A Discrete Mathematics Approach for Understanding Risk Factors in Overactive Bladder Treatment

Introduction Discrete mathematics, a branch of mathematics that includes graph theory, combinatorics, and logic, focuses on discrete mathematical structures. Its application in the medical field, particularly in analyzing patterns in patient data and optimizing treatment methods, is invaluable. This study, focusing on post-void residual (PVR) urine following overactive bladder (OAB) treatment, utilized discrete mathematics techniques to analyze PVR and its associated risk factors. Methods A retrospective study was conducted on 128 OAB patients who received intradetrusor onabotulinum toxin A injections between 2020 and 2022. Network graphs based on graph theory were used to analyze correlations between clinical variables, and clustering analysis was performed with PVR as the primary variable. Results The network graph analysis revealed that frailty, daytime frequency, and nocturia episodes were closely related to PVR. Clustering analysis with PVR as the primary variable divided the patients into three groups, suggesting that the group with particularly high frailty (Cluster 1) is at high risk for PVR. Moreover, significant differences in clinical indicators such as age, voiding efficiency, Overactive Bladder Symptom Score, and International Consultation on Incontinence Questionnaire-Short Form were observed in the remaining two clusters (Cluster 0 and 2). Conclusion This study demonstrates the effectiveness of discrete mathematics methods in identifying risk factors for PVR after OAB treatment and in distinguishing clinical subgroups based on patient characteristics. This approach could contribute to the formulation of individualized treatment strategies and the improvement of patient care quality. Further development and clinical application of this methodology are expected in future research.

A network-based analysis to assess COVID-19 disruptions in the Bogotá BRT system

The global COVID-19 crisis has severely affected mass transit in the cities of the global south. Fear of widespread propagation in public spaces and the dramatic decrease in human mobility due to lockdowns have resulted in a significant reduction of public transport options. We analyze the case of TransMilenio in Bogotá, a massive Bus Rapid Transit system that is the main mode of transport for an urban area of roughly 10 million inhabitants. Concerns over social distancing and new health regulations reduced the number of trips to under 20% of its historical values during extended periods of time during the lockdowns. This has sparked a renewed interest in developing innovative data-driven responses to COVID-19 resulting in large corpora of TransMilenio data being made available to the public. In this paper we use a database updated daily with individual passenger card swipe validation microdata including entry time, entry station, and a hash of the card's ID. The opportunity of having daily detailed minute-to-minute ridership information and the challenge of extracting useful insights from the massive amount of raw data (∼1,000,000 daily records) require the development of tailored data analysis approaches. Our objective is to use the natural representation of urban mobility offered by networks to make pairwise quantitative similarity measurements between daily commuting patterns and then use clustering techniques to reveal behavioral disruptions as well as the most affected geographical areas due to the different pandemic stages. This method proved to be efficient for the analysis of large amount of data and may be used in the future to make temporal analysis of similarly large datasets in urban contexts.

Chain Reversion for Detecting Associations in Interacting Variables-St. Nicolas House Analysis

(1) Background: We present a new statistical approach labeled as “St. Nicolas House Analysis” (SNHA) for detecting and visualizing extensive interactions among variables. (2) Method: We rank absolute bivariate correlation coefficients in descending order according to magnitude and create hierarchic “association chains” defined by sequences where reversing start and end point does not alter the ordering of elements. Association chains are used to characterize dependence structures of interacting variables by a graph. (3) Results: SNHA depicts association chains in highly, but also in weakly correlated data, and is robust towards spurious accidental associations. Overlapping association chains can be visualized as network graphs. Between independent variables significantly fewer associations are detected compared to standard correlation or linear model-based approaches. (4) Conclusion: We propose reversible association chains as a principle to detect dependencies among variables. The proposed method can be conceptualized as a non-parametric statistical method. It is especially suited for secondary data analysis as only aggregate information such as correlations matrices are required. The analysis provides an initial approach for clarifying potential associations that may be subject to subsequent hypothesis testing.