群聚存活資料應用於雙階層或是治癒模式之統計分析

Abstract

群聚資料常見於各類的應用中。在論文中我們從兩個研究方向探討分析群聚資料的統計方法。第一個主題針對兩階層的群聚資料，第二個主題探討容許群聚存活資料發生“治癒”的情形。

在第一個計畫中，我們採用了Brechmann (2014) 所提出多層次Kendall copula 關聯模式，以描述兩階層的群聚資料。論文主要的貢獻在提出三階段的參數估計與檢驗模式配適度的推論方法。當資料發生設限的情形時，我們提出利用補差法來取代不完整的資料。我們推導了方法的大樣本性質，並藉由模擬檢驗其在有限樣本的表現。所提出的方法亦被套用於分析一筆實際的資料。

針對第二個計畫,我們考慮兩組容許治癒者的機率模式，建議把參數表示為“解釋變數”與“隨機效應”的函數。所提出的方法簡單且具備相當的彈性，能容許“治癒者”只發生於某些特定的群組。我們推導了大樣本性質，並以模擬檢驗其在有限樣本的表現。也將所提出的方法分析實際的資料。

Clustered data are commonly seen in real-world applications. The thesis considers two directions of statistical analysis for clustered data. The first data type is clustered data with a two-level hierarchical structure. In the second direction, we study clustered survival data in the presence of cure.

To model the two-level clustered data, we adopt the hierarchical Kendall copula proposed by Brechmann (2014). We develop statistical inference methods, including a three-stage estimation procedure and a goodness-of-fit test. The proposed methods are suitable for handling censored data. Large-sample properties of the proposed methods are derived. Simulation and data analysis results are also presented.

For the second topic of the thesis, we propose a class of mixed-effects parametric models to fit clustered survival data in the presence of cure. Possible model candidates can be the generalized Gompertz distribution or four-parameter log-logistic distribution which permit improper distributions. The model parameters are specified as a function of observed covariates and random effects. Simulation studies are performed to evaluate finite-sample performances of the proposed estimators. Two real datasets are analyzed for illustration purposes.