一個新的時間序列分析法及其在大型醫學資料庫的應用

Abstract

近年來，大型臨床醫學資料庫的研究越來越受到關注。傳統的統計與時間序列分析方法經常被使用，但都有其侷限性。因此，發展一個更好的時間序列分析法是必須的。本論文中，我們發展了傅立葉－高斯分解方法，利用傅立葉轉換、高斯函數與一個最佳化演算法，可將一個訊號分解出數個具有不同代表意義的趨勢。傅立葉－高斯分解法可萃取出一個訊號中具有相同頻率的不同趨勢，這是其他方法所做不到的。此外，我們將傅立葉－高斯分解法應用在分析台灣全民健康保險研究資料庫的疾病及到院前心肺功能停止資料庫，並且得到了一些有趣的發現。我們在過敏性鼻炎、氣喘、急性心肌梗塞的看病人次中找到了特殊的趨勢。過敏性鼻炎的看病人次在每年的三月和十一月達到最高峰；氣喘的看病人次在四月和十一月達到最高峰；急性心肌梗塞的看病人次則是在在立春、立夏、立冬達到最高峰。此外，我們發現循環系統疾病與消化系統疾病的看病人次有相同的趨勢。它們都在春分、芒種、冬至大幅下降。在到院前心肺功能停止資料庫中，我們發現非創傷性到院前心肺功能停止的病患人數在冬天大幅增加而夏天小幅度增加。非創傷性到院前心肺功能停止病患的存活率則在春天與秋天上升，與病患人數呈現相反的趨勢。

In recent years, more and more studies have focused on the large medical databases. Traditional statistical approaches and time series analysis methods are frequently used, but they have some limitations. Therefore, to develop an advanced time series analysis method is required. In this thesis, we develop the Fourier-Gaussian decomposition method and show that it can decompose a signal into a finite and small number of components. Fourier-Gaussian decomposition can extract different components with the same frequency from a signal, which is not available in other methods. Furthermore, we apply Fourier-Gaussian decomposition to analyze several diseases in Taiwan’s National Health Insurance Research Database (NHIRD) and the out of hospital cardiac arrest (OHCA) database. Finally, we get some interesting findings. We find special patterns in allergic rhinitis visits, asthma visits, and AMI visits. Allergic rhinitis visits contained one-year period and peaked in March and November; asthma visits peaked in April and November; AMI visits peaked in Spring Begins, Summer Begins and Winter Begins. Besides, we find that circulatory system diseases visits and digestive system diseases visits have the same pattern. The number of patients decreased rapidly at Vernal Equinox, Grain in Ear and Winter Solstice. In OHCA database, we find that the number of non-traumatic OHCA patients increased rapidly in winter and slightly in summer. The survival rate of non-traumatic OHCA patients increased in spring and autumn, which is reverse to the number of non-traumatic OHCA patients.