A modelling tool for capacity planning in acute and community stroke services

Management of capacity in acute and community pathways is complex. To analyse these systems the mathematical sciences have developed a wide range of robust analytical methods focused on queuing and patient flow, but the uptake and implementation of these methods in routine decision making remains limited in healthcare compared to other sectors [1‐3]. In the absence of these models, decision makers must make capacity planning decisions based on average occupancy of wards and, in some cases, aware of the limitations of doing so, apply arbitrary uplifts to these figures. Simulation modelling is an intuitive approach to modelling that synthesises a range of data sources to support decision making for complex problems [4]. For capacity planning problems simulation modelling offers a way to translate the large knowledge base of relevant mathematical models to a form accessible and transparent to healthcare professionals and managers.

The performance of acute and community stroke services typifies the difficulties in capacity planning decisions. Suspected stroke patients, actual stroke and mimics, require urgent access to an acute stroke unit followed by timely transfer to early support discharge services (ESD) or inpatient rehabilitation in a community hospital. Indeed in the United Kingdom the performance of stroke services is measured by the proportion of stroke patients admitted to the stroke unit within four hours of hospital arrival and the proportion of stroke patients that spend 90 % of their hospital stay on a stroke unit, with large financial penalties for underperforming services. Performance against these targets is influenced by three interacting factors [5, 6] – capacity, variation in patient length of stay and difficulties in discharging patients to the community (so called ‘bed blocking’). As the number of patients suffering a stroke increases, the pressure on acute, ESD and community rehabilitation services will rise, and accurate capacity planning that delivers a cost-effective service will become even more critical. Whilst appropriate capacity planning techniques have been implemented and used in both cardiothoracic surgery [5] and emergency departments (ED) [7], they are only outlined and encouraged with respect to stroke services [8, 9].

In any financially constrained health service there is a need for accurate capacity planning of stroke services. The present UK policy for the centralisation of hyperacute stroke services [10‐13] makes it especially relevant as some stroke units will see large increases in the number of patients admitted. Capacity planning simply using average occupancy, even Bagust et al’s [14] suggested 85 % target bed occupancy, is imprecise and can lead to severe delays within the stroke pathway. Transfer delays to rehabilitation negatively affect patient outcomes [15] and may have financial penalties for hospitals. Mathematical modelling of the whole pathway provides a rational and robust way to mitigate against these problems.

At our study hospital the model demonstrates that an increase from 10 to 14 acute stroke unit beds reduces the number of patients experiencing delays from 1 in every 7 patients to 1 in every 50. This is a substantial improvement in smoothing the flow of patients through the stroke unit and significantly increases the time clinicians can focus on patient care as opposed to bed management. Moreover, the model demonstrates that the additional four beds is relatively robust to a 5 % increase in admissions. The modelling also predicts a capacity shortfall in the inpatient rehabilitation wards. An increase from 12 to at least 14 beds is again required to smooth the flow and reduce the likelihood of transfer delays. Obvious extensions to the study are to use the model to explore the impact of reductions in rehabilitation length of stay that could result from improved discharge planning; reduction in the time to set up a community care package (reductions in ‘bed blocking’); or extending the capacity of ESD services to care for more severely affected patients – potential greatly reducing length of stay [16].

The study hospital was also planning to co-locate the acute stroke unit and rehabilitation wards. Even if bed pooling between the two units is not officially sanctioned, in practice it is likely that some temporary bed pooling will happen in order to cope with the spontaneous variation in rates of patient admissions and discharges. The model therefore provides a prospective way to plan the implementation of bed pooling and to fully understand the trade-offs when pooling only a subset of beds.

The model was also used to analyse the impact of complex-neurological patients on flow through the pathway. The utility of such information is in the dialog between clinicians and healthcare commissioners to understand the implications of service provision to different patient subgroups on overall performance.

There are several further ways in which our model can be used, depending on the issues seen to be important in different contexts. For example, it could be used to explore scenarios where stroke beds are reserved exclusively for patients suffering an acute stroke (so called ‘ring-fencing’), or ‘partial ring-fencing’ in which admissions of other cases is dependent on ward occupancy. The unfettered demand approach used in our model is generalizable and hence is applicable to other relevant wards. For example, a second use for our model would be to adapt it for other hospital wards, such as those for the cardiac surgery, where timely admission and discharge are important.

The strengths of our approach to capacity planning are threefold. First, the model provides a sophisticated analysis of capacity requirements accounting for the spontaneous and unpredictable variability in patient arrivals and lengths of stay. This level of detail is often missing from capacity calculations. Planning models that rely on average occupancy only will greatly underestimate bed requirements as they take insufficient account of variability. In this study average occupancy of the 10-bedded acute stroke unit was nine patients, corresponding to delays for one in every five patients. Our study provides a scientific methodology for analysing how many beds above average occupancy are necessary in order to limit the probability of delay. Second, although sophisticated, the model is driven by routinely collected data that is readily available from patient administration systems. Last, as the planning model has no capacity constraints, it is not necessary to model what happens to patients when stroke wards are full. Its independence of these details, which can vary considerably across hospitals, greatly increases the applicability of the model to other settings.

When adapting our model for similar studies, modellers may face the issue of dealing with the impact of ‘bed blocking’ increasing the lengths of stay recorded in routinely collected data. That is, the length of stay data do not separate treatment duration and transfer/discharge delays. If sensitivity analyses show that these discrepancies are likely to cause misleading results, a small prospective sample of times where patients are fit for transfer to rehabilitation versus when they are transferred, or a historic sample of lengths of stay during periods of time when beds are not blocked can be used.

As our model focuses on capacity requirements, a limitation is that it cannot predict the length of a delay that a patient experiences. This means that the model cannot be used to investigate performance metrics such as the UK’s four hour stroke unit target or the proportion of patients that spend 90 % of their stay on a stroke unit. Although creation of such models is possible the complexity increases by several orders of magnitude and will inevitably require data that is not routinely collected – for example regarding the management and repatriation of outlying stroke patients. The exclusion of such measures not only reduces our model’s data requirements, but also makes our approach more general internationally (where targets such as the 90 % stay metric do not apply). The model is easily adaptable to other acute stroke units which transfer patients to multiple inpatient rehabilitation wards in the community and could be used to explore the impact of introducing new cost effective services such as ESD [33].

The simulation-based method used here was chosen in preference to attempting to derive heuristics based on queueing theory for calculating the uplifts to associate with different occupancy levels as a more direct way to incorporate the characteristics of the particular problem. However, the simulation model development was guided by a knowledge of relevant queueing theories, in the spirit of complementary use of simulation and queueing theory [34].

Planning by average occupancy plus an arbitrary uplift, even up to 30-40 %, fails to provide sufficient reserve capacity to adequately manage the variation in admission and discharges seen in our stroke pathway. Our method draws on long available, intuitive, but underused mathematical techniques for capacity planning. Implementation via simulation at our study hospital provided valuable decision support for planners to assess future bed numbers and organisation of the acute and rehabilitation services.

In recent years some aspects of stroke services have been modelled using discrete-event simulation approaches, [8, 19‐25] including access to time-sensitive treatments such as thrombolysis. Our method, with its focus on capacity, is complementary to these models and will be particularly useful for cases of stroke service reconfigurations where acute stroke units will face substantially increased admissions, including patients for whom the final diagnosis is not stroke. To enable cost-effective and efficient provision planning decisions in such complex systems requires all of the relevant information to be considered in a way that is not possible for simple average-based estimates. Our method accounts for the variation in admission patterns, length of stay by patient type and eligibility for ESD, greatly increasing the precision with which services can be planned and the ability to predict and respond to short and long-term variation in demand for emergency stroke services.