三種不同資料結構下累積發生函數的無母數估計量研究

Abstract

在本論文中，我們考慮兩個在生物醫學上常被應用的量：累積發生函數以及長期發生率；針對感興趣的發生原因，我們探討這兩個量的無母數估計。在三種不同的資料結構下(競爭風險和治癒模式在右設限存在下、競爭風險在左截切存在下)，我們分別應用三種不同的想法去得到無母數估計量：分解法，加權法以及補值法。在本文中，我們證明出在每一種資料結構下，使用不用想法所得到的無母數估計量都是相同的。另外，我們也利用數值分析來比較在競爭風險和治癒模式下，何者的無母數估計量更為有效率。

In this thesis we consider nonparametric inference of the cumulative incidence function for a particular type of failure and its long-term incidence rate, both of which are useful descriptive measures for biomedical data with multiple endpoints. A unified framework is provided to study different inference techniques under various incomplete data structures. Specifically three approaches, namely decomposition, weighting and imputation, are studied under data settings which include the conventional competing risks data, the framework of a cure model and truncated data. Identity between these methods for each data structure is examined. Numerical examples are provided for comparing the first two data formulations.