The self-regulating nature of occupancy in ICUs: stochastic homoeostasis

As pressure on the health system grows, intensive care units (ICUs) are increasingly operating close to their capacity. This has led a number of authors to describe a link between admission and discharge behaviours, labelled variously as: ‘bumping’, ‘demand-driven discharge’, ‘premature discharge’ etc. These labels all describe the situation that arises when a patient is discharged to make room for the more acute arriving patient. This link between the admission and discharge behaviours, and other potential occupancy-management behaviours, can create a correlation between the arrival process and LOS distribution. In this paper, we demonstrate the considerable problems that this correlation structure can cause capacity models built on queueing theory, including discrete event simulation (DES) models; and provide a simple and robust solution to this modelling problem. This paper provides an indication of the scope of this problem, by showing that this correlation structure is present in most of the 37 ICUs in Australia. An indication of the size of the problem is provided using one ICU in Australia. By incorrectly assuming that the arrival process and LOS distribution are independent (i.e. that the correlation structure does not exist) for an occupancy DES model, we show that the crucial turn-away rates are markedly inaccurate, whilst the mean occupancy remains unaffected. For the scenarios tested, the turn-away rates were over-estimated by up to 46 days per year. Finally, we present simple and robust methods to: test for this correlation, and account for this correlation structure when simulating the occupancy of an ICU.