Framingham冠狀動脈心臟病風險因子之建模及敏感度分析

Modeling and Sensitivity Analysis for Framingham Coronary-Heart-Disease Risk Factors

李承恩(Cheng-En Lee)

指導教授 ： 陳慧芬

中原大學/電機資訊學院/工業與系統工程研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600631

摘要

本研究主要為建立Framingham冠狀動脈心臟病風險因子的多變量時間序列機率模式，Framingham冠狀動脈心臟病風險因子(簡稱風險因子)為年齡、總膽固醇、高密度膽固醇、收縮壓、有無吸菸及有無糖尿病等六項，本研究並利用此機率模式進行模擬實驗以進行敏感度分析，目的在探討六個風險因子對冠狀動脈心臟病的影響。
我們採用Biller and Nelson在2003年所提出的VARTA多變量時間序列模式來建模，將自相關係數的階數設為1，時間單位為年。資料來源為桃園市平鎮區壢新醫院2006至2011年的社區篩檢資料，VARTA模式包含六變數的相關係數矩陣、一階自相關係數矩陣及各變數的邊際分配。VARTA模式假設各年邊際分配相同，經由Friedman檢定得到接受各年邊際分配相同的假設，因此利用壢新醫院資料建立各變數之邊際分配模式以及六變數的相關係數矩陣及一階自相關係數矩陣的估計值。
本研究為了瞭解風險因子對冠狀動脈心臟病發生機率的影響，利用所建立的VARTA模式來進行模擬實驗，藉由Framingham風險評估表來估算冠狀動脈心臟病十年內發生機率，將每個風險因子的觀察值範圍分成數個水準進行敏感度分析，比較在不同水準下冠狀動脈心臟病發生機率的分佈變化。
敏感度分析顯示，男性冠狀動脈心臟病發生機率普遍較女性大，而當年齡、總膽固醇、收縮壓等數值增加時，冠狀動脈心臟病發生機率分佈的眾數明顯提高，對高密度膽固醇數值低於60mg/dl者，其冠狀動脈心臟病發生機率較高密度膽固醇高於60mg/dl者高，最後有糖尿病者其冠狀動脈心臟病發生機率較沒有糖尿病者高，有吸菸者其冠狀動脈心臟病發生機率較沒有吸菸者高。另外，若將發生機率分成三個區間：<10%、[10%,20%)與≧20%，分別代表低、中與高風險，敏感度分析顯示，年齡增加、患有糖尿病者，其低風險人數明顯較少、高風險人數明顯增加，總膽固醇、患有高血壓、有吸菸者，低風險人數減少，且幾乎全移至中風險。最後不論男性或女性，對於冠狀動脈心臟病，年齡、高血壓以及糖尿病為較敏感因子，因此高血壓以及糖尿病的控制極為重要。

關鍵字

VARTA法,多變量時間序列模式,相關係數矩陣,自相關係數矩陣,敏感度分析,Framingham風險分數,冠狀動脈心臟病

並列摘要

This study is to establish a multivariate-time-series model for Framingham coronary-heart-disease (CHD) risk factors, which are age, total cholesterol, high density lipoprotein (HDL) cholesterol, systolic blood pressure, smoking, and the presence/absence of diabetes. To investigate effects of the six risk factors, we performed a sensitivity analysis via conducting simulation experiments of the proposed probability model.
Our proposed probability model is based on the VARTA multivariate time series model by Biller and Nelson (2003). We arbitrarily set the lag to 1 (with time unit being year). We used the LIONS data from Years 2006 to 2011, provided by Landseed Hospital in Chungli County, Taoyuan City in Taiwan. Since the VARTA model assumes that the marginal distributions for different years are the same, we conducted the Friedman test; such hypothesis is accepted. Therefore, the marginal distributions and the lag-0 and lag-1 autocorrelation matrices can be modeled with the LIONS data.
To determine the effects of the six risk factors on the probability of CHDs, we conducted simulation experiments of the VARTA model. For each simulated case, a 10-year probability of CHD is evaluated based on Framingham risk scores. The distributions of the CHD probability for different levels of each risk factor are then compared.
Sensitivity analysis shows that higher probability of coronary diseases is found in males than females. Besides, increasing values of factors in age, total cholesterol and systolic blood pressure results in a larger mode of the CHD probability. Furthermore, people with HDL cholesterol below 60 mg/dl have a higher CHD probability than people with HDL cholesterol above 60 mg/dl. In addition, people with diabetes have a higher CHD probability than people without diabetes; people with smoking habit have a higher CHD probability than people without. We further divided the CHD probability into three intervals: <10%、[10%,20%), and ≧20%, indicating low, medium, and high risk, respectively. The sensitivity analysis shows that the increase in age and/or presence of diabetes decrease the proportion of people with low risk and increases the proportion of people with high risk. Furthermore, the increase in total cholesterol, increases in high blood pressure, and presence of smoke decreases the proportion of people with low risk and increases the proportion of people with medium risk. Finally, for both males and females, the CHD probability is more sensitive to the age, systolic blood pressure, and diabetes than the other factors.

並列關鍵字

VARTA method, Multivariate time series model, Correlation matrix, Autocorrelation coefficient matrix, Sensitivity analysis, Framingham risk score, Coronary heart disease

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