Booked inpatient admissions and hospital capacity: mathematical modelling study

Objectives: To Investigate the variability of patients' length of stay in intensive care after cardiac surgery. To investigate potential interactions between such variability, booked admissions, and capacity requirements. Design Mathematical modelling study using routinely collected data. Setting: A cardiac surgery department. Source of data: Hospital records of 7014 people entering intensive care after cardiac surgery. Main outcomes measures: Length of stay in intensive care; capacity requirements of an intensive care unit for a hypothetical booked admission system. Results: Although a vast majority of patients (89.5%) had a length of stay in intensive care of less than or equal to 48 hours, there was considerable overall variability and the distribution of stays has a lengthy tail. A mathematical model of the operation of a hypothetical booking system indicates that such variability has a considerable impact on intensive care capacity requirements, indicating that a high degree of reserve capacity is required to avoid high rates of operation cancellation because of unavailability of suitable postoperative care. Conclusion: Despite the considerable enthusiasm for booked admissions systems, queuing theory suggests that caution is required when considering such systems for inpatient admissions. Such systems may well result in frequent operational difficulties if there is a high degree of variability in length of stay and where reserve capacity is limited. Both of these are common in the NHS.