored data[J].Ann Stat,1993,21(2):611-624.
5. 刘淑霞.区间删失资料的非参数分析方法[D].广州:中山大学,2004.
6. BELYAEV Y,KRISTROM B.Approach to analysis of self-selected interval data[J/OL].(2010-04-01)[2013-04-11].http://ssrn.com/abstract=1582853.
7. DEHGHAN M H,DUCHESNE T.A generalization of Turnbull's estimator for nonparametric estimation of the conditional survival function with interval-censored data[J].Lifetime Data Anal,2011,17(2):234-255.
8. YU Q Q,LI X L,WONG G Y C.On consistency of the self-consistency estimator of survival functions with interval-censored data[J].Scand J Stat,2000,27(1):35-44.
9. 杨军,赵宇.辅助变量不完全情形下的回归插补及其方差估计[J].系统工程理论与实践,2008,28(1):146-150.
10. 田兵.缺失数据的单一插补方法[J].阴山学刊:自然科学版,2011,25(3):17-19.
11. SHAO J,WANG H S.Confidence intervals based on survey data with nearest neighbor imputation[J].Stat Sinica,2008,18(1):281-297.
12. SUN J G.The statistical analysis of interval-censored failure time data[M].New York:Springer-Verlag,2006.
13. EFRON B.Bootstrap methods:another look at the jackknife[J].Ann Stat,1979,7(1):1-26.
14. WAN J P,ZHANG K S,CHEN H.The bootstrap and Bayesian bootstrap method in assessing bioequivalence[J].Chaos Soliton Fract,2009,41(5):2246-2249.

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