Use of the p-values as a size-dependent function to address practical differences when analyzing large datasets.

Biomedical research has come to rely on p-values as a deterministic measure for data-driven decision-making. In the largely extended null hypothesis significance testing for identifying statistically significant differences among groups of observations, a single p-value is computed from sample data. Then, it is routinely compared with a threshold, commonly set to 0.05, to assess the evidence against the hypothesis of having non-significant differences among groups, or the null hypothesis. Because the estimated p-value tends to decrease when the sample size is increased, applying this methodology to datasets with large sample sizes results in the rejection of the null hypothesis, making it not meaningful in this specific situation. We propose a new approach to detect differences based on the dependence of the p-value on the sample size. We introduce new descriptive parameters that overcome the effect of the size in the p-value interpretation in the framework of datasets with large sample sizes, reducing the uncertainty in the decision about the existence of biological differences between the compared experiments. The methodology enables the graphical and quantitative characterization of the differences between the compared experiments guiding the researchers in the decision process. An in-depth study of the methodology is carried out on simulated and experimental data. Code availability at https://github.com/BIIG-UC3M/pMoSS .

On sparse ensemble methods: An application to short-term predictions of the evolution of COVID-19.

Since the seminal paper by Bates and Granger in 1969, a vast number of ensemble methods that combine different base regressors to generate a unique one have been proposed in the literature. The so-obtained regressor method may have better accuracy than its components, but at the same time it may overfit, it may be distorted by base regressors with low accuracy, and it may be too complex to understand and explain. This paper proposes and studies a novel Mathematical Optimization model to build a sparse ensemble, which trades off the accuracy of the ensemble and the number of base regressors used. The latter is controlled by means of a regularization term that penalizes regressors with a poor individual performance. Our approach is flexible to incorporate desirable properties one may have on the ensemble, such as controlling the performance of the ensemble in critical groups of records, or the costs associated with the base regressors involved in the ensemble. We illustrate our approach with real data sets arising in the COVID-19 context.

Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization.

Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors' interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.

On Building Online Visualization Maps for News Data Streams by Means of Mathematical Optimization.

In this article we develop a novel online framework to visualize news data over a time horizon. First, we perform a Natural Language Processing analysis, wherein the words are extracted, and their attributes, namely the importance and the relatedness, are calculated. Second, we present a Mathematical Optimization model for the visualization problem and a numerical optimization approach. The model represents the words using circles, the time-varying area of which displays the importance of the words in each time period. Word location in the visualization region is guided by three criteria, namely, the accurate representation of semantic relatedness, the spread of the words in the visualization region to improve the quality of the visualization, and the visual stability over the time horizon. Our approach is flexible, allowing the user to interact with the display, as well as incremental and scalable. We show results for three case studies using data from Danish news sources.

Preliminary Study of the Differences in Optic Nerve Head Hemoglobin Measures Between Patients With and Without Childhood Glaucoma.

PURPOSE: To evaluate the effectiveness of quantifying color changes in the optic nerve head in retinal photographs of patients with childhood glaucoma. METHODS: In this observational study, three photographs of the optic nerve head were obtained in 28 patients with childhood glaucoma and 28 age- and sex-matched healthy participants (the childhood glaucoma and control groups, respectively). The Laguna Optic Nerve Head Hemoglobin (ONhE) software (Insoft SL, Tenerife, Spain) was used to determine hemoglobin levels in the optic nerve head. The following parameters were quantified: the hemoglobin levels in the optic nerve head across the whole disc, in 24 sectors (the optic nerve head divided by two concentric rings and eight 45-degree radial sectors), and in the vertical disc diameter (sectors 8 and 20), and the estimated cup-disc ratio and Glaucoma Discriminant Function, which combines the slope of the hemoglobin amount with the mean vertical disc diameter. RESULTS: Patient ages ranged from 9 to 14 years (median: 11 years) in the childhood glaucoma group, and 7 to 13 years (median: 9 years) in the control group (P < .061). Eyes in the childhood glaucoma group showed a significantly higher cup-disc ratio compared to eyes in the control group (0.6 ± 0.2 vs 0.5 ± 0.1, respectively; P < .0001). In the childhood glaucoma group, the Glaucoma Discriminant Function was found to be significantly lower than in the control group (-6.5 ± 31.1 vs 9.4 ± 17.1, respectively; P < .0001). There were no significant differences in the hemoglobin levels in the optic nerve head across the whole disc between eyes in the childhood glaucoma and control groups (58.2% ± 10.9% vs 58.5% ± 6.7%, respectively; P = .847). The Laguna ONhE software showed good reproducibility in measuring percentages of hemoglobin levels in both groups. CONCLUSIONS: The Laguna ONhE software is useful for patients with childhood glaucoma. However, hemoglobin levels in the optic nerve head across the whole disc may have normal values. This method had good reliability and is easy to implement in routine clinical practice. [J Pediatr Ophthalmol Strabismus. 2017;54(6):387-394.].