This study investigates use of echocardiography to assess the related issues about whether the heart function of a subject examined is normal or not. Two-dimensional echocardiography can make the heart inspection, and provide very detailed informations for each part of the cardiovascular structures with a high degree of accuracy. Many studies indicated that the systolic and diastolic function with left ventricle of heart disease in patients was poorer than those of normal patients. Therefore it is of interest to study the systolic and diastolic function for examining whether there are heart problems. In this work, the data is the gray-scale values of left ventricular static ultrasound images. The gray-scale differences between systolic and diastolic period, are used to assess whether the patient suffers from the heart diseases or not. Here, we use factor analysis to simplify and select the crucial factors, namely the function in different area of the left ventricle. Finally, linear and quadratic discriminant analyses are used to distinguish the normal and the abnormal subjects.

Non-invasive physical examination helps to make disease diagnosis with minimum injury to the body. Cardiology ultrasound is a non-invasive examination which can be used as a auxiliary tool for diagnose cardiac structure abnormalities. With more understanding of heart diseases, it has been recognized that heart failures are closely related to left ventricular systolic and diastolic function. Following Chen (2011) and Kao (2011), we study association of heart diseases with the change of gray-scale values in the cardiology ultrasound images of left ventricular systolic and diastolic. Since data obtained from ultrasound image is of matrix type with high dimensions, following the method proposed by Chen (2011) and Kao (2011), factor scores obtained from factor analysis are used as a basis for classification. We take the factor scores of normal subjects to establish the bench mark and calculate the Mahalanobis distance of each abnormal subject with the model established by the data from normal group. Later based on this distance to the normal group, cardiac function of the subject is distinguished as normal or not. In order to improve the accuracy of the classification, influential points which may cause inaccurate covariance matrix estimate on the subjects in normal group are identified. Based on concepts from optimal designs theory, some criteria are established for screening out the influential points.

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.