易感受性之區間設限資料在轉換模型的核函數估計方法

隨著醫學科技的進步，臨床醫學研究的發展也越來越蓬勃，藉由臨床研究所獲得的區間設限資料也越來越多。實務上臨床研究追蹤病患的狀況，未能得知確切發病(事件發生)時間，常觀察到發生時間在某個區間時間。此外，感興趣的事件未發生時，一般將此種資料稱為不易感受性的資料，也可稱為治癒資料。因此考慮混合治癒模型並使用邏輯斯迴歸模型對不易感受性的比例做估計。本篇考慮使用線性轉換模型分析不易感受性區間設限資料，在未知基底風險函數(Unknown baseline hazard function)的估計利用核函數(Kernel)做平滑估計，並考慮EM演算法和牛頓迭代法估計參數，並經由模擬驗證。

關鍵字

區間設限；不易感受性；線性轉換模型； EM演算法；核函數

並列摘要

As time progresses, continuous development, there are more and more interval censoring data with clinical trials. Sometimes, it is hard to observe the exact time of event, but we know the observed failure time falls within a time period. In this thesis, we consider mixture cure models for interval censored data with a cured subgroup, where subjects in this subgroup are not susceptible to the event of interest. We suppose logistic regression to estimate cure proportion. In addition, we consider semiparametric transformation models to analysis the event data. We focus on reparametrizing the step function of unknown baseline hazard function by the logarithm of its jump sizes in Chapter 3, and a kernel-based approach for smooth estimation of unknown baseline hazard function in Chapter 4. The EM algorithm is developed for the estimation and simulation studies are conducted.

並列關鍵字

Interval Censoring ； Cure Model ； Transformation Model ； EM Algorithm ； Kernel

參考文獻

Wand, M. P. and Jones, M. C. Jones (1995). Kernel Smoothing. Chapman and Hall, London.

Chen, K., Jin, Z. and Ying, Z. (2002). Semiparametric analysis of transformation models with censored data. Biometrics,89, 659-668.

Farewell V. T. (1982). The use of mixhwe models for the analysis of survival data with long-term survivors. Biometrics, 38, 1041-1046.

Sun, J. (2006). The statistical analysis of interval-censored failure time data.Springer, New York.

Lu, W., and Ying, Z. (2004). On semiparametric transformation cure models. Biometrika, 91, 331-343.

國際替代計量

易感受性之區間設限資料在轉換模型的核函數估計方法

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