單一監測之序列事件資料的無母數估計與檢定方法

Abstract

當一系列的事件有次序地發生時即形成所謂序列事件資料(serial event data)，以糖尿病史為例，其疾病的演進必為健康、糖尿病、糖尿病併發症等三個依時間發生先後順序之事件。首先，由於單一時間監測所觀察到序列事件資料，同時獲得兩序列事件目前狀態的資訊，故可視為兩個單變量現時狀態資料(univariate current status data)，因此即可運用以現時狀態資料對存活函數的無母數估計方法，得到兩序列事件時間的邊際存活函數的無母數估計。再者，在假設兩組之監測時間服從相同分布的現時狀態資料的兩個樣本之檢定方法比較方面，本文提出Wilcoxon型式之檢定方法，可視為一種廣義Gehan檢定方法。由於兩序列事件通常存在相關性，因此本文亦提出對兩序列事件相關性具穩健性(robustness)的無母數檢定方法，檢定兩組之序列過程是否有差異。此方法為推廣本文所提出Wilcoxon型式之檢定方法，以及Sun和Kalbfleisch(1993)對相同監測時間分布的單變量現時狀態資料所提出的以殘差為基礎之檢定方法。最後由模擬比較兩方法於各情況下之表現，並以一實例資料說明本文所提之統計方法。

Serial event data arise when a series of events occur orderly. Taking the diabetes course as an example, the progression of the disease is necessarily from health to diabetes and subsequently to diabetic complication. Because of the ordinal characteristic of serial events, the current status of two serial events can be observed simultaneously under univariate monitoring. Specifically, two serial event data under univariate monitoring can be regarded as two univarate current status data sets. First, we can obtain nonparametric estimation of the marginal survival function of time to each serial event by using the nonparametric estimation method developed for the current status data. In addition, for comparison of two survival functions based on current status data with the same monitoring time distribution, we proposed a Wilcoxon-type test which is generalized from Gehan test. Secondly, for comparison of the difference between two processes with two serial events under univariate monitoring, we developed two robust nonparametric tests which are extended from our proposed Wilcoxon-type test and the residual-based test proposed by Sun and Kalbfleisch (1993) for univariate current status data with the same monitoring time distribution. Specifically, our proposed methods do not specify the correlation structure of two serial events. Finally, we compare the performance of two proposed nonparametric tests by simulations and illustrate them with a real data.