On 16 May 2022, Doris Behrens dedicated her inaugural lecture to decision-making in healthcare from a mathematical perspective. She was appointed as a university professor according to § 98 UG 2002 at the University for Continuing Education Krems on 1 January 2021, serving as head of the Department for Economy and Health.
In his welcome address, Friedrich Faulhammer, Rector of the University for Continuing Education Krems, stressed the importance of the occasion, as the inaugural lectures of university professors send out a vital signal for the development of a university. Prof Stefan Nehrer, Dean of the Faculty of Health and Medicine, outlined in his introduction important career steps of Prof Doris Behrens.
Using models to make reality comprehensible
In her introduction to the topic, mathematician Doris Behrens discussed the meaning of the term “model”. In the context of the inaugural lecture, it was used in the sense of a complexity-reduced representation of reality for specific purpose. Behrens illustrated the benefits of mathematical modeling in healthcare by referring to three effects: Processes can be accelerated by applying mathematical methods, complex systems are managed better, and fluctuations in health care planning are managed better due to mathematical support.
How Operations Research helps scheduling shifts and appointments
Demonstrating her first use case, Doris Behrens showed how mathematical optimization can often speed up time-consuming tasks in planning. An everyday situation in hospital management exemplified this, in the course of which personnel from different work shifts had to be deployed in the best possible way according to a previously determined requirement. These kinds of plans are often drawn up manually, even today, and are tedious tasks that are also prone to errors due to changes. Meanwhile, with appropriate programs, these schedules can be automatically prepared with just a few inputs. This is one of the fields of application of Operations Research.
How to successfully deal with complexity
The following scenario is considerably more challenging: In complex systems feedback effects and unexpected side effects make decision-making difficult. The usual process in which the initial situation and goals are determined, the discrepancy with the target condition is identified, a decision is made, and appropriate action is taken does, in complex systems, not end with achieving the targeted results. Decision results not only change the original situation, but can also cause new events, which in turn require setting the course again. Thus, intuitively sensible actions can lead to unexpected, negative consequences.
Patient care in the emergency room
As an example, Behrens chose a classic issue in the emergency room: Concerning the management of patients, a decision has be made quickly as to whether they are discharged or be admitted. For this decision making, diagnostic tests are usually required. More tests help to reach a clear decision more quickly, but consequently increase the number of tests. This on the other hand enhances the effort required to evaluate the tests, which leads to longer waiting times for the results. Thus, the supposedly accelerating measure of "more tests" causes patients to stay longer in the emergency room overall. So, how is it possible to shorten the time? As a rule, medical staff working at the initial admission does not have the longest experience in examining patients; in cases of doubt, more experienced physicians are consulted, which leads to longer lengths of stay. By having the most experienced staff perform the initial examinations, it is possible to reduce the length of stay of patients, along with the volume of testing. This unusual measure would not even have been considered as an experimental project without the model’s evidence. By modeling complex systems, adverse events in the decision process become visible beforehand. Viewing processes from a different angle also allows processes to be rethought.
A similar problem arose in the COVID-19 period: Which test strategy should be applied to accelerate the planned discharge of hospital patients in order to make the beds available again to COVID-19-free patients? In this case, it was apparent that prioritizing the patients to be discharged from the hospital over emergency patients was effective. Again, this paradigm shift in testing would have been unthinkable without model-based evidence.
Dealing with fluctuations
The third example of applying mathematical modeling highlights the importance of fluctuations. Here, the processes of a dentist's office were examined: On average, ten minutes were calculated per patient at the reception desk, ten minutes for the preliminary examination, such as an X-ray, and ten minutes calculated for the actual medical examination. Thus, every visit to the practice is expected only to take up 30 minutes. However, if the average values were replaced by more realistic time periods, in this case if 95 percent of the cases require between 5 and 15 minutes for each of the three steps (but still exactly 10 minutes on average), a completely different picture was obtained. For example, by running a program through hundreds of patients, visiting time increased to as much as four hours, and it also revealed how large waiting rooms needed to be. Counterintuitively, large waiting areas are needed due to backlog effects caused by time variations in the individual steps, and existing capacities are invariably overestimated when planning with average values.
This result was also evident at one COVID-19 vaccination station studied. With registration performed by six people and twelve staff members performing the clinical examination, an observation room, to accommodate 64 people, is needed in case of any reactions appearing to the vaccination.
Doris Behrens received her PhD in technical sciences with a focus on operations research and biomathematics from the Vienna University of Technology in 1998, and her habilitation in operations research in 2008. Her scientific career took her to various universities, including the University of Klagenfurt, University Cardiff, and the TU Wien. She also worked as a visiting professor at the University of Ljubljana, the Medical University of Vienna, and the University of Graz, among others. From 2017 she worked at the Aneurin Bevan University Health Board, took up the position of senior mathematician at the in-house Continuous Improvement Centre in 2020, and is a senior epidemiologist for the Gwent Test Trace Protect Service.