Comparison for three Classification Techniques

In this paper we show the results of a comparison simulation study for three classification techniques: Multinomial Logistic Regression (MLR), No Metric Discriminant Analysis (NDA) and Linear Discriminant Analysis (LDA). The measure used to compare the performance of the three techniques was the Error Classification Rate (ECR). We found that MLR and LDA techniques have similar performance and that they are better than DNA when the population multivariate distribution is Normal or Logit-Normal. For the case of log-normal and Sinh(-1)-normal multivariate distributions we found that MLR had the better performance.

Propriedades e aspectos geométricos de estimadores tipo James-Stein e do estimador de Hartigan

The James-Stein estimator is a biased shrinkage estimator with uniformly smaller risk than the risk of the sample mean estimator for the mean of multivariate normal distribution, except in the one-dimensional or two-dimensional cases. In this work we have used more heuristic arguments and intensified the geometric treatment of the theory of James-Stein estimator. New type James-Stein shrinking estimators are proposed and the Mahalanobis metric used to address the James-Stein estimator. . To evaluate the performance of the estimator proposed, in relation to the sample mean estimator, we used the computer simulation by the Monte Carlo method by calculating the mean square error. The result indicates that the new estimator has better performance relative to the sample mean estimator.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Multivariate gene expression analysis reveals functional connectivity changes between normal/tumoral prostates

Abstract Background Prostate cancer is a leading cause of death in the male population, therefore, a comprehensive study about the genes and the molecular networks involved in the tumoral prostate process becomes necessary. In order to understand the biological process behind potential biomarkers, we have analyzed a set of 57 cDNA microarrays containing ~25,000 genes. Results Principal Component Analysis (PCA) combined with the Maximum-entropy Linear Discriminant Analysis (MLDA) were applied in order to identify genes with the most discriminative information between normal and tumoral prostatic tissues. Data analysis was carried out using three different approaches, namely: (i) differences in gene expression levels between normal and tumoral conditions from an univariate point of view; (ii) in a multivariate fashion using MLDA; and (iii) with a dependence network approach. Our results show that malignant transformation in the prostatic tissue is more related to functional connectivity changes in their dependence networks than to differential gene expression. The MYLK, KLK2, KLK3, HAN11, LTF, CSRP1 and TGM4 genes presented significant changes in their functional connectivity between normal and tumoral conditions and were also classified as the top seven most informative genes for the prostate cancer genesis process by our discriminant analysis. Moreover, among the identified genes we found classically known biomarkers and genes which are closely related to tumoral prostate, such as KLK3 and KLK2 and several other potential ones. Conclusion We have demonstrated that changes in functional connectivity may be implicit in the biological process which renders some genes more informative to discriminate between normal and tumoral conditions. Using the proposed method, namely, MLDA, in order to analyze the multivariate characteristic of genes, it was possible to capture the changes in dependence networks which are related to cell transformation.

Multivariate analyses of variance and covariance for simulation studies involving normal time series

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Joint Densities of Correlation Coefficients for Samples from Multivariate Standard Normal Distribution

2000 Mathematics Subject Classification: 62H10.

Discriminant analysis of trace elements in normal, benign and malignant breast tissues measured by total reflection X-ray fluorescence

In this work total reflection X-ray fluorescence spectrometry has been employed to determine trace element concentrations in different human breast tissues (normal, normal adjacent, benign and malignant). A multivariate discriminant analysis of observed levels was performed in order to build a predictive model and perform tissue-type classifications. A total of 83 breast tissue samples were studied. Results showed the presence of Ca, Ti, Fe, Cu and Zn in all analyzed samples. All trace elements, except Ti, were found in higher concentrations in both malignant and benign tissues, when compared to normal tissues and normal adjacent tissues. In addition, the concentration of Fe was higher in malignant tissues than in benign neoplastic tissues. An opposite behavior was observed for Ca, Cu and Zn. Results have shown that discriminant analysis was able to successfully identify differences between trace element distributions from normal and malignant tissues with an overall accuracy of 80% and 65% for independent and paired breast samples respectively, and of 87% for benign and malignant tissues. (C) 2009 Elsevier B.V. All rights reserved.

Standard errors of fitted component means of normal mixtures

In this paper use consider the problem of providing standard errors of the component means in normal mixture models fitted to univariate or multivariate data by maximum likelihood via the EM algorithm. Two methods of estimation of the standard errors are considered: the standard information-based method and the computationally-intensive bootstrap method. They are compared empirically by their application to three real data sets and by a small-scale Monte Carlo experiment.

Factors determining normal adult height in girls with gonadotropin-dependent precocious puberty treated with depot gonadotropin-releasing hormone analogs

Context: Several factors can affect adult height (AH) of patients with gonadotropin-dependent precocious puberty (GDPP) treated with depot GnRH analogs. Objective: Our objective was to determine factors influencing AH in patients with GDPP treated with depot GnRH analogs. Patients: A total of 54 patients (45 girls) with GDPP treated with depot GnRH analog who reached AH was included in the study. Design: Univariate and multivariate analyses of the factors potentially associated with AH were performed in all girls with GDPP. In addition, clinical features of the girls who attained target height (TH) range were compared with those who did not. Predicted height using Bayley and Pinneau tables was compared with attained AH. Results: In girls the mean AH was 155.3 +/- 6.9 cm (-1.2 +/- 1 SD) with TH range achieved by 81% of this group. Multiple regression analysis revealed that the interval between chronological age at onset of puberty and at the start of GnRH analog therapy, height SD scores (SDSs) at the start and end of therapy, and TH explained 74% of AH variance. The predicted height at interruption of GnRH therapy, obtained from Bayley and Pinneau tables for average bone age, was more accurate than for advanced bone age in both sexes. In boys the mean AH was 170.6 +/- 9.2 cm (-1 +/- 1.3 SDS), whereas TH was achieved by 89% of this group. Conclusions: The major factors determining normal AH in girls with GDPP treated with depot GnRH analogs were shorter interval between the onset of puberty and start of therapy, higher height SDS at the start and end of therapy, and TH. Therefore, prompt depot GnRH analog therapy in properly selected patients with GDPP is critical to obtain normal AH.

Myocardial abnormalities in hypertensive patients with normal and abnormal left ventricular filling: a study of ultrasound tissue characterization and strain

Abnormal left ventricular (LV) filling is common, but not universal, in hypertensive LV hypertrophy (LVH). We sought to elucidate the relative contributions of myocardial structural changes, loading and hypertrophy to LV dysfunction in 113 patients: 85 with hypertensive LVH and 28 controls without LVH and with normal filling. Patients with normal dobutamine stress echocardiography and no history of coronary artery disease were selected, in order to exclude a contribution from ischaemia or scar. Abnormal LV filling was identified in 65 LVH patients, based on Doppler measurement of transmitral filling and annular velocities. All patients underwent grey-scale and colour tissue Doppler imaging from three apical views, which were stored and analysed off line. Integrated backscatter (113) and strain rate imaging were used to detect changes in structure and function; average cyclic variation of 113, strain rate and peak systolic strain were calculated by averaging each segment. Calibrated 113 intensity, corrected for pericardial 113 intensity, was measured in the septum and posterior wall from the parasternal long-axis view. Patients with LVH differed significantly from controls with respect to all backscatter and strain parameters, irrespective of the presence or absence of abnormal LV filling. LVH patients with and without abnormal LV filling differed with regard to age, LV mass and incidence of diabetes mellitus, but also showed significant differences in cyclic variation (P < 0.01), calibrated 113 in the posterior wall (P < 0.05) and strain rate (P < 0.01), although blood pressure, heart rate and LV systolic function were similar. Multivariate logistic regression analysis demonstrated that age, LV mass index and calibrated IB in the posterior wall were independent determinants of abnormal LV filling in patients with LVH. Thus structural and functional abnormalities can be detected in hypertensive patients with LVH with and without abnormal LV filling. In addition to age and LVH, structural (not functional) abnormalities are likely to contribute to abnormal LV filling, and may be an early sign of LV damage. 113 is useful for the detection of myocardial abnormalities in patients with hypertensive LVH.

Haemodynamic response to TENS applied to upper thoracic nerve roots in normal subjects

This study investigated the haemodynamic response to the 90-minute application of 85 Hz transcutaneous electrical nerve stimulation (TENS) to the T1 and T5 nerve roots. Comparison was made between 20 healthy subjects who had TENS stimulation and a separate group of 20 healthy subjects who rested for 90 minutes. Pulse and blood pressure were measured just prior to the start of TENS stimulation, after 30 minutes of stimulation, and after 90 minutes of stimulation (immediately after stopping TENS) or at completion of the rest time depending on group allocation. The rate pressure product was calculated from the pulse and systolic blood pressure data. Multivariate repeated measures analysis showed a significant group effect for TENS (p = 0.048). Univariate repeated measures analyses showed a significant group by time effect due to TENS on systolic blood pressure over the 90-minute time period (p = 0.028). Separate group repeated measures ANOVA showed a significant decline in heart rate (p = 0.000), systolic blood pressure (p = 0.013) and rate pressure product (p = 0.000) for the TENS group, while the control resting group showed a significant decline in heart rate only (p = 0.04). The application of 85 Hz TENS to the upper thoracic nerve roots causes no adverse haemodynamic effects in healthy subjects.

Multiparametric brainstem segmentation using a modified multivariate mixture of Gaussians

The human brainstem is a densely packed, complex but highly organised structure. It not only serves as a conduit for long projecting axons conveying motor and sensory information, but also is the location of multiple primary nuclei that control or modulate a vast array of functions, including homeostasis, consciousness, locomotion, and reflexive and emotive behaviours. Despite its importance, both in understanding normal brain function as well as neurodegenerative processes, it remains a sparsely studied structure in the neuroimaging literature. In part, this is due to the difficulties in imaging the internal architecture of the brainstem in vivo in a reliable and repeatable fashion. A modified multivariate mixture of Gaussians (mmMoG) was applied to the problem of multichannel tissue segmentation. By using quantitative magnetisation transfer and proton density maps acquired at 3 T with 0.8 mm isotropic resolution, tissue probability maps for four distinct tissue classes within the human brainstem were created. These were compared against an ex vivo fixated human brain, imaged at 0.5 mm, with excellent anatomical correspondence. These probability maps were used within SPM8 to create accurate individual subject segmentations, which were then used for further quantitative analysis. As an example, brainstem asymmetries were assessed across 34 right-handed individuals using voxel based morphometry (VBM) and tensor based morphometry (TBM), demonstrating highly significant differences within localised regions that corresponded to motor and vocalisation networks. This method may have important implications for future research into MRI biomarkers of pre-clinical neurodegenerative diseases such as Parkinson's disease.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

MBIS: multivariate Bayesian image segmentation tool.

We present MBIS (Multivariate Bayesian Image Segmentation tool), a clustering tool based on the mixture of multivariate normal distributions model. MBIS supports multichannel bias field correction based on a B-spline model. A second methodological novelty is the inclusion of graph-cuts optimization for the stationary anisotropic hidden Markov random field model. Along with MBIS, we release an evaluation framework that contains three different experiments on multi-site data. We first validate the accuracy of segmentation and the estimated bias field for each channel. MBIS outperforms a widely used segmentation tool in a cross-comparison evaluation. The second experiment demonstrates the robustness of results on atlas-free segmentation of two image sets from scan-rescan protocols on 21 healthy subjects. Multivariate segmentation is more replicable than the monospectral counterpart on T1-weighted images. Finally, we provide a third experiment to illustrate how MBIS can be used in a large-scale study of tissue volume change with increasing age in 584 healthy subjects. This last result is meaningful as multivariate segmentation performs robustly without the need for prior knowledge.