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

## TL;DR

This study uses discrete mathematics to identify risk factors for post-void residual urine in overactive bladder patients after treatment.

## Contribution

The novel use of discrete mathematics techniques, such as network graphs and clustering, to analyze OAB treatment outcomes and risk factors.

## Key findings

- Frailty, daytime frequency, and nocturia episodes are closely related to post-void residual (PVR) urine.
- Clustering analysis divided patients into three groups, with high frailty in Cluster 1 indicating a high risk for PVR.
- Significant differences in clinical indicators were observed between the remaining two patient clusters.

## Abstract

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.