在統計學中，存活分析(survival analysis)特別是指應變數為存活時間或事件發生時間的相關統計分析，這類研究常存在不同的領域中，例如臨床試驗、醫學、生物醫學、流行病理學等等。然而並非所有的觀察對象其被追蹤(follow-up)的時間都足夠，現狀數據(current status data)是常見的存活設限資料。
    當共變數有測量誤差(measurement error)時，如果忽略測量誤差，會導致估計值的偏差，處理這個問題有校正分數(corrected score)函數、條件分數(conditional score)函數等常被使用的誤差校正方法；最近提出的延伸校正分數(extensively corrected score)，可以解決分數函數不偏估計式不存在時的困境，是另一個可供選擇的方法。
    現狀數據的加法性涉險模型在共變數有測量誤差時，目前尚無相關論文探討。因此，我們利用此模型具有可以轉換成比例性涉險模型的特性，針對此問題提出我們的做法。

The need for analyzing time-to-event data can arise in a number of applied fields, such as medicine, biology, public health, epidemiology, engineering, economics and demography. A common feature of such data sets is that the event time may not be known completely due to censorings or truncations. In current status data, the event time is not observed directly and is only known to lies before some examining time or not. We consider the estimation problems for current status data under the assumption of additive hazards models when covariates are subject to homogeneous measurement errors.
  We proposed to adopt the point of view from Lin, Oakes and Ying(1998) to transform the problem to a Cox proportional hazard model with right censored data. Nevertheless, the measurement errors in “covariates” become heterogeneous after transform. Some modifications were then developed to accommodate such heterogeneous errors for conventional analyzing methods that include corrected score, conditional score and a newly developed method--the extensively corrected score.  Our proposal is shown to perform well in simulation study and is applied to diabetes survey data as an illustration of implementation.

目  錄

1.	緒論	1
2.	現狀數據的加法性涉險函數模型 	4
2.1	 模型定義	4
2.2	 檢查時間與共變數獨立	5
2.3	 檢查時間與共變數不獨立	6
3.	右設限資料的比例性涉險模型在共變數有測量誤差時的校正方法	9
3.1	 校正分數與條件分數	10
3.2	 延伸校正分數	12
   3.2.1 利用兩個重複測量值建立不偏估計函數	12
   3.2.2 複製和平均過程	14
   3.2.3 右設限資料的延伸校正分數函數	15
4.	現狀數據的加法性涉險模型在共變數有測量誤差時的校正方法	18
   4.1 檢查時間與共變數獨立	18
       4.1.1 校正分數與條件分數	18
       4.1.2 延伸校正分數	19
4.2 檢查時間與共變數不獨立	20
    4.2.1 校正分數與條件分數	20
    4.2.2 延伸校正分數	22
5.	模擬分析	26
5.1 模擬條件	26
5.2 模擬結果分析	26
6.	實例說明	28
7.	結論	31
參考文獻	32
附錄A  模擬表格對照表	35
附錄B  模擬結果	36

參考文獻
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