風險函數之局部多項式估計：針對資料稀少問題之改良

Abstract

存活分析當中，真實的存活時間可能因其他事件先發生而無法觀察得到。本文考慮隨機右設限資料（right censoring survival data），並假設存活時間與設限時間互相獨立。我們改良Jiang and Doksum (2003) 的方法，同樣對一般化的經驗風險函數作局部多項式逼近，而進一步把每筆資料的訊息，分到其鄰近的區間，以改善資料稀少的問題。最後，我們利用模擬所得資料比較Jiang and Doksum的原始方法與我們改良後的方法。

In survival studies, observations on the occurrence of the event of interest (called a failure) may be preceded by the previous occurrence of another event (called a censoring event). We assume the random censorship model, and consider Jiang and Doksum (2003) method to estimate the hazard function. By averaging each observation to its neighborhood, we adapt the estimator to sparse data. Finally, we compare our adaptive method with the original one by simulation studies.