# Interrelations between Drug Prescriptions and Diagnoses for SHI Diabetes Patients using Graph Theoretic Methods and a Markov Model

### Reinhard Schuster, Marc Heidbreder, Timo Emcke, Martin Schuster

#### 2020

#### Abstract

We analyze large data sets of diabetes patients in order to get new insights into the dependencies between drug groups and diagnoses using age, polypharmacy and multimorbidity as covariates. Diagnostic data using the ICD-10 classification are available with the resolution of quarters. For drugs the exact day of prescription is available. The analysis uses all co-medication and all diagnoses of all physicians a patient has consulted within a quarter and is thereby wider than the point of view related to a special physician. The communication between physicians may be confounded by information deficits due to informal self-diagnostics by the patients. Differently specialized physicians may apply different guidelines which point to specific diseases. Interactions between different drugs and different therapy schemes may lead to new diseases for multimorbid patients. Large data sets create opportunities to detect such interactions. We use a graph theoretic approach with drug groups as nodes. Using a diagnose vector edges are given by therapeutic neighborhood using the Manhattan distance. A graph clustering determines drug groups for similarly sick patients which contains indirectly age and multimorbidity. This can explain cost effects due to the degree of sickness. The graph clustering uses the modularity method. The underlying algorithm leads to an integer linear program (ILP) which is in general NP-hard. For the calculations we use Mathematica from Wolfram Research in combination with a python program using CPLEX from IBM. Drug innovations may lead to changes in drug therapy. Therefore we compare the steady state solution of the related Markov model with the status quo of drug prescription.

Download#### Paper Citation

#### in Harvard Style

Schuster R., Heidbreder M., Emcke T. and Schuster M. (2020). **Interrelations between Drug Prescriptions and Diagnoses for SHI Diabetes Patients using Graph Theoretic Methods and a Markov Model**. In *Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 5: HEALTHINF*; ISBN 978-989-758-398-8, SciTePress, pages 345-352. DOI: 10.5220/0008911603450352

#### in Bibtex Style

@conference{healthinf20,

author={Reinhard Schuster and Marc Heidbreder and Timo Emcke and Martin Schuster},

title={Interrelations between Drug Prescriptions and Diagnoses for SHI Diabetes Patients using Graph Theoretic Methods and a Markov Model},

booktitle={Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 5: HEALTHINF},

year={2020},

pages={345-352},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0008911603450352},

isbn={978-989-758-398-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 5: HEALTHINF

TI - Interrelations between Drug Prescriptions and Diagnoses for SHI Diabetes Patients using Graph Theoretic Methods and a Markov Model

SN - 978-989-758-398-8

AU - Schuster R.

AU - Heidbreder M.

AU - Emcke T.

AU - Schuster M.

PY - 2020

SP - 345

EP - 352

DO - 10.5220/0008911603450352

PB - SciTePress