大部分的心臟結構異常可以透過心臟超音波來檢查。隨著對心臟疾病更多的認識，了解到心臟衰竭與左心室的收縮舒張功能密切相關。本文延續 Chen (2011) 中所提之問題，藉由對左心室超音波圖片灰階值的分析，從左心室收縮與舒張的變化，探討灰階值改變與罹患心臟疾病間的關聯。由於資料矩陣維度相當大，經由因素分析將影響因素簡化後，以因素分數來呈現受試者的資料特性。
此處使用二種分類準則，分別為距離指標邏輯斯模型與區別分析。依據 Guo et al. (2001)，距離指標邏輯斯模型計算每位受試者資料與正常組及異常組之間的馬氏距離 (Mahalanobis Distance)，以此距離配適邏輯斯模型，進而區分心臟功能正常與否。參考 Friedman (1989) 所提之正規化方法，使共變異矩陣的估計更有彈性，調整因樣本數較少所產生的估計不準確情形。亦參考 Hanley et al. (1982) 中 ROC 曲線分界點的想法，在分類準則不變的情況下，找到最合適的分界點，使敏感度與特異度皆有良好表現。在分類準則中納入正規化方法與 ROC 曲線的想法，討論二種分類準則所得之分類正確性，找出區分正常組與異常組較合適的方法。

Most of the cardiac structural abnormalities will be examined by echocardiography. With more understanding of heart diseases, it is commonly recognized that heart failures are closely related to left ventricular systolic and diastolic functions. This work discusses the association between gray-scale differences and the risk of heart disease from the changes in left ventricular systole and diastole of ultrasound image. Owing to the large dimension
of data matrix, following Chen (2011), we also simplify the influence factors by factor analysis and calculate factor scores to present the characteristics of subjects.
Two kinds of classification criteria are used in this work, namely logistic model with distance indicator and discriminant function. According to Guo et al. (2001), we calculate the Mahalanobis distance from each subject to the center of normal and abnormal group, then use logistic model to fit the distances for classification later. This is called logistic model with distance indicator. For the discriminant analysis, the regularized method by Friedman (1989) for estimation of covariance matrix is used, which is more flexible and can improve the covariance matrix estimates when the sample size is small. As far as the
cut-point of ROC curve, following the approach as in Hanley et al. (1982), we find the most appropriate cut-point which has good performances for both sensitivity and specificity under the same classification criteria. Then the regularized method and the cut-point of ROC curve are combined to be a new classification criterion. The results under the new
classification criterion are presented to classify normal and abnormal groups.

目錄
論文審定書i
誌謝ii
摘要iii
Abstract iv
1 背景簡介1
1.1 研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 左心室與心臟超音波. . . . . . . . . . . . . . . . . . . . 1
1.2.1 左心室. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.2 心臟超音波. . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 資料描述3
2.1 資料蒐集. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 資料處理. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.1 灰階值校正. . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 資料縮減. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 研究方法6
3.1 因素分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1.1 因素分析模型. . . . . . . . . . . . . . . . . . . . . . . . 6
3.1.2 因素模型參數估計─主成分估計法. . . . . . . 7
3.1.3 因素轉軸. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.1.4 因素分數. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 距離指標邏輯斯模型. . . . . . . . . . . . . . . . . . . . 9
3.2.1 馬氏距離指標. . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.2 邏輯斯模型. . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2.3 邏輯斯模型參數估計. . . . . . . . . . . . . . . . . . 10
3.3 區別分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4 正規化方法與ROC曲線. . . . . . . . . . . . . . . . . 11
3.4.1 正規化方法. . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4.2 不偏估計與最大概似估計. . . . . . . . . . . . . . 12
3.4.3 最佳參數選取. . . . . . . . . . . . . . . . . . . . . . . . 12
3.4.4 ROC曲線. . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 研究結果15
4.1 全部因素的分類結果. . . . . . . . . . . . . . . . . . . . 15
4.2 縮減變數的分類結果. . . . . . . . . . . . . . . . . . . . 16
4.3 選取不同因素個數的比較. . . . . . . . . . . . . . . . 17
4.4 區別分析與邏輯斯模型的比較. . . . . . . . . . . . 20
5 討論與結語21
參考文獻22
A 附錄23

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