二元追蹤資料與存活時間的聯合模型 - 以台灣地區中老年人身心社會生活狀況長期追蹤為例

Joint models for longitudinal binary and survival data - an application to survey of health and living status for elderly population in Taiwan

林姿吟(Tzu-Yin Lin)

指導教授 ： 黃怡婷

國立臺北大學/商學院/統計學系/碩士(2011年)

摘要

在逐漸老化的台灣人口中, 老年人若有很高的慢性病罹患率、 失能、 無法獨立生活, 將造成醫療成本耗用增加。 生活型態是否健康不只影響老年人的個人健康, 對整體社會也有極大的影響。 生活型態是否健康可以由存活時間長短和生活品質好壞兩大方面來考量, 然而如何同時估算存活時間與重複測量生活品質便是最重要的議題。
Tsiatis (1995) 提出的二階段模型以及 Tsiatis 和 Wulfsohn (1997) 提出的聯合模型, 皆可建立存活時間和重複觀測連續變數之間的關聯。 過去所提的模型中, 重複測量模型皆為一般線性模型 (general linear model), 其模型的依變項資料型式只適用於連續型式, 但當觀測變量為離散型時, 需要改用廣義線性模型 (generalized linear model)。
本論文提出二元離散長期變數與存活時間整合估計的二階段模型與聯合模型, 其中聯合模型用來估計的 Cox 模型與廣義線性模型中, 包含了不可觀測的資訊, 必須利用蒙地卡羅 EM 演算法 (Monte Carlo EM algorithm) 及 Metropolis-Hastings 演算法來估計參數。 並利用蒙地卡羅模擬分析評估所提模型, 比較二階段模型與聯合模型的結果與適用情況,最後將模型應用到臨床實務資料上。

關鍵字

生活品質 ； 二階段模型 ； 聯合模型 ； 一般線性模型 ； 廣義線性模型 ； Cox 模型 ； 蒙地卡羅 EM 演算法 ； Metropolis-Hastings 演算法

並列摘要

The medical cost will increase substantially, if the elderly have higher incidence of chronic diseases, disability and unable to live independently, especially in an aging society. Healthy lifestyle not only affects elderly individuals but also affects the whole community. When assessing the healthy lifestyle, survival and quality of life should be considered simultaneously. Thus, how to simultaneously identify the association between the survival and long-term quality of life becomes an important issue.
The two-stage model proposed by Tsiatis (1995) and the joint model proposed by Tsiatis and Wulfsohn (1997) can be used to model a sequence of repeated continuous measures and survival jointly. All the preceding models have a sequence of continuous repeated measurements which are modeled by the general linear model for longitudinal data. However, when the repeated measurements are discrete, the generalized linear model for longitudinal data should be implemented. The thesis proposes a modified two-stage model and a modified joint model for modeling survival and the longitudinal binary covariates simultaneously. Besides the usual estimation procedure for the Cox model and generalized linear model, owing to some unobservable information in the model, some parameters in joint model have to be estimated by Monte Carlo EM algorithm and Metropolis-Hastings algorithm. The performance of the proposed model based on the accuracy and precision of the estimates is evaluated by Monte Carlo simulations. A real data is used to illustrate the feasibility of the proposed model.

並列關鍵字

quality of life ； two-stage model ； joint model ； general linear Model ； generalized linear model ； Cox model ； Monte Carlo EM algorithm ； Metropolis-Hastings algorithm

參考文獻

黃于庭 (2010), ⌈台灣中老年人身心社會生活狀況長期追蹤調查⌋之存活分析. 國立成功大學統計學研究所碩士論文.

呂雅惠 (2010), 台灣地區中老年人長期生活滿意度研究, 國立台北大學統研所碩士論文.

Hwang, Y. T., Tsai, H. Y., Chang, Y. J., Kuo, H. C. and Wang, C. C. (2011). The Joint Model of the Logistic Model and Linear Random Effect Model - An Application

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