在倖存分析中，Cox PH模型是一個最基本且用途很廣的模式之一。而區間設限資料（interval censored data）是眾多倖存分析資料型態中較難估計其模式未知參數，因為我們僅能從該區間設限資料中得知包含未知失敗時間（failure time）的時間區間上下限，使的其所能提供參數估計的訊息較其他資料型態要來的少，因此提升了估計參數的困難度。本篇論文主要是在Cox PH模式下使用區間設限資料時提出兩種估計方法：即猜秩法（missing-rank approach）與猜時法（missing-failure time approach）。猜秩法是利用Gibbs抽樣法來生成所有可能的秩，並利用這些秩來估計參數；猜時法是利用生成所有可能的失敗時間，並以羅法（Monte Carlo method）來估計參數。
此外，我們根據Satten (1998) 等人所得到的漸進分配性質，可以得知在某些條件狀況下，會造成估計參數偏誤的區域混淆現象（Local confounding effect）有可能會發生。最後，在三種不同型態的區間設限資料下，我們得到一些猜秩法和猜時法的模擬結果，並進行一些比較與討論。

The missing-rank approach and missing-failure time approach of estimating unknown parameter of the Cox proportional hazards model for the interval censored data are compared in this article. In missing-rank approach, it does not require specification of the baseline hazard function and use a Gibbs sampling scheme to generate rankings for estimating parameters. In missing-failure time approach, the parameters of the baseline function are estimated simultaneously with the regression parameters, and the estimating equation is solved using Monte Carlo techniques. Further using the asymptotic result of Satten et al. (1998), we study the local confounding effect of interval censored data which may cause the estimator bias. Finally, we show some simulation results of comparison and their discussion in three types of data set.
2 Model . . . . . . . . . . . . . . . . . . . . . . . . . 3

3 Estimation of β . . . . . . . . . . . . . . . . . . . . 4

3.1 Missing-rank approach . . . . . . . . . . . . . . . 4

3.2 Missing-failure approach . . . . . . . . . . . . . . 9

4 The local confounding effect . . . . . . . . . . . . . . 12

5 Simulation . . . . . . . . . . . . . . . . . . . . . . . 19

6 Discussion . . . . . . . . . . . . . . . . . . . . . . . 27

7 Appendix A . . . . . . . . . . . . . . . . . . . . . . . 29

8 Reference . . . . . . . . . . . . . . . . . . . . . . . 33

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