左截断双删失数据下可加可乘风险率模型的估计
|
摘要
在生存分析中,可加可乘风险率模型常用来研究协变量对初始事件和终止事件之间持续时间的影响效应。在本文中,我们考虑了在初始事件存在部分区间删失,同时终止事件存在左截断右删失的情形下,持续时间的可加可乘风险率模型的估计问题。我们提出了一个两阶段估计过程来估计模型的回归参数。并通过模拟分析验证了估计的大样本性质。最后利用该方法分析了恶性黑色素瘤手术治疗数据。
In survival studies,additive-multiplicative hazards model is often used to analyze covariate effects on the duration time,defined as elapsed time between the initial event and the terminal event.In this article,we consider the situation when the initial event suffers partly interval censoring and the terminal event suffers left truncation and right censoring.We proposed a two-step estimation procedure for estimating the regression coefficients of the additive-multiplicative hazards model on the duration time.Simulation studies are conducted to investigate the performance of the proposed estimator.The proposed method is applied to the malignant melanoma surgery treatment data.
In survival studies,additive-multiplicative hazards model is often used to analyze covariate effects on the duration time,defined as elapsed time between the initial event and the terminal event.In this article,we consider the situation when the initial event suffers partly interval censoring and the terminal event suffers left truncation and right censoring.We proposed a two-step estimation procedure for estimating the regression coefficients of the additive-multiplicative hazards model on the duration time.Simulation studies are conducted to investigate the performance of the proposed estimator.The proposed method is applied to the malignant melanoma surgery treatment data.
引文
[1]Cox D R.Regression models and life tables(with discussion)[J],Journal of the Royal Statistical Society,1972,34:187-220.
[2]Lin D Y,Zhiliang Ying.Semiparametric analysis of the additive risk model[J].Biometrics,1994,81:61-71.
[3]Sun L,Kim Y,Sun J.Regression analysis of doubly censored failure time data using the additive hazards model[J].Biometrics,2004,60:637-643.
[4]Guadalupe Gomez,Luz Calle M.Non-parametric estimation with doubly censored data[J].Journal of Applied Statistics,1999,26(1):45-58.
[5]Turnbull B W.The empirical distribution function with arbitrarily grouped censored and truncated data[J].Journal of the Royal Statistical Society,1976,38:290-295.
[6]Frydman H.A note on nonparametric estimation of the distribution function from interval-censored and truncated observations[J].Journal of the Royal Statistical Society,1994,56(1):71-74.
[7]Hudgens M G.On nonparametric maximum likelihood estimation with interval censoring and left truncation[J].Journal of the Royal Statistical Society,2005,67(4):573-587.
[8]Pao-Sheng Shen.Estimation in the Cox proportional hazards model with doubly censored and truncated data[J].Journal of Statistical Computation and Simulation,2011,81:1717-1725.
[9]Pao-Sheng Shen.Additive hazards model with truncated and doubly censored data[J].Journal of Applied Statistics,2013,40(7):1520-1532.
[10]Lin D Y,Zhiliang Ying.Semiparametric analysis of general additive-multiplicative hazard models for counting processes[J].The Annals of Statistics,1995,23(5):1712-1734.
[11]Zhao X,Lim H,Sun J.Estimating equation approach for regression analysis of failure time data in the presence of interval-censoring[J].Journal of Statistical Planning and Inference,2005,129:145-157.
[12]Shick A,Yu Q.Consistency of the GMLE with mixed case interval-censored data[J].Board of the Foundation of the Scandinavian Journal of Statistics,2000,27:45-55.
[13]Song S.Estimation with univariate'mixed case'interval censored data[J].Sinica,2004,14:269-282.
[14]Andersen P K,Borgan O,Gill R D,Keiding N.Statistical Models Based on Counting Processes[M].Springer-Verlag,1993.
[2]Lin D Y,Zhiliang Ying.Semiparametric analysis of the additive risk model[J].Biometrics,1994,81:61-71.
[3]Sun L,Kim Y,Sun J.Regression analysis of doubly censored failure time data using the additive hazards model[J].Biometrics,2004,60:637-643.
[4]Guadalupe Gomez,Luz Calle M.Non-parametric estimation with doubly censored data[J].Journal of Applied Statistics,1999,26(1):45-58.
[5]Turnbull B W.The empirical distribution function with arbitrarily grouped censored and truncated data[J].Journal of the Royal Statistical Society,1976,38:290-295.
[6]Frydman H.A note on nonparametric estimation of the distribution function from interval-censored and truncated observations[J].Journal of the Royal Statistical Society,1994,56(1):71-74.
[7]Hudgens M G.On nonparametric maximum likelihood estimation with interval censoring and left truncation[J].Journal of the Royal Statistical Society,2005,67(4):573-587.
[8]Pao-Sheng Shen.Estimation in the Cox proportional hazards model with doubly censored and truncated data[J].Journal of Statistical Computation and Simulation,2011,81:1717-1725.
[9]Pao-Sheng Shen.Additive hazards model with truncated and doubly censored data[J].Journal of Applied Statistics,2013,40(7):1520-1532.
[10]Lin D Y,Zhiliang Ying.Semiparametric analysis of general additive-multiplicative hazard models for counting processes[J].The Annals of Statistics,1995,23(5):1712-1734.
[11]Zhao X,Lim H,Sun J.Estimating equation approach for regression analysis of failure time data in the presence of interval-censoring[J].Journal of Statistical Planning and Inference,2005,129:145-157.
[12]Shick A,Yu Q.Consistency of the GMLE with mixed case interval-censored data[J].Board of the Foundation of the Scandinavian Journal of Statistics,2000,27:45-55.
[13]Song S.Estimation with univariate'mixed case'interval censored data[J].Sinica,2004,14:269-282.
[14]Andersen P K,Borgan O,Gill R D,Keiding N.Statistical Models Based on Counting Processes[M].Springer-Verlag,1993.