Adjusted empirical likelihood estimation of the youden index and associated threshold for the bigamma model

The Youden index is a widely used measure in the framework of medical diagnostic, where the effectiveness of a biomarker (screening marker or predictor) for classifying a disease status is studied. When the biomarker is continuous, it is important to determine the threshold or cut-off point to be used in practice for the discrimination between diseased and healthy populations. We introduce a new method based on adjusted empirical likelihood for quantiles aimed to estimate the Youden index and its associated threshold. We also include bootstrap based confidence intervals for both of them. In the simulation study, we compare this method with a recent approach based on the delta method under the bigamma scenario. Finally, a real example of prostatic cancer, well known in the literature, is analyzed to provide the reader with a better understanding of the new metho

Unbalanced groups in nonparametric survival tests

It is fairly common to find medical examples with survival data with unequal sample size among the groups. There are several tests for those cases, but in practice, the use of one test instead of another is done without justifying the election. Sometimes, the choice of one test or another can lead to different conclusions, so it is important to have some guidelines to help to choose the suitable test in unbalanced groups. The computation of the tests is done with the statistical software (BMDP, SAS, SPSS, Stata, Statgraphics, and S-Plus). However the commercial software only covers tests for the family of the weigthed tests, none of the score tests, and the nomenclature is not unified, using different names for the same test. We perform several simulations to give some pieces of advice for picking out the right test. Due to the fact that there are situations where it is advisable to use a test from the family of the score tests against a weighted one, we have developed a new software in JavaScript for Internet that computes score and weighted tests versions (10 tests) that unifies the nomenclature (this software is available from the authors upon request). We include real examples where we apply, using the new JavaScript programs, the recommendations suggested by the simulations

GsymPoint: An R Package to Estimate the Generalized Symmetry Point, an Optimal Cut-off Point for Binary Classification in Continuous Diagnostic Tests

In clinical practice, it is very useful to select an optimal cutpoint in the scale of a continuous biomarker or diagnostic test for classifying individuals as healthy or diseased. Several methods for choosing optimal cutpoints have been presented in the literature, depending on the ultimate goal. One of these methods, the generalized symmetry point, recently introduced, generalizes the symmetry point by incorporating the misclassification costs. Two statistical approaches have been proposed in the literature for estimating this optimal cutpoint and its associated sensitivity and specificity measures, a parametric method based on the generalized pivotal quantity and a nonparametric method based on empirical likelihood. In this paper, we introduce GsymPoint, an R package that implements these methods in a user-friendly environment, allowing the end-user to calculate the generalized symmetry point depending on the levels of certain categorical covariates. The practical use of this package is illustrated using three real biomedical datasetsThis research has been supported by several Grants from the Spanish Ministry of Science and Innovation. M. López-Ratón and C. Cadarso-Suárez acknowledge support to MTM2011-15849-E, MTM2011-28285-C02-00, MTM2014-52975-C2-1-R and MTM2015-69068-REDT. E.M. Molanes-López acknowledges support to MTM2011-28285-C02-02, ECO2011-25706, MTM2011-15849-E and MTM2015-69068-REDT. E. Letón acknowledges support to MTM2011-15849-E, MTM2011-28285-C02-02, PI13/02446 and MTM2015-69068-REDTS

Image guided SBRT for multiple liver metastases with ExacTrac Adaptive Gating

AimTo report the outcome and toxicity of sequential stereotactic body radiotherapy (SBRT) for multiple liver metastases in patients treated with ExacTrac Adaptive Gating.BackgroundIn selected patients with a limited number of liver metastases, SBRT has been evaluated as a safe and effective treatment, with minimal toxicity and high rates of local control.Materials and methodsFrom April 2008 to October 2013, 21 patients with multiple (3–14) liver metastases (n[[ce:hsp sp="0.25"/]]=[[ce:hsp sp="0.25"/]]101) were treated sequentially with SBRT at our institution. Maximum tumor diameter was 7.5[[ce:hsp sp="0.25"/]]cm. Prior to treatment, internal markers were placed inside or near the tumor. CT or PET-CT simulation was used for the definition of gross tumor volume (GTV). Median planning target volume was 32.3[[ce:hsp sp="0.25"/]]cc (3.6–139.3[[ce:hsp sp="0.25"/]]cc). Treatment consisted of 3 fractions (12–20[[ce:hsp sp="0.25"/]]Gy/fraction) or 5 fractions (10[[ce:hsp sp="0.25"/]]Gy/fraction), prescribed to the 90–95% of the PTV volume. Daily intra-fraction image guidance was performed with ExacTrac Adaptive Gating. Regular follow-up included CT or PET-CT imaging.ResultsAfter a median of 23.2 months, the estimated local control rate was 94.4%, 80.6%, 65% and 65% after 1, 2, 3 and 4 years; the median overall survival was 62 months (95% CI 49.12–74.87) and the actuarial survival reached at 60 months was 57.6%. The univariate data analysis revealed that only primary histology other than colorectal adenocarcinoma was shown as an independent significant prognostic factor for local control (p[[ce:hsp sp="0.25"/]]=[[ce:hsp sp="0.25"/]]0.022). Number of treated metastases did not modify significantly the overall survival (p[[ce:hsp sp="0.25"/]]=[[ce:hsp sp="0.25"/]]0.51). No toxicity higher than G3 (1 patient with chest wall pain) and no radiation-induced liver disease were observed.ConclusionsSequential SBRT with ExacTrac Adaptive Gating for multiple liver metastases can be considered an effective, safe therapeutic option, with a low treatment-related toxicity. Excellent rates of local control and survival were obtained

Generalización y equivalencias de tests no paramétricos para el análisis de datos censurados

El contenido de esta memoria se encuentra estructurado en siete capítulos, de los cuales el primero de ellos es de introducción al problema. En el capítulo II se recopilan los principales tipos de censura que se pueden dar, se resumen las funciones teóricas que se asocian al tiempo de supervivencia y se ven distintas formas de estimación no paramétrica de la función de supervivencia. Dado que los tests no paramétricos de comparación de curvas de supervivencia son una generalización de los tests no paramétricos habituales para datos no censurados, se estudian dichos tests en el capítulo III. En este capítulo se revisan y amplían las propiedades fundamentales de los rangos, se dan nuevas expresiones para los tests en el caso general de empates y se prueban sus equivalencias con expresiones anteriores, detectando inconsistencias en la literatura. En el capítulo IV se estudian los principales tests de supervivencia para dos grupos y en el capítulo V su generalización a varios grupos y grupos ordenados. En estos capítulos se introduce una nueva clasificación de los tests, se dan nuevas expresiones para ellos en el caso general de empates y mediante el estudio de sus equivalencias se proponen nuevos tests.En el capítulo VI se contemplan tres secciones. En la primera, se describe un estudio de simulaciones que sirve para dar recomendaciones de uso para cada test. En la segunda, se incluyen casos prácticos donde se intenta poner en práctica las recomendaciones elaboradas en la sección anterior. En la tercera, se describe el software de desarrollo propio en JavaScript para el cálculo de los tests utilizados en los ejemplos. Para terminar, se incluyen en el capítulo VII dos apéndices con el código SAS para las simulaciones y el código JavaScript

Tipos de demostraciones

Este mini-libro pretende ayudar a entender los tipos de demostraciones que aparecen de forma habitual en el campo de las Matemáticas, buscando los siguientes objetivos: Distinguir las demostraciones directas de las demostraciones a la contra. Interpretar las condiciones necesarias y suFIcientes. Estudiar las demostraciones por reducciön al absurdo y por marcha hacia atrás. Manejar el principio de inducción en su versión simple y completa. Manejar el principio de buena ordenación y de descenso infinito

Accessible mathematics videos for non-disabled students in primary education.

Our work applies Universal Design criteria for producing and using Mathematics videos for primary education students, at a time when many countries are shifting towards inclusive education policies. We have focused on how the accessibility criteria used for students with visual impairments might affect non-disabled students. For this, we reviewed applicable Universal Design principles as well as best practices in multimedia learning. We took into account the roles, procedures, tools and standards involved in the multimedia lifecycle. We then undertook an experiment consisting of producing two videos about prime numbers with the same pedagogical contents; one video was accessible for students with visual impairments and the other one was not accessible to them. We conducted a trial in real world school settings with 228 non-disabled children, who were randomly assigned a version, either accessible or not accessible, and were then asked to take a test to measure objective aspects of their learning concerning retention and transfer as well as several subjective aspects, including the attractiveness of the videos. Results indicate that there were no significant differences in the scores obtained by students using either video, although the group who watched the accessible video obtained higher score medians in the retention questions. Moreover, students found the accessible video significantly more attractive (p = 0.042). Our study provides recommendations for different stakeholders and stages within the process of producing multimedia mathematics materials that are accessible to primary students with visual impairments, as well as evidence demonstrating that everybody can benefit from the recommendations for developing good quality, accessible multimedia material

Acute skin toxicity of ultra-hypofractionated whole breast radiotherapy with simultaneous integrated boost for early breast cancer

Background: Whole-breast irradiation (WBI) after breast conserving surgery (BCS) is indicated to improve loco-regional control and survival. Former studies showed that addition of tumor bed boost in all age groups significantly improved local control although no apparent impact on overall survival but with an increased risk of worse cosmetic outcome. Even though shortened regimens in 3 weeks are considered the standard, recent studies have shown the non-inferiority of a treatment regimen of 5 fractions in one-week in both locoregional control and toxicity profile, although simultaneous integrated boost (SIB) in this setting has been scarcely studied. Materials and Methods: From March-2020 to March-2022, 383 patients with early breast cancer diagnosis and a median age of 56 years-old (range 30–99)were included in a prospective registry of ultra-hypofractionated WBI up to a total dose of 26 Gy in 5.2 Gy/fraction with a SIB of 29 Gy in 5.8 Gy/fraction in 272 patients (71%), 30–31 Gy in 6–6.2 Gy/fraction in 111 patients (29%) with close/focally affected margins. Radiation treatment was delivered by conformal 3-D technique in 366 patients (95%), VMAT in 16patients (4%) and conformal 3-D with deep inspiration breath hold (DIBH) in 4patients (1%). Ninety-three per cent of patients received endocrine therapy and 43% systemic or targeted chemotherapy. Development of acute skin complications was retrospectively reviewed. Results: With a median follow-up of 18 months (range 7–31), all patients are alive without evidence of local, regional or distant relapse. Acute tolerance was acceptable, with null o mild toxicity: 182 (48%) and 15 (4%) patients developed skin toxicity grade 1 and 2 respectively; 9 (2%) and 2 (0.5%) patients breast edema grade 1and 2 respectively. No other acute toxicities were observed. We also evaluated development of early delayed complications and observed grade 1 breast edema in 6 patients (2%); grade 1 hyperpigmentation in 20 patients (5%); and grade 1 and 2 breast induration underneath boost region in 10(3%) and 2 patients (0.5%) respectively. We found a statistically significant correlation between the median PTVWBI and presence of skin toxicity (p = 0.028) as well as a significant correlation between late hyperpigmentation with the median PTVBOOST (p = 0.007) and the ratio PTVBOOST/PTVWBI (p = 0.042). Conclusion: Ultra-hypofractionated WBI + SIB in 5 fractions over one-week is feasible and well tolerated, although longer follow-up is necessary to confirm these results