On the unification of long-term survival models

被引:106
|
作者
Rodrigues, Josemar [1 ]
Cancho, Vicente G. [2 ]
de Castro, Mario [2 ]
Louzada-Neto, Francisco [1 ]
机构
[1] Univ Fed Sao Carlos, Dept Estat, BR-13565905 Sao Carlos, SP, Brazil
[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil
关键词
FRACTION;
D O I
10.1016/j.spl.2008.10.029
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this paper we extend the long-term survival model proposed by Chen et al. [Chen, M.-H., Ibrahim, J.G., Sinha, D., 1999. A new Bayesian model for survival data with a surviving fraction. journal of the American Statistical Association 94, 909-919] via the generating function of a real sequence introduced by Feller [Feller, W., 1968. An Introduction to Probability Theory and its Applications, third ed., vol. 1, Wiley, New York]. A direct consequence of this new formulation is the unification of the long-term survival models proposed by Berkson and Gage [Berkson, J., Gage, R.P., 1952. Survival cure for cancer patients following treatment. journal of the American Statistical Association 47, 501-515] and Chen et al. (see citation above). Also, we show that the long-term survival function formulated in this paper satisfies the proportional hazards property if, and only if, the number of competing causes related to the occurrence of an event of interest follows a Poisson distribution. Furthermore, a more flexible model than the one proposed by Yin and Ibrahim [Yin, G., Ibrahim, J.G., 2005. Cure rate models: A unified approach. The Canadian journal of Statistics 33, 559-570] is introduced and, motivated by Feller's results, a very useful competing index is defined. (c) 2008 Elsevier B.V. All rights reserved.
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页码:753 / 759
页数:7
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