臺灣博碩士論文加值系統

許多社會科學和醫學研究中往往會選定固定的樣本,
在研究期間內針對樣本內每個人做追蹤並收集若干研究變項(包含應變項,解釋變項)之觀測值。這種長期追蹤研究之目的, 不外乎想了解某些應變項的分配是否隨時間而改變,而這些改變是否由其他變項影響所致。 關於這些問題在統計上可用迴歸模型的方法來分析長期追蹤資料,以了解某些應變項之分佈是否隨其他解釋變項的影響而改變。

文獻上, 為數不少的迴歸模型已發展成熟能來處理單應變項二元型資料,包含二元叢聚型資料, 二元長期追蹤資料及二元叢聚型長期追蹤資料之情形。近年來, 雙應變項二元型長期追蹤資料之若干迴歸模型也被提出來,但不是很豐富。本文擬針對心臟血管疾病之社區性長期追蹤研究中常見的雙應變項二元叢聚型長期追蹤資料,提出一種邊際效應模型分析方法。此模型中二元型應變項是利用有著常態分佈的連續型潛在變數, 經門檻模型概念所引出;並用羅吉(logit)函數來連接應變項的邊際機率與解釋變項。我們用廣義估計方程式法估計參數, 並以Gauss語言撰寫程式來執行實際的參數估計。

高血壓為國人十大致死疾病之一。希望能藉由分析1989年到1999年在竹東及朴子地區收集到的心臟血管疾病長期追蹤資料，得知那些為明顯的致病因子， 及舒張壓和收縮壓資料間相關性的來源,為流行病研究專家提供一些資訊和參考。

In many sociological and medical studies, repeated measurements of several response variables,
along with other covariate variables, are taken from a fixed sample of subjects, resulting in
longitudinal data. These data are often fitted by regression models to study the relationships
between the response variables and the covariates.

Many regression models have been proposed in the literature for univariate binary data,
including settings of clustered data, longitudinal data and longitudinal clustered data.
In recent years, only a few
regression models for bivariate longitudinal binary data were proposed.
Motivated by a community-based longitudinal study on cardio-vascular disease, a marginal
regression model is proposed for analyzing bivariate longitudinal clustered binary data arising
in the study. The binary response variables are derived from normally distributed latent
variables through the threshold model; the marginal probabilites are related to a set of covariates
by the logit link function. The parameters are estimated using the generalized estimating equation
approach. A computer program was written in Gauss for parameter estimation.

Hypertension is one of the top ten diseases with highest mortality in Taiwan.
Using the proposed model, we analyzed the diastolic and systolic blood pressure data from
a longitudinal study on cardio-vascular disease mentioned above.
%that were collected in Chu-Dong and Pu-Tzu between 1989 and 1999.
Not only a risk assessment of hypertension but also sources of correlations among repeated
measurements of the diastolic and systolic blood pressure were obtained which might
be informative to epidemiologists.

1 緒言 4
2 相關背景知識 8
2.1 潛在變數 .. . . . . . . . . . . . . . . . . . 9
2.2 羅吉斯迴歸模型. . . . . . . . ….. . . . . . 11
2.3 廣義估計方程式.. . . . . . . . . . . . . . . ..12
3 潛在變數模型與雙應變項二元叢聚型長期追蹤資料
3.1 隨機成份的組成….. . . . . . . . . . . . . . . . 14
3.2 四格相關係數….. . . . . . . . . . . . . . . . . 16
3.3 二元應變數之邊際機率模型.. . . . . . . . . . . . . . 17
3.4 參數估計…… . . .. . . . . . . . . . . . . . . . . 17
3.4.1 雙應變項之廣義估計方程式 . . . . . . . . . . . . . 17
3.4.2 雙應變項之廣義估計方程式的共變異矩陣. . . . . . 19
3.4.3 牛頓迭代法. . . . . . . . . . . . . . . . . . . . . 20
4 實際資料分析 24
5 結論和討論 31
A 附錄1 33
B 附錄2 34

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