在這篇文章，我們估計Cox比例危險模型中的參數$S_0(t)$與$ eta$，當資料是區間刪減數據。為了要運用這個模型，資料應該要是精確的或是右刪減資料，因此我們利用三種方法將區間刪減資料轉換成精確資料，並且利用 Nelson-Aalen 估計法來估計參數$S_0(t)$與$ eta$。而檢定統計量不是接近自由度1的卡方分配，而是相當接近自由度1的卡方分配乘上一個常數。

In this paper, we estimate the parameters $S_0(t)$ and $ eta$ in Cox proportional hazard model when data are all interval-censored. For the application of this model, data should be either exact or right-censored, therefore we
transform interval-censored data into exact data by three di®erent methods and then apply Nelson-Aalen estimate to obtain $S_0(t)$ and $ eta$. The test statistic
$hat{ eta}^2I(hat{ eta})$ is not approximately distributed as $chi^2_{(1)}$ but $chi^2_{(1)}$ times a
constant c.

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. Turnbull's algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Generate discrete interval-censored data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. How to choose exact data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
5. Parameter estimation of $ eta$ and $S_0(t)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5.1. Estimation and test for the parameter $ eta$ . . . . . . . . . . . . . . . . . . . . . . . . 7
5.2. Estimation of $S_0(t)$ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6. Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
7. Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.1. A hemophilia study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
7.2. A breast cosmesis study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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