隨機設限下風險函數之局部多項式估計

Abstract

在存活分析當中，實際存活時間可能因為其他事件先發生而無法觀察到，例如研究個體搬家失去追蹤造成資料上的設限。在此我們考慮隨機右設限資料，假設存活時間和設限時間相互獨立。我們對累積風險函數的Nelson-Aalen估計量作局部多項式逼近，得到風險函數的局部一次、二次多項式估計式。在理論方面，我們推導出估計式在大樣本之下逼近常態分配，並由模擬資料畫圖以及計算估計的MSE，來比較我們的估計式和先前相關文獻所提出的估計式。

In many survival studies, observation on the occurance of the event of interest (called a failure) may be prevented by the previous occurance of another event(called a censoring event). We assume the random censorship model. By considering a local polynomial approximation to the Nelson-Aalen estimator of cumulative hazard function, based on local linear and local quadratic fits, we obtain the estimators of the linear coefficients which are called the local linear and local quadratic estimators of the hazard rate, respectively. The asymptotic normality of the local linear and local quadratic estimators are established. The results are illustrated by simulations. We compare our estimators with the kernel estimator and the Jiang and Doksum estimator by means of the figures and the estimated MISE. The local quadratic estimator behaves favorably compared with the Jiang and Doksum estimator.