Receiver operating characteristic (ROC) curves are widely used in medical decision making. It was recognized in the last decade that only a specific region of the ROC curve is of clinical interest, which can be summarized by the partial area under the ROC curve (partial AUC). Early statistical methods for evaluating partial AUC assume that the data are from a specified underlying distribution. Nonparametric estimators of the partial AUC emerged recently, but there are theoretical issues to be addressed. In this dissertation, we propose two new nonparametric statistics, partially integrated ROC and partially integrated weighted ROC, for estimating partial AUC. We show that our partially integrated ROC statistic is a consistent estimator of the partial AUC, and derive its asymptotic distribution which is distribution free under the null hypothesis. In the partially integrated ROC statistic, when the ROC curve crosses the Uniform distribution function (CDF) and if the partial area evaluated contains the crossing point, or when there are multiple crossing, the partially integrated ROC statistic might not perform well. To address this issue, we propose the partially integrated weighted ROC statistic. This statistic evaluates the partially weighted AUC, where larger weight is given when the ROC curve is above the Uniform CDF and smaller weight is given when the ROC curve is below the Uniform CDF. We show that our partially integrated weighted ROC statistic is a consistent estimator of the partially weighted AUC. We derive its asymptotic distribution which is distribution free under the null hypothesis. We propose to apply our two nonparametric statistics to functional category analysis in microarray experiments. We define the functional category analysis to be the statistical identification of over-represented functional gene categories in a microarray experiment based on differential gene expression. We compare our statistics with existing methods for the functional category analysis both via simulation study and application to a real microarray data, and demonstrate that our two statistics are effective for identifying over-represented functional gene categories. We also emphasize the essential role of the empirical distribution function plots and the ROC curves in the functional category analysis.

Fourier Transform Infrared (FTIR) microscopy is a sensitive method for detecting difference in the morphology of biological cells. In this study FTIR spectra were obtained for uninfected cells, and cells infected with two different viruses. The spectra obtained are difficult to discriminate visually. Here we apply advanced statistical methods to the analysis of the spectra, to test if such spectra are useful for diagnosing viral infections in cells. Logistic Regression (LR) and Partial Least Squares Regression (PLSR) were used to build models which allow us to diagnose if spectral differences are related to infection state of the cells. A three-fold, balanced cross-validation method was applied to estimate the shrinkages of the area under the receiving operator characteristic curve (AUC), and specificities at sensitivities of 95%, 90% and 80%. AUC, sensitivity and specificity were used to gauge the goodness of the discrimination methods. Our statistical results shows that the spectra associated with different cellular states are very effectively discriminated. We also find that the overall performance of PLSR is better than that of LR, especially for new data validation. Our analysis supports the idea that FTIR microscopy is a useful tool for detection of viral infections in biological cells.

Fourier transform infrared (FTIR) spectroscopy, one method of electromagnetic radiation for detecting specific cellular molecular structure, can be used to discriminate different types of cells. The objective is to find the minimum time (choice among 2 hour, 4 hour and 6 hour) to record FTIR readings such that different viruses can be discriminated. A new method is adopted for the datasets. Briefly, inner differences are created as the control group, and Wilcoxon Signed Rank Test is used as the first selecting variable procedure in order to prepare the next stage of discrimination. In the second stage we propose either partial least squares (PLS) method or simply taking significant differences as the discriminator. Finally, k-fold cross-validation method is used to estimate the shrinkages of the goodness measures, such as sensitivity, specificity and area under the ROC curve (AUC). There is no doubt in our mind 6 hour is enough for discriminating mock from Hsv1, and Coxsackie viruses. Adeno virus is an exception.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2016-05-20T12:55:18Z No. of bitstreams: 2 Dissertação - Thales Baliero Takáo - 2015.pdf: 2798998 bytes, checksum: f90a7c928230875abd5873753316f766 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-05-20T12:56:48Z (GMT) No. of bitstreams: 2 Dissertação - Thales Baliero Takáo - 2015.pdf: 2798998 bytes, checksum: f90a7c928230875abd5873753316f766 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2016-05-20T12:56:48Z (GMT). No. of bitstreams: 2 Dissertação - Thales Baliero Takáo - 2015.pdf: 2798998 bytes, checksum: f90a7c928230875abd5873753316f766 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-07-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The aim of this work was to assess the performance of computational methods to classify ground reaction force (GRF) to identify on which surface was done the gait initiation. Twenty-five subjects were evaluated while performing the gait initiation task in two experimental conditions barefoot on hard surface and barefoot on soft surface (foam). The center of pressure (COP) variables were calculate from the GRF and the principal component analysis was used to retain the main features of medial-lateral, anterior-posterior and vertical force components. The principal components representing each force component were retained using the broken stick test. Then the support vector machines and multilayer neural networks ware trained with Backpropagation and Levenberg-Marquartd algorithm to perform the GRF classification . The evaluation of classifier models was done based on area under ROC curve and accuracy criteria. The Bootstrap cross-validation have produced area under ROC curve a and accuracy criteria using 500 samples database. The support vector machine with linear kernel and margin parameter equal 100 produced the best result using medial-lateral force as input. It registered area under ROC curve and accuracy with 0.7712 and 0.7974. Those results showed significance difference from the vertical and anterior-posterior force. Then we may conclude that the choice of GRF component and the classifier model directly influences the performance of the classification. / O objetivo deste trabalho foi avaliar o desempenho de ferramentas de inteligência computacional para a classificação da força de reação do solo (FRS) identificando em que tipo de superfície foi realizada a inicialização da marcha. A base de dados foi composta pela força de reação do solo de 25 indivíduos, adquiridas por duas plataformas de força, durante a inicialização da marcha sobre uma superfície macia (SM - colchão), e depois sobre uma superfície dura (SD). A partir da FRS foram calculadas as variáveis que descrevem o comportamento do centro de pressão (COP) e também foram extraídas as características relevantes das forças mediolateral (Fx), anteroposterior (Fy) e vertical (Fz) por meio da análise de componentes principais (ACP). A seleção das componentes principais que descrevem cada uma das forças foi feita por meio do teste broken stick . Em seguida, máquinas de vetores de suporte (MVS) e redes neurais artificiais multicamada (MLP) foram treinadas com o algoritmo Backpropagation e de Levenberg-Marquartd (LMA) para realizar a classificação da FRS. Para a avaliação dos modelos implementados a partir das ferramentas de inteligência computacional foram utilizados os índices de acurácia (ACC) e área abaixo da curva ROC (AUC). Estes índices foram obtidos na validação cruzada utilizando a técnicas bootstrap com 500 bases de dados de amostras. O melhor resultado foi obtido para a máquina de vetor de suporte com kernel linear com parâmetro de margem igual a 100 utilizando a Fx como entrada para classificação das amostras. Os índices AUC e ACC foram 0.7712 e 0.7974, respectivamente. Estes resultados apresentaram diferença estatística em relação aos modelos que utilizaram as componentes principais da Fy e Fz, permitindo concluir que a escolha da componente da FRS assim como o modelo a ser implementado influencia diretamente no desempenho dos índices que avaliam a classificação.