Diagnostic and modeling of elderly flow in a French healthcare institution

- Three Markov chains are provided to capture elderly flow in the hospital.
- Collected data in French hospital is fitted to chains to predict the length of stay.
- Elderly are classified into three classes based on frailty, pathology and lifestyle.
- A perspective of possible utilization and economic benefits of results is discussed.

One of the highest priorities in the French health care system is to deal with the continuous growth of the percentage population older than 65 years, expected to reach 31% in 2030. This development poses enormous challenges to the operations of the health care system, especially, related to elder patients. The elderly flow in the hospital services is typically uncertain and subject to variations on the length of stay in each stage and on the path or sequence of stages followed by the patient. For that reason, we propose to model the patient flow in a hospital as a continuous-time Markov chain with an absorbing state representing the elderly discharge from the hospital. Three Markov chains are provided with different levels of details and computation complexity. The first model called aggregated provides a prediction of the length of stay per service, the second model called Coxian provides a reliable prediction of the total length of stay, and the third model called detailed provides a prediction of the length of stay per class of elderly. A classification of elderly based on multiple correspondence technique is considered before the application of the third model. Our models are fitted with the data collected from Roanne Hospital, a typical French health care structure.