gms | German Medical Science

Introduction: Pharmaceutical expenditure is the second largest category of spending in the German Statutory Health Insurance (SHI) system and has increased more rapidly than other SHI expenditures over the past decade. The coronavirus pandemic has presented additional challenges, including changes in disease patterns and severity, as well as supply bottlenecks. Since the early days of structural consultations by the SHI funds, the Association of SHI physicians and the Medical Service for SHI doctors have developed analysis tools, algorithms, and consultation documents for pharmacotherapy for SHI doctors. The aim is to create an optimal strategy for designing pharmaceutical target agreements in Schleswig-Holstein that offers high-quality drug therapy while minimizing therapy costs.

Materials und methods: The following analysis examines the first six target areas of the pharmaceutical target agreement from 2023. These areas include lead substances from various active ingredient groups. The analysis was conducted using approximately 25 million prescription data records from 1488 doctors. Each doctor must have at least 25 prescriptions per year. For each doctor, we calculated the costs per treatment day according to PDD (Χ), per defined quantity of active ingredient in the ATC-DDD-system (Y) according to WHO, with adjustments according to German authorization law and the costs per prescription (Z).

The elliptical Jacobian functions, the spherical trigonometry and the associated modulus value κ are employed to ascertain in which instances the third influencing variable exerts a strengthening or weakening influence on the correlation of the other two variables.

The modulus value κ can determine whether the correlation or partial correlation is greater. Elliptic functions can be derived from quadratic differential equations. In the current application in cryptography, elliptic functions are employed on finite fields.

Results: The correlation ρ_ΧY [0.2908; 0.9927]. Across all target fields, the correlation is 0.9250. Additionally, there is an almost linear positive correlation Χ and Z, with ρ_ΧY [0.8279; 0.9787]. The correlation between Y and Z falls within the interval of [0.1164; 0.9842]. However, most of the target fields do not exhibit a positive linear correlation.

The value of the modulus k [0.9765; 4.8530]. For one target field is k<1, X positively affect the correlation between Y and Z. In the other two combinations, the third cost consideration has a negative impact. When k=4.8530, the correlation is significantly greater than the partial correlations, indicating that the third variable has a positive influence on the correlation in each case.

Conclusion: The correlation between costs per prescription, per treatment day according to PDD, and costs per defined quantity of active ingredients can inform the design of future target agreements. This can help to ensure good care while also saving costs.

In statistics, three variables can be linked and their correlation calculated. It is also possible to examine this connection trigonometrically. The objects are regarded as the corners of a spherical triangle and the correlation corresponds to the length of the lines connecting the corners. Trigonometry also plays a role in classical statistics. By triangulating a large contiguous number of such spherical triangles, an entire surface can be described overall, including more than three objects.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.