Liver inflammation due to HCV infection leads to fibrosis, which is an independent predictor of treatment response to interferon therapy in Chronic Hepatitis C (CHC) patients. This relationship has not been studied for liver inflammation on pretreatment liver biopsy and End of Treatment Response (ETR). ALT is a less invasive test than liver biopsy for measuring liver inflammation. Aim of this study was to compare ETR to Interferon α (recombinant Interferon) & Ribavirin in CHC patients having higher and lower grades of liver inflammation and to determine the diagnostic accuracy of pretreatment ALT for grades of liver inflammation.

Normal distribution based discriminant methods have been used for the classification of new entities into different groups based on a discriminant rule constructed from the learning set. In practice if the groups are not homogeneous, then mixture discriminant analysis of Hastie and Tibshirani (J R Stat Soc Ser B 58(1):155–176, 1996) is a useful approach, assuming that the distribution of the feature vectors is a mixture of multivariate normals. In this paper a new logistic regression model for heterogenous group structure of the learning set is proposed based on penalized multinomial mixture logit models. This approach is shown through simulation studies to be more effective. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using this penalized multinomial mixture logit model as compared to the classical discriminant rules. It also showed better results when applied to practical life data problems producing smaller errors.

This article addresses the use of different biweight functions in high breakdown mixture discriminant analysis approach of Bashir and Carter ( 2005). The translated biweight S function of Rocke ( 1996) is used in the robust estimation of the mixture distributions parameters. As in discriminant analysis, the main purpose is to classify the test observations with greater accuracy, so the estimators producing smaller errors of misclassification are preferred. In the simulation studies, the use of Tukey's biweight function was proved to be more effective in producing better classification results as compared to the translated biweight function.

Robust S-estimation is proposed for multivariate Gaussian mixture models generalizing the work of Hastie and Tibshirani (J. Roy. Statist. Soc. Ser. B 58 (1996) 155). In the case of Gaussian Mixture models, the unknown location and scale parameters are estimated by the EM algorithm. In the presence of outliers, the maximum likelihood estimators of the unknown parameters are affected, resulting in the misclassification of the observations. The robust S-estimators of the unknown parameters replace the non-robust estimators from M-step of the EM algorithm. The results were compared with the standard mixture discriminant analysis approach using the probability of misclassification criterion. This comparison showed a slight reduction in the average probability of misclassification using robust S-estimators as compared to the standard maximum likelihood estimators.

ABSTRACT In the case of a large number of feature vector variables, using multivariate Gaussian mixture models, discrimination in a reduced subspace is studied, generalizing Hastie and Tibshirani's (1996) work, to a situation in which the outliers are present in the data. In the case of the Gaussian Mixture models, the reduced rank discriminant analysis is equivalent to the weighted rank k linear discriminant analysis (LDA). The reduced rank solution in the mixtures of multivariate Gaussian models was obtained from the full rank robust mixture solution. The classification in the new dimensions was compared with the discriminant analysis approach based on the original coordinates, using robust S-estimators. In most of the cases, the robust reduced rank mixture discriminant analysis (mda) performed better for the test data. However, for the case of common component covariance being diagonal, the robust reduced rank mixture discriminant analysis performed better than the robust full rank mixture discriminant analysis producing smaller errors in classification.