A Conditional Approach for Modelling Patient Re-admissions in Hospital using a mixture of Coxian phase-type distributions incorporating Bayes Theorem

The number of elderly patients requiring hospitalisation in Europe is rising. With a greater proportion of elderly people in the population comes a greater demand for health services and, in particular, hospital care. Thus, with a growing number of elderly patients requiring hospitalisation competing with non-elderly patients for a fixed (and in some cases, decreasing) number of hospital beds, this results in much longer waiting times for patients, often with a less satisfactory hospital experience. However, if a better understanding of the recurring nature of elderly patient movements between the community and hospital can be developed, then it may be possible for alternative provisions of care in the community to be put in place and thus prevent readmission to hospital. The research in this paper aims to model the multiple patient transitions between hospital and community by utilising a mixture of conditional Coxian phase-type distributions that incorporates Bayes' theorem. For the purpose of demonstration, the results of a simulation study are presented and the model is applied to hospital readmission data from the Lombardy region of Italy.

Addressing Bed Costs for the Elderly: A New Methodology for Modelling Patient Outcomes and Length of Stay

The proportion of elderly in the population has dramatically increased and will continue to do so for at least the next 50 years. Medical resources throughout the world are feeling the added strain of the increasing proportion of elderly in the population. The effective care of elderly patients in hospitals may be enhanced by accurately modelling the length of stay of the patients in hospital and the associated costs involved. This paper examines previously developed models for patient length of stay in hospital and describes the recently developed conditional phase-type distribution (C-Ph) to model patient duration of stay in relation to explanatory patient variables. The Clinics data set was used to demonstrate the C-Ph methodology. The resulting model highlighted a strong relationship between Barthel grade, patient outcome and length of stay showing various groups of patient behaviour. The patients who stay in hospital for a very long time are usually those that consume the largest amount of hospital resources. These have been identified as the patients whose resulting outcome is transfer. Overall, the majority of transfer patients spend a considerably longer period of time in hospital compared to patients who die or are discharged home. The C-Ph model has the potential for considering costs where different costs are attached to the various phases or subgroups of patients and the anticipated cost of care estimated in advance. It is hoped that such a method will lead to the successful identification of the most cost effective case-mix management of the hospital ward.