臺灣博碩士論文加值系統

在現有的文獻當中，許多的研究探討長期追蹤結果與存活時間之聯合模型分析。個案常會被間歇性的追蹤，使得感興趣的變項可以重複地被測量，並且也能同時關注於是否有發生感興趣的存活事件，而大多數的研究主要關注於右設限資料。但是，在許多臨床或流行病學的研究裡，當個案有來進行回診檢查時，才能夠觀察到感興趣的存活事件是否發生，這就導致了區間設限資料的產生。目前對於描述長期追蹤資料和區間設限資料的聯合模型較少，所以在此篇論文中，我們對長期追蹤變項與存活時間都有相同的興趣，並提出一個聯合模型，結合隨機效應來解釋重複測量與存活時間之間的關係。半參數迴歸模型與Cox脆弱模型分別應用於長期追蹤資料與存活資料，並透過樣條的方法來估計未知的基底平均函數以及基底累積風險函數。我們採用EM演算法以及觀察資料下之概似函數來獲得參數與變異數估計值，並執行了許多的模擬情境以評估所提之方法表現。結果顯示參數和變異數估計皆良好，未知的基底平均函數和基底累積風險函數的平均估計也有良好的表現。最後我們將所提之方法應用於一筆慢性腎臟病第五期患者的資料上，進行實際資料分析。

There is an abundant literature on the analysis of joint modeling of longitudinal outcome and survival time, in which subjects are often followed-up intermittently such that the longitudinal variables of interest are repeatedly measured and event time of interest is subject to right censoring. However, in many clinic studies and epidemiology research, the event status is examined at the same inspection time, which results in the interval-censored failure time data. The joint analysis of longitudinal measurements and interval-censored failure time is sparse in the literature. In this study, we have equal interest in both longitudinal variables and failure time and propose a joint model incorporating a random effect to account for the dependence between the repeated measures and failure time. A semiparametric regression model and the Cox frailty model are adopted for longitudinal data and survival data, respectively. The unknown baseline mean function and baseline cumulative hazard function are approximated by splines. The EM algorithm is applied to obtain the maximum likelihood estimators and the estimated standard deviations are computed by the observed-data likelihood. Extensive simulation studies are conducted to assess the performance of the proposed estimators. The result shows that the estimates are close to true parameters and that estimated standard error is close to the sample standard deviation from the 500 estimates and the 95% confidence interval coverage rates are close to nominal level. Average estimates of unknown baseline mean function and baseline cumulative hazard function perform reasonably well. Finally, we apply the proposed approach to analyze the chronic kidney disease among people with chronic kidney disease of stage 5.

目錄
誌謝 i
中文摘要 ii
Abstract iii
目錄 iv
圖目錄 v
表目錄 vi
第一章 緒論 1
1.1 研究背景與文獻回顧 1
第二章 研究方法 5
2.1 模型假設 5
2.2 概似函數 7
2.3 估計方法 8
2.4 變異數估計 14
第三章 資料模擬 15
3.1 模擬情境設定 15
3.2 模擬結果 16
第四章 資料分析 18
4.1 資料描述 18
4.2 敘述統計 19
4.3 資料分析結果 20
4.4 個別資料分析 21
第五章 總結與討論 22
參考文獻 41
 
圖目錄
圖一 μ(t)為線性之μ(t)和Λ(t) 33
圖二 μ(t)為非線性之μ(t)和Λ(t) 34
圖三 個案鉀離子濃度變化趨勢 36
圖四 慢性腎臟病資料之λ(t)、Λ(t)以及μ(t) 39


 
表目錄

表一 10種模擬情境 16
表二 情境一 23
表三 情境二 24
表四 情境三 25
表五 情境四 26
表六 情境五 27
表七 情境六 28
表八 情境七 29
表九 情境八 30
表十 情境九 31
表十一 情境十 32
表十二 敘述統計表 35
表十三 AIC選擇 37
表十四 資料分析結果 38
表十五 個別資料分析結果(長期追蹤資料) 40
表十六 個別資料分析結果(存活資料) 40

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