One- and two-sample nonparametric tests for the signal-to-noise ratio based on record statistics

A new family of nonparametric statistics, the r-statistics, is introduced. It consists of counting the number of records of the cumulative sum of the sample. The single-sample r-statistic is almost as powerful as Student's t-statistic for Gaussian and uniformly distributed variables, and more powerful than the sign and Wilcoxon signed-rank statistics as long as the data are not too heavy-tailed. Three two-sample parametric r-statistics are proposed, one with a higher specificity but a smaller sensitivity than Mann-Whitney U-test and the other one a higher sensitivity but a smaller specificity. A nonparametric two-sample r-statistic is introduced, whose power is very close to that of Welch statistic for Gaussian or uniformly distributed variables.Comment: 12 pages, 13 figure

Parametric imaging of FET PET using nonlinear based fitting

Tese de mestrado integrado em Engenharia Biomédica e Biofísica , apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2016A importância do uso de aminoácidos marcados com isótopos radioativos em estudos de Tomografia de Emissão de Positrões (PET) tem sido amplamente demonstrada. Dentro deste grupo de traçadores, a metionina marcada com 11C tem sido o mais estudado. No entanto, a curta semi-vida do radioisótopo 11C tem levado ao desenvolvimento de marcadores análogos. Os marcadores com o radioisótopo 18F revelam-se os mais promissores para deteção de tumores no cérebro. Mais especificamente, o marcador O-(2-18F-Fluoroetil)-L-tirosina (FET) provou ser de grande importância na determinação da dimensão de tumores cerebrais e dos locais onde realizar a biopsia, no planeamento do tratamento a aplicar, e na deteção de recorrências. Foi também demonstrado que a forma como o FET é metabolizado ao longo do tempo depende do grau do tumor em estudo. Em gliomas de alto grau (HGG), a taxa de captação do FET é caracterizada por um pico inicial, seguido de uma diminuição da captação de FET, enquanto que em gliomas de baixo-grau (LGG) a taxa de captação do marcador tem um aumento contínuo ao longo do tempo. O presente estudo contou com 11 pacientes (3 mulheres, 8 homens, idade: 45 ± 15 anos) com tumores cerebrais primários não tratados confirmados por histologia. Seis pacientes foram diagnosticados com HGG, enquanto os restantes 5 foram diagnosticados com LGG. Os dados de PET foram adquiridos com o PET Insert do sistema híbrido Siemens 3T MR-BrainPET. As imagens foram segmentadas de forma a extrair apenas o volume correspondente ao tumor. Após a segmentação, calculou-se a média das curvas de tempo-atividade (TAC) dos volumes tumorais segmentados (STVs), e foram usados métodos de regressão linear e não linear para fazer o ajuste à TAC de cada volume. Para calcular os ajustes com o modelo linear, foram descartados os primeiros 5 minutos de aquisição. Os ajustes baseados na regressão não-linear foram aplicados à TAC correspondente à média entre os 2 e os 60 minutos de aquisição após a injeção. As imagens dos parâmetros foram calculadas a partir dos ajustes baseados na regressão não linear e aplicados a cada voxel. Foram testados três modelos não lineares diferentes: um modelo linear amortecido exponencialmente, um modelo linear amortecido exponencialmente e com um offset, e um modelo linear amortecido exponencialmente com o tempo dependente da raiz quadrada. Dos ajustes não lineares, foram extraídos dois parâmetros: a amplitude, A, e o parâmetro κ. De seguida, geraram-se as imagens dos parâmetros calculados sobre uma área tridimensional selecionada manualmente e contendo o tumor. Para tal, além dos três modelos não lineares, utilizou-se também o modelo linear, de modo a permitir uma comparação entre os diferentes métodos. No caso dos ajustes lineares, os parâmetros extraídos foram a ordenada na origem e o declive. Calcularam-se também as imagens dos parâmetros da regressão não linear usando o modelo linear amortecido exponencialmente com o tempo dependente da raiz quadrada para a cabeça inteira. Os modelos não-lineares foram mais precisos na reprodução das curvas de FET. Os modelos mais robustos foram os modelos lineares exponencialmente amortecidos sem offset. Nos ajustes aplicados à TAC média dos STVs, o modelo linear amortecido exponencialmente com o tempo dependente da raiz quadrada provou ser o que reproduz mais precisamente os dados, com valores de 2 entre 0,94 e 1,00. O parâmetro A do modelo linear amortecido exponencialmente com o tempo dependente da raiz quadrada foi o único que revelou uma diferença significativa entre HGG e LGG (p-value= 0.04, α=0.05). Ao gerar imagens paramétricas com base nos ajustes aplicados a cada voxel, os modelos de regressão não-linear com 2 parâmetros tiveram o melhor desempenho, com valores de 2 perto de 1. Combinando as imagens do parâmetro amplitude e as imagens da atividade total ao longo do tempo, foi possível distinguir entre graus tumorais. Os LGGs assumem valores de amplitude próximos dos valores do tecido saudável à sua volta, e por isso “desaparecem” da imagem paramétrica da amplitude. No caso dos HGGs, a imagem da amplitude reproduz a atividade no tumor. Os ajustes realizados com base na regressão linear devolveram valores de 2 próximos de zero, quer no caso dos STVs, quer no cálculo das imagens paramétricas. A distinção entre HGG e LGG é possível com base nas imagens paramétricas do declive, com os LGGs a assumirem valores de declive superiores aos do tecido saudável adjacente. Com os HGGs, a situação é a oposta: os valores do declive no tumor são inferiores aos do tecido saudável que o rodeia. Em geral, os modelos não lineares reproduzem melhor os dados provenientes de FET PET, mas a distinção entre HGG e LGG baseada num parâmetro apenas é melhor conseguida através de regressão linear. No entanto, a distinção entre HGG e LGG também é possível analisando simultaneamente as imagens dos parâmetros A e κ.The importance of radiolabeled amino acids in Positron Emission Tomography (PET) imaging of the brain has been demonstrated by several studies. The most well studied amino acid tracer is 11C-metionine, but because of the short half-life of 11C, 18F-labeled amino acid analogues have been developed for tumour imaging. A number of studies have proven the importance of O-(2-18F-Fluoroethyl)-L-tyrosine (FET) in determining the extent of cerebral gliomas, biopsy guidance, treatment planning, and detecting recurrence of brain tumours. It was also demonstrated that dynamic changes of FET accumulation in gliomas are variable. High-grade gliomas (HGG) are characterized by an early peak, followed by decrease of FET uptake, whereas the uptake in low-grade gliomas (LGG) steadily increases. Eleven patients (3 female, 8 male, age: 45±15 years) with untreated primary brain tumours and histopathologic confirmation were studied. Six patients had HGG, while the remaining 5 were diagnosed with LGG. PET acquisition was done with the PET Insert of a hybrid Siemens 3T MR-BrainPET system. For tumour volume fitting, a segmentation procedure was applied. After segmentation, the mean time-activity curve (TAC) of the segmented tumour volumes (STVs) was calculated. Linear and nonlinear regression were used to fit to the TAC of each volume. When performing the fits with the linear model, the first 5 minutes of acquisition were discarded. For the nonlinear regression, the fits were applied to the mean TAC from 2 to 60 minutes after injection. Parametric images were calculated based on nonlinear regression fitting of FET data in each voxel. Three different nonlinear models were tested: an exponentially damped linear model, an exponentially damped linear model with an offset, and an exponentially damped linear model with square-root time dependence. The considered nonlinear model parameters were amplitude, A, and κ. The parametric images of manually selected tridimensional volumes containing the tumour were generated. Linear regression based parametric images were also computed for comparison, and the assessed parameters were intercept and slope. Whole-head parametric images were calculated based on nonlinear regression fitting using the exponentially damped linear model with square-root time dependence. Nonlinear regression models were more accurate at reproducing FET TAC characteristics. The most robust models are the exponentially damped linear models without offset. For mean TAC fitting, a model with square-root time dependence reproduced FET activity curves more accurately, with coefficient of determination (2) values between 0.94 and 1.00. The A parameter from the exponentially damped linear model with square-root time dependence was the only one significantly different between HGG and LGG (p-value= 0.04, α=0.05). When generating parametric images based on voxel-wise fit, the nonlinear regression models with 2 parameters performed the best, with 2 close to 1. Visual distinction between tumour grades was possible by comparing the amplitude images with the images of the summed activity across time. In the amplitude, LGGs take values similar to the ones of the surrounding background, thus disappearing from the image. On the other hand, HGGs amplitude images reproduce tumour uptake. Linear regression model fits returned 2 values that were close to zero in both mean TAC fitting, and parametric image calculation. Grade distinction was possible based on the slope parameter alone, with LGGs showing higher slope values than the neighbouring tissue, and HGGs showing lower slope values than their surroundings. In general, though nonlinear models reproduce FET time activity curves more accurately, the distinction between low-grade and high-grade tumours based on one parameter only is better achieved by using linear regression model fitting. However, a reliable differentiation seems to be possible with joint analysis of A and κ parametric images

Semi-Empirical Likelihood Confidence Intervals for the ROC Curve with Missing Data

The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performances of two or more laboratory or diagnostic tests. In this thesis, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric while the other one is non-parametric and both populations have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It has been shown that the log-semi-empirical likelihood ratio statistic is asymptotically chi-square distributed. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. Simulation studies are conducted to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing rates

Fast and Unbiased Estimation of Volume Under Ordered Three-Class ROC Surface (VUS) With Continuous or Discrete Measurements

Receiver Operating Characteristic (ROC) surfaces have been studied in the literature essentially during the last decade and are considered as a natural generalization of ROC curves in three-class problems. The volume under the surface (VUS) is useful for evaluating the performance of a trichotomous diagnostic system or a three-class classifier's overall accuracy when the possible disease condition or sample belongs to one of three ordered categories. In the areas of medical studies and machine learning, the VUS of a new statistical model is typically estimated through a sample of ordinal and continuous measurements obtained by some suitable specimens. However, discrete scales of the prediction are also frequently encountered in practice. To deal with such scenario, in this paper, we proposed a unified and efficient algorithm of linearithmic order, based on dynamic programming, for unbiased estimation of the mean and variance of VUS with unidimensional samples drawn from continuous or non-continuous distributions. Monte Carlo simulations verify our theoretical findings and developed algorithms

Using ROC surface to predict preterm delivery based on hemoglobin level in the first trimester of pregnancy

Receiver Operating Characteristics (ROC) curves have numerous applications for identifying a cut-off point in diagnostic tests. Nonetheless, given that sometimes two cut-off points have to be specified simultaneously, the ROC curve can be used to identify such points. The Volume under the ROC Surface (VUS) serves as a criterion for the accuracy of diagnostic tests. One of the unfortunate outcomes in pregnancy is pre-term delivery; it has been noted that an increase in the level of hemoglobin in the first trimester of pregnancy could result in preterm delivery in weeks 34 to 37 and that an ongoing hemoglobin increase could result in the delivery of a premature fetus before the 34th week of pregnancy. In this regard, in order to separate three groups of on-time delivery, pre-term delivery and immature delivery two cut-off points have to be identified, simultaneously. A suitable measure to identify such points is the ROC surface. In the current study, the hemoglobin information of the first trimester of pregnancy and delivery time of 623 pregnant ladies referring to Milad Hospital in Tehran in 2009-2010 was obtained. ROC surface was adopted to draw two ideal cut-off points for the first trimester of pregnancy. The optimal points for hemoglobin of the first trimester computed with the ROC surface were 12.54 and 13.2. While a hemoglobin rate less than 12.54 indicated an on-time delivery, a rate between the two cut-off points referred to pre-term delivery and hemoglobin more than 13.2 showed a premature fetus. The three-dimensional ROC surface is a useful tool that can visually summarize the ability of a biological marker to classify individuals between more than two groups.

Dark signalling and code division multiple access in an optical fibre LAN with a bus topology

This thesis describes an optical fibre network that uses a bus topology and Code Division Multiple Access (CDMA). Various potential configurations are analysed and compared and it is shown that a serious limitation of optical CDMA schemes using incoherent correlators is the effect of optical beating due to the presence of multiple incoherent optical signals at the receiver photodiode. The network proposed and analysed in this thesis avoids beating between multiple optical fields because it only uses a single, shared, optical source. It does this through the SLIM (Single Light-source with In-line Modulation) configuration in which there is a continuously-operating light source at the head-end of a folded bus, and modulators at the nodes to impose signals on the optical field in the form of pulses of darkness which propagate along the otherwise continuously bright bus. Optical CDMA can use optical-fibre delay-line correlators as matched filters, and these may be operated either coherently or incoherently.Coherent operation is significantly more complex than incoherent operation, but incoherent correlators introduce further beating even in a SLIM network. A new design of optical delay-line correlator, the hybrid correlator, is therefore proposed, analysed and demonstrated. It is shown to eliminate beating. A model of a complete network predicts that a SLIMbus using optical CDMA with hybrid correlators can be operated at TeraBaud rates with the number of simultaneous users limited by multiple access interference (MAI), determined only by the combinatorics of the code set

Quantitative water T2 relaxometry in the early detection of neuromuscular diseases: a retrospective biopsy-controlled analysis.

OBJECTIVES To assess quantitative water T2 relaxometry for the early detection of neuromuscular diseases (NMDs) in comparison to standard qualitative MR imaging in a clinical setting. METHODS This retrospective study included 83 patients with suspected NMD who underwent multiparametric MRI at 3 T with a subsequent muscle biopsy between 2015 and 2019. Qualitative T1-weighted and T2-TIRM images were graded by two neuroradiologists to be either pathological or normal. Mean and median water T2 relaxation times (water T2) were obtained from manually drawn volumes of interests in biopsied muscle from multi-echo sequence. Histopathologic pattern of corresponding muscle biopsies was used as a reference. RESULTS In 34 patients, the T1-weighted images showed clear pathological alternations indicating late-stage fatty infiltration in NMDs. In the remaining 49 patients without late-stage changes, T2-TIRM grading achieved a sensitivity of 56.4%, and mean and median water T2 a sensitivity of 87.2% and 97.4% to detect early-stage NMDs. Receiver operating characteristic (ROC) analysis revealed an area under the curve (AUC) of 0.682, 0.715, and 0.803 for T2-TIRM, mean water T2, and median water T2, respectively. Median water T2 ranged between 36 and 42 ms depending on histopathologic pattern. CONCLUSIONS Quantitative water T2 relaxometry had a significantly higher sensitivity in detecting muscle abnormalities than subjective grading of T2-TIRM, prior to late-stage fatty infiltration signal alternations in T1-weighted images. Normal-appearing T2-TIRM does not rule out early-stage NMDs. Our findings suggest considering water T2 relaxometry complementary to T2-TIRM for early detection of NMDs in clinical diagnostic routine. KEY POINTS • Quantitative water T2 relaxometry is more sensitive than subjective assessment of fat-suppressed T2-weighted images for the early detection of neuromuscular diseases, prior to late-stage fatty infiltration signal alternations in T1-weighted images. • Normal-appearing muscles in fat-suppressed T2-weighted images do not rule out early-stage neuromuscular diseases. • Quantitative water T2 relaxometry should be considered complementary to subjectively rated fat-suppressed T2-weighted images in clinical practice

Bias in trials comparing paired continuous tests can cause researchers to choose the wrong screening modality

<p>Abstract</p> <p>Background</p> <p>To compare the diagnostic accuracy of two continuous screening tests, a common approach is to test the difference between the areas under the receiver operating characteristic (ROC) curves. After study participants are screened with both screening tests, the disease status is determined as accurately as possible, either by an invasive, sensitive and specific secondary test, or by a less invasive, but less sensitive approach. For most participants, disease status is approximated through the less sensitive approach. The invasive test must be limited to the fraction of the participants whose results on either or both screening tests exceed a threshold of suspicion, or who develop signs and symptoms of the disease after the initial screening tests.</p> <p>The limitations of this study design lead to a bias in the ROC curves we call <it>paired screening trial bias</it>. This bias reflects the synergistic effects of inappropriate reference standard bias, differential verification bias, and partial verification bias. The absence of a gold reference standard leads to inappropriate reference standard bias. When different reference standards are used to ascertain disease status, it creates differential verification bias. When only suspicious screening test scores trigger a sensitive and specific secondary test, the result is a form of partial verification bias.</p> <p>Methods</p> <p>For paired screening tests with bivariate normally distributed scores, we give formulae and programs to quantify the effect of <it>paired screening trial bias </it>on a paired comparison of area under the curves. We fix the prevalence of disease, and the chance a diseased subject manifests signs and symptoms. We derive the formulas for true sensitivity and specificity, and those for the sensitivity and specificity observed by the study investigator.</p> <p>Results</p> <p>The observed area under the ROC curves is quite different from the true area under the ROC curves. The typical direction of the bias is a strong inflation in sensitivity, paired with a concomitant slight deflation of specificity.</p> <p>Conclusion</p> <p>In paired trials of screening tests, when area under the ROC curve is used as the metric, bias may lead researchers to make the wrong decision as to which screening test is better.</p

Univariate parametric survival analysis using GS-distributions.

The GS-distribution is a family of distributions that provide an accurate representation of any unimodal univariate continuous distribution. In this contribution we explore the utility of this family as a general model in survival analysis. We show that the survival function based on the GS-distribution is able to provide a model for univariate survival data and that appropriate estimates can be obtained. We develop some hypotheses tests that can be used for checking the underlying survival model and for comparing the survival of different groups.Peer Reviewe