Mathematical modelling of patient flows to predict critical care capacity required following the merger of two district general hospitals into one

Abstract

SummaryThere is both medical and political drive to centralise secondary services in larger hospitals throughout the National Health Service. High‐volume services in some areas of care have been shown to achieve better outcomes and efficiencies arising from economies of scale. We sought to produce a mathematical model using the historical critical care demand in two District General Hospitals to determine objectively the requisite critical care capacity in a newly built hospital. We also sought to determine how well the new single unit would be able to meet changes in demand. The intention is that the model should be generic and transferable for those looking to merge and rationalise services on to one site. One of the advantages of mathematical modelling is the ability to interrogate the model to investigate any number of different scenarios; some of these are presented.

Policy: A novel modelling technique to predict resource ­requirements in critical care – a case study

“…Acute non-clinical transfers to other hospitals are the main 'relief valve' for an overloaded system; these are difficult for the model to accurately predict as clinicians may adopt more stringent standards for admission when the unit is full. 9 Other subcategories are also reported to show whether cancellations are due to physical bed or nursing capacity, or the use of 'staffing up' if it is selected as an option in the model. All statistics are reported as medians with quartiles to illustrate the range of possibilities in each scenario.…”

“…Similar difficulties exist around the concept of acute transfers out as clinicians may behave differently when the unit is full. 9 The figure therefore represents a total of patients who in real life came to the unit, but in the modelled scenario would have to be cared for elsewhere -whether by transfer to another hospital, or in some cases remaining in the same hospital but with extra support.…”

“…6 Bottom-up approaches are much more commonly used in resource-allocation modelling. [7][8][9] Patients are modelled as discrete entities passing through activities according to defined decision rules. Approaches include Markov chain models, 10 where a patient may arrive on the ICU in one state, and at each time point have a probability of moving to another (eg deteriorating, improving, or requiring some resource), or simply distributing a patient's resource requirements based on a classification system.…”

Measuring the price of anarchy in critical care unit interactions

“…After an initial analysis of the data, behavioural aspects became apparent; for example, delaying patients discharge if there was no pressure on CCU beds, or admitting fewer patients if bed occupancy levels were high. As a result of this, a state-dependent queueing model has been developed, which includes the dependency of admission rate on actual occupancy (Williams et al 2015). This state dependent model was applied to both NH and RG separately.…”

Role of critical care in improving outcomes for high-risk surgical patients

“…What is needed are robust methods of predicting which patients may need admission, and when this demand will be greatest. For example, the number of critical care beds required can be modelled and optimal capacity determined in advance. Given that adequate numbers of critical care beds to meet demand are associated with improved patient outcomes, with a potential reduction in mortality of 6 per cent for every additional ICU bed per 100 hospital beds, these tools could be embraced by healthcare commissioners and used to support operational planning, and flexible commissioning of more beds and staff.…”