非混合治癒模型之統計推論

Statistical Inference for Cure Models-The Non-mixture Approach

陳瀅竹(Ying-jhu Chen)

指導教授 ： 王維菁

國立交通大學/理學院/統計學研究所/碩士(2009年)

https://doi.org/10.6842/NCTU.2009.00264

摘要

在存活分析中，若在實驗期間能無限延長下，有部分的資料能夠永久存活或者不會經歷到所感興趣的事件發生，必須考慮使用治癒模型。本論文主要探討的是Tsodikov (1998) 所提出的非混合治癒模型，討論在數學模型的架構下代表的生物意義，藉模擬討論在有母數與無母數的統計推論方法中對治癒率以及發病時間函數參數估計的影響。最後在有解釋變數對模型的影響中，提供符合比例風險迴歸模型(PH) 與加速失敗時間模式(accelerated failure time model)的圖型診斷方法。

關鍵字

治癒率 ； 非混合治癒模型 ； 模型診斷

並列摘要

Cure models are survival models which allows for the existence of cure despite of long-term follow-up. In this thesis, we consider statistic inference for cure models based on the non-mixture approach proposed by Tsodikov(1998). This model has some interesting biological interpretations. Parametric and semi-parametric methods will be investigated. We propose a model diagnostic tool to verify the form of regression models.

並列關鍵字

Cure rate ； Non-mixture model ； Model checking

參考文獻

[1] J. Berkson and R. P. Gage (1952). Survival Curve for Cancer Patients Following Treatment. J. Amer. Statist. Assoc. 47, 501-515.

[3] Tsodikov, A. D. (1998). A Proportional Hazards Model Taking Account of Long-Term Survivors. Biometrics 54, 1508-1516.

[4] Tsodikov, A. D. (2001). Estimating of Survival Based on Proportional Hazards When Cure is a Possibility. Mathematical and Computer modelling. 33, 1227-1236.

[5] Tsodikov, A. D., Ibrahim, J. G. and Yakovlev A. Y. (2003). Estimating Cure Rates From Survival Data : An Alternative to Two-Component Mixture Models . E. J. Am. Statist. Assoc. 98, 1063-1078.

[2] Boag, JW. (1949). Maximum Likelihood Estimates of the Proportion of Patients Cured by Cancer Therapy. J. Royal Statist. Soc., Series B 11:15-44.