在嵌入型病例對照研究法之下條件存活函數的估計

Abstract

在隨機設限的假設之下,Beran提出的Kaplan-Meier型態的估計式已經被廣泛的使用在檢查事件的時間和解釋變數的關係。但是,仍然沒有一個自動選擇帶寬的方法。在世代研究法之下,有些解釋變數在搜集的時候可能要花很多錢。因此,嵌入型病例對照研究法是一種可以節省世代研究法花費的一種方法,然而,有些人的解釋變數可能會遺失。在這篇文章中,我們可以從一個估計方程式得到Beran的估計式。從這個估計方程式,我們可以用逆機率加權的方法解決抽樣誤差的問題,並且提出兩階段的帶寬選擇方法來估計Kaplan-Meier型式的存活函數最佳的帶寬。此外,我們使用隨機加權估計式來估計估計式的近似變異數。在模擬中,帶寬的選擇以及變異數的估計在有限樣本之下都表現得很好。

Under random censorship, the Kaplan-Meier type estimator of Beran(1981) has been wildly used to detect the relationship between event time and covariates of interest. However, there is still no automatic selection procedure for bandwidth selection. In cohort study, some covariates might be expansive in collection. Thus, the nested case control study is an alternative avenue to reduce the cost of cohort studies. Whereas the covariates of some subjects will be missing. In this article, the Beran estimator was shown as a solution of our developed estimating equation. In terms of the estimating equation, the sampling bias can be solved by using the inverse probability weighted approach. Meanwhile, the two-step bandwidth selection procedure is developed the estimate the optimal bandwidth of the Kaplan-Meier type survival estimator. In addition, the random weighted estimator is employed to approximate the asymptotic variance of the resulting estimator. In the simulation studies, the performance of bandwidth selection and variance estimation are quite well for finite-samples.