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.

Due to the association of heart diseases and the patterns of the diastoles and systoles of heart in left ventricle, we analyze and classify the data gathered form Kaohsiung Veterans General Hospital by using the cardiology ultrasound images. We make use of the differences between the gray-scale values of diastoles and systoles in left ventricle to evaluate the function of heart. Following Chen (2011) and Kao (2011), we modified the way about the reduction and alignment of the image data. We also add some more subjects into the study. We treat images in two manners, saving the parts of concern. Since the ultrasound image after transformation to data form is expressed as a high-dimensional matrix, the principal component analysis is adapted to retain the important factors and reduce the dimensions. In this work, we compare the loadings calculated by the usual principal and sparse principal component analysis, then the factor scores are used to carry out the discriminant analysis and discuss the accuracy of classification. By the statistical methods in this work, the accuracy, sensitivity and specificity of the original classifications are over 80% and the cross validations are over 60%.

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.

Alcohol dependence (AD) is a serious and common public health problem that contributes to great societal, medical, and legal costs. It has taken work from multiple disciplines, including developmental psychology, genetic epidemiology, and molecular genetics, to achieve our current understanding of environmental and genetic risk factors for AD as well as its variable developmental trajectories. Nevertheless, there is still much to be learned in order to improve treatment outcomes. One approach to augmenting our understanding of this disorder is through genetically informative study designs that either examine risk in aggregate or assess specific susceptibility variants. In this dissertation, we utilize both study designs and provide support for the idea that they are both important and useful approaches to continue to pursue.

Factor score regression has recently received growing interest as an alternative for structural equation modelling. Two issues causing uncertainty for researchers are addressed in this thesis. Firstly, more knowledge is needed on how different approaches to calculating factor score estimates compare when estimating factor score regression models. Secondly, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. This thesis examines how factor scoring methods compare when estimating regression coefficients in generalised linear factor score regression. An evaluation is made of the regression, correlation-preserving, total sum, and weighted sum method in ordinary, logistic, and Poisson factor score regression. In contrast to previous studies, both the mean and variance of loading coefficients and the degree of inter-factor correlation are varied in the simulations. A meta-analysis demonstrates that the choice of factor scoring method can substantially influence research conclusions. The regression and correlation-preserving method outperform the other two methods in terms of coefficient and standard error bias, accuracy, and empirical Type I error rates. Moreover, the regression method generally has the best performance. It is also noticed that performance can differ notably across the considered regression models.