Comparing the performance of the EQ-5D-3L and the EQ-5D-5L in young Portuguese adults

Background Some studies have reported a ceiling effect in EQ-5D-3L, especially in healthy and/or young individuals. Recently, two further levels have been included in its measurement model (EQ-5D-5L). The purposes of this study were (1) to assess the properties of the EQ-5D-5L in comparison with the standard EQ-5D-3L in a sample of young adults, (2) to foreground the importance of collecting qualitative data to confirm, validate or refine the EQ-5D questionnaire items and (3) to raise questions pertaining to the wording in these questionnaire items. Methods The data used came from a sample of respondents aged 30 or under (n = 624). They completed both versions of the EQ-5D, which were compared in terms of feasibility, level of inconsistency and ceiling effect. Agreement between the instruments was assessed using correlation coefficients and Bland-Altman plots. Known-groups validity of the EQ-5D-5L was also assessed using non-parametric tests. The discriminative properties were compared using receiver operating characteristic curves. Finally, four interviews were conducted for retrospective reports to elicit respondents’ understanding and perceptions of the format, instructions, items, and responses. Results Quantitative results show a ceiling effect reduction of 25.3 % and a high level agreement between both indices. Known-groups validity was confirmed for the EQ-5D-5L. Explorative interviews indicated ambiguity and low degree of certainty in regards to conceptualizing differences between levels moderate-slight across three dimensions. Conclusions The EQ-5D-5L performed better than the EQ-5D-3L. However, the explorative interviews demonstrated several limitations in the EQ-5D questionnaire wording and high context-dependent answers point to lack of illnesses’ experience amongst young adults.

Threshold values of sagittal abdominal diameter for the detection of cardio-metabolic risk factors in Northeastern Mexico: a cross-sectional study

Background: The use of sagittal abdominal diameter (SAD) has been proposed for screening cardio-metabolic risk factors; however, its accuracy can be influenced by the choice of thresholds values. Aim: To determine the SAD threshold values for cardio-metabolic risk factors in Mexican adults; to assess whether parallel and serial SAD testing can improve waist circumference (WC) sensitivity and specificity; and to analyze the effect of considering SAD along with WC and body mass index (BMI) in detecting cardio-metabolic risk. Methods: This cross-sectional study was conducted during 2012-2014 in Northeast Mexico (n = 269). Data on anthropometric, clinical, and biochemical measurements were collected. Sex-adjusted receiver-operating characteristic curves (ROC) were obtained using hypertension, dysglycemia, dyslipidemia and insulin resistance as individual outcomes and metabolic syndrome as a composite outcome. Age-adjusted odds ratios and 95% confidence intervals (CI) were estimated using logistic regression. Results: The threshold value for SAD with acceptable combination of sensitivity and specificity was 24.6 cm in men and 22.5 cm in women. Parallel SAD testing improved WC sensitivity and serial testing improved WC specificity. The co-occurrence of high WC/high SAD increased the risk for insulin resistance by 2.4-fold (95% CI: 1.1-5.3), high BMI/high SAD by 4.3-fold (95% CI: 1.7-11.9) and SAD alone by 2.2-fold (95% CI: 1.2.-4.2). Conclusions: The use of SAD together with traditional obesity indices such as WC and BMI has advantages over using either of these indices alone. SAD may be a powerful screening tool for interventions for high-risk individuals.

A Diagnostic Calculator for Detecting Glaucoma on the Basis of Retinal Nerve Fiber Layer, Optic Disc, and Retinal Ganglion Cell Analysis by Optical Coherence Tomography

Purpose: The purpose of this study was to develop and validate a multivariate predictive model to detect glaucoma by using a combination of retinal nerve fiber layer (RNFL), retinal ganglion cell-inner plexiform (GCIPL), and optic disc parameters measured using spectral-domain optical coherence tomography (OCT). Methods: Five hundred eyes from 500 participants and 187 eyes of another 187 participants were included in the study and validation groups, respectively. Patients with glaucoma were classified in five groups based on visual field damage. Sensitivity and specificity of all glaucoma OCT parameters were analyzed. Receiver operating characteristic curves (ROC) and areas under the ROC (AUC) were compared. Three predictive multivariate models (quantitative, qualitative, and combined) that used a combination of the best OCT parameters were constructed. A diagnostic calculator was created using the combined multivariate model. Results: The best AUC parameters were: inferior RNFL, average RNFL, vertical cup/disc ratio, minimal GCIPL, and inferior-temporal GCIPL. Comparisons among the parameters did not show that the GCIPL parameters were better than those of the RNFL in early and advanced glaucoma. The highest AUC was in the combined predictive model (0.937; 95% confidence interval, 0.911–0.957) and was significantly (P = 0.0001) higher than the other isolated parameters considered in early and advanced glaucoma. The validation group displayed similar results to those of the study group. Conclusions: Best GCIPL, RNFL, and optic disc parameters showed a similar ability to detect glaucoma. The combined predictive formula improved the glaucoma detection compared to the best isolated parameters evaluated. The diagnostic calculator obtained good classification from participants in both the study and validation groups.

Normative reference values for the 20-meter shuttlerun test in a population-based sample of schoolchildren in Bogota, Colombia: The FUPRECOL Study

Our aim was to determine the normative reference values of cardiorespiratory fitness (CRF) and to establish the proportion of subjects with low CRF suggestive of future cardio-metabolic risk.

Cardiorespiratory fitness and cardiometabolic risk factors in schoolchildren from Colombia: The FUPRECOL Study

The objectives of this study are to investigate the association between cardiorespiratory fitness and cardiovascular risk factors in schoolchildren and to evaluate the degree of association between overall and abdominal adiposity and cardiorespiratory fitness. A total of 1,875 children and adolescents attending public schools in Bogota, Colombia (56.2% girls; age range of 9–17.9 years). A cardiovascular risk score (Z-score) was calculated and participants were divided into tertiles according to low and high levels of overall (sum of the skinfold thicknesses) and abdominal adiposity. Schoolchildren with a high level of overall adiposity demonstrated significant differences in seven of the 10 variables analyzed (i.e. systolic and diastolic blood pressure, triglycerides, triglycerides/HDL-c ratio, total cholesterol, glucose and cardiovascular risk score). Schoolchildren with high levels of both overall and abdominal adiposity and low cardiorespiratory fitness had the least favorable cardiovascular risk factors score. These findings may be relevant to health promotion in Colombian youth.

On certain curves of genus three in characteristic two

We study curves of genus 3 over algebraically closed fields of characteristic 2 with the canonical theta characteristic totally supported in one point. We compute the moduli dimension of such curves and focus on some of them which have two Weierstrass points with Weierstrass directions towards the support of the theta characteristic. We answer questions related to order sequence and Weierstrass weight of Weierstrass points and the existence of other Weierstrass points with similar properties.

Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.

Nonparametric estimation of time-dependent ROC curves conditional on a continuous covariate

The receiver-operating characteristic (ROC) curve is the most widely used measure for evaluating the performance of a diagnostic biomarker when predicting a binary disease outcome. The ROC curve displays the true positive rate (or sensitivity) and the false positive rate (or 1-specificity) for different cut-off values used to classify an individual as healthy or diseased. In time-to-event studies, however, the disease status (e.g. death or alive) of an individual is not a fixed characteristic, and it varies along the study. In such cases, when evaluating the performance of the biomarker, several issues should be taken into account: first, the time-dependent nature of the disease status; and second, the presence of incomplete data (e.g. censored data typically present in survival studies). Accordingly, to assess the discrimination power of continuous biomarkers for time-dependent disease outcomes, time-dependent extensions of true positive rate, false positive rate, and ROC curve have been recently proposed. In this work, we present new nonparametric estimators of the cumulative/dynamic time-dependent ROC curve that allow accounting for the possible modifying effect of current or past covariate measures on the discriminatory power of the biomarker. The proposed estimators can accommodate right-censored data, as well as covariate-dependent censoring. The behavior of the estimators proposed in this study will be explored through simulations and illustrated using data from a cohort of patients who suffered from acute coronary syndrome.

Receiver operating characteristic (ROC) curve for classification of18F-NaF uptake on PET/CT

Abstract Objective: To assess the cutoff values established by ROC curves to classify18F-NaF uptake as normal or malignant. Materials and Methods: PET/CT images were acquired 1 hour after administration of 185 MBq of18F-NaF. Volumes of interest (VOIs) were drawn on three regions of the skeleton as follows: proximal right humerus diaphysis (HD), proximal right femoral diaphysis (FD) and first vertebral body (VB1), in a total of 254 patients, totalling 762 VOIs. The uptake in the VOIs was classified as normal or malignant on the basis of the radiopharmaceutical distribution pattern and of the CT images. A total of 675 volumes were classified as normal and 52 were classified as malignant. Thirty-five VOIs classified as indeterminate or nonmalignant lesions were excluded from analysis. The standardized uptake value (SUV) measured on the VOIs were plotted on an ROC curve for each one of the three regions. The area under the ROC (AUC) as well as the best cutoff SUVs to classify the VOIs were calculated. The best cutoff values were established as the ones with higher result of the sum of sensitivity and specificity. Results: The AUCs were 0.933, 0.889 and 0.975 for UD, FD and VB1, respectively. The best SUV cutoffs were 9.0 (sensitivity: 73%; specificity: 99%), 8.4 (sensitivity: 79%; specificity: 94%) and 21.0 (sensitivity: 93%; specificity: 95%) for UD, FD and VB1, respectively. Conclusion: The best cutoff value varies according to bone region of analysis and it is not possible to establish one value for the whole body.

Eventually minimal curves

A curve defined over a finite field is maximal or minimal according to whether the number of rational points attains the upper or the lower bound in Hasse-Weil's theorem, respectively. In the study of maximal curves a fundamental role is played by an invariant linear system introduced by Ruck and Stichtenoth in [6]. In this paper we define an analogous invariant system for minimal curves, and we compute its orders and its Weierstrass points. In the last section we treat the case of curves having genus three in characteristic two.

Duality of osculating developables of projective curves

We give a description of the dual varieties of all developables of osculating linear spaces to a projective curve in terms of the higher order dual varieties of the curve, in arbitrary characteristic. We also determine for these varieties the inseparable degrees of the projections from the conormal varieties onto their dual varieties.

Euler characteristics and elliptic curves

Let E be a modular elliptic curve over ℚ, without complex multiplication; let p be a prime number where E has good ordinary reduction; and let F∞ be the field obtained by adjoining to ℚ all p-power division points on E. Write G∞ for the Galois group of F∞ over ℚ. Assume that the complex L-series of E over ℚ does not vanish at s = 1. If p ⩾ 5, we make a precise conjecture about the value of the G∞-Euler characteristic of the Selmer group of E over F∞. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg.

Growth curves of four crustose lichens

The growth curves of four common species of crustose lichens, viz., Buellia aethalea (Ach.) Th. Fr., Lecidea tumida Massai., Rhizocarpon geographicum (L.) DC., and Rhizocarpon reductum Th. Fr. were studied at a site in south Gwynedd, north Wales, UK. Radial growth rates (RGR, mm 1.5 yr-1) were greatest in thalli of R. reductum and least in R. geographicum. Variation in RGR between thalli was greater in B. aethalea and L. tumida than in the species of Rhizocarpon. The relationship between growth rate and thallus diameter was not asymptotic; RGR increasing in smaller thalli to a maximum and then declining in larger diameter thalli. A polynomial curve was fitted to the data; the growth curves being fitted best by a second-order (quadratic) curve, the best fit to this model being shown by B. aethalea. A significant linear regression with a negative slope was also fitted to the growth of the larger thalli of each species. The data suggest that the growth curves of the four crustose lichens differ significantly from the asymptotic curves of foliose lichen species. A phase of declining RGR in larger thalli appears to be characteristic of crustose lichens and is consistent with data from lichenometric studies.

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

ROC curves of obesity indicators have a predictive value for children hypertension aged 7-17 years

Objective: The aim of the study is to examine the distribution of integrated covariate and its association with blood pressure (BP) among children in Anhui province, China, and assess the predictive value of integrated covariate to children hypertension. Methods: A total of 2,828 subjects (1,588 male and 1,240 female) aged 7-17 years participated in this study. Height, weight, waistline, hipline and BP of all subjects were measured, obesity and overweight were defined by an international standard, specifying the measurement, the reference population, and the age and sex specific cut off points. High BP status was defined as systolic blood pressure (SBP) and/or diastolic blood pressure (DBP) > 95th percentile for age and gender. Results: Our results revealed that the prevalence of children hypertension was 11.03%, the SBP and DBP of obesity group were significantly higher than that of normal group. Anthropometric obesity indices such as body mass index (BMI) were positively correlated with SBP and DBP. Integrated covariate had a better performance than the single covariate in the receiver-operating characteristic (ROC) curve, the cut-off value; the sensitivity and the specificity of the integrated covariate were 0.112, 0.577, 0.683, respectively. Conclusion: Integrated covariate is a simple and effective anthropometric index to identify childhood hypertension.