COVID-19 places a substantial burden on a range of resources, including oxygen, general ward (GW) beds, intensive care (ICU) beds, ventilators, anaesthetists, intensivists, nursing staff (RN), mortuary, consumables, and personal protection equipment (PPE). Combined with the push over the last decades to increase resource utilisation and minimise safety stock levels through just-in-time principles, hospitals now face extreme resource scarcity [36]. In order to understand the magnitude of the resource requirements, resource prediction models were developed [2]. These data-driven approaches are increasingly more popular for decision-makers to make informed decisions on resource allocations affecting millions of people.

Predominantly, epidemiological models were used to predict the spread of the virus on a national and regional level. The models predicted the number of COVID-19 infections and hospital admissions, subsequently translated into bed requirements and deaths [10, 22, 24, 28, 31]. Additionally, epidemiological models were extended by incorporating lock-down measures and other non-pharmaceutical interventions to inform public policy [19]. Despite the benefits of the vast number of pandemic resource prediction models, three drawbacks limit the usefulness of these models for hospitals.

Firstly, prediction models lack the ability to integrate multiple patient flows and stochastic parameters (e.g. assumes fixed Length-of-Stay (LoS) for every patient). This reduces the accuracy and validity of the model in representing reality. However, Costa et al. [12] stated that “Using [...], average length of stay, [...] to calculate the number of critical care beds needed is mathematically incorrect because of nonlinearity and variability in the factors that control length of stay” (p.320). Additionally, Weissman et al. [45] stated that there is a need to inform the model with local data and local parameters, and to include multiple patient flows to predict resource requirements more accurately. In response, Zhang et al. [50] did model different patient flows, but failed to incorporate stochastic parameters. A systematic review of LoS parameters concluded that there is a need for stochastic LoS distributions, fitted to local and patient flow-dependent data [32].

Secondly, the prediction models concentrate on modelling a limited set of resources: (ICU) beds, ventilators and deaths. Woodul et al. [49] summarised the common strategy adopted in literature to decrease modelling complexity: “Hospital beds, [...] is used as a proxy for space, resources and providers” (p.4). Nevertheless, this approach is too simplistic and does not accurately reflect the resource scarcity in hospitals during the first wave: there were hundreds of empty beds, but there is a lack of PPE, staff, oxygen and mortuary capacity [6, 46]. Some models [37, 38] included more resources, such as PPE and staff. However, these models did not account for different patient flows (e.g. a complicated patient flow: general ward → ICU → general ward).

Finally, the overwhelming majority of the resource prediction models discussed do not predict non-COVID-19 care, whilst these activities were significantly cut down during the pandemic. This was recognised as a significant shortcoming, requiring further research [27, 30].

Scarcity of hospital resources calls for effective resource allocation strategies [44], regardless of COVID-19: “Efficient functioning of a hospital depends on how it allocates its resources, particularly allocating beds to patients, a problem fraught with complexities and uncertainties” (p.298) [5]. Models were developed to evaluate resource allocation decisions, such as bed-plan expansions [11], and specific events, such as the annual winter bed crisis [43].

Literature proposed several methods to allocate scarce resources. Hospital resources can be allocated based on i) patient flows or demand intensity [8, 44], ii) priority of patient groups (e.g. by ‘ring-fencing’ capacity [1, 14]), and iii) the likelihood of favourable outcome (i.e. triage of patients [39]). In this section, we describe the limitations of models evaluating resource allocation decisions.

Firstly, disaster resource allocation models fail to provide a holistic view on health care during a disaster. Apart from resource scarcity in regular times, there is an increased scarcity of healthcare resources during disasters (incl. pandemics). However, the literature has only analysed resource allocation within the disaster [4, 42]. This implies that a fixed set of resources is shared between the patients affected by the disaster, rather than balanced between all patients requiring care.

Secondly, allocation models fail to acknowledge that non-pandemic care cannot be modelled as a constant baseload during a pandemic. The impact of surging pandemic care on non-pandemic care is often not evaluated in prediction or allocation models. For example, Wood et al. [48] stated that the act of balancing resources and evaluating the opportunity cost of surging capacity is left as an exercise for decision-makers. Zhang et al. [50] included regular care as a baseload factor to the model. Nevertheless, this baseload is independent of lock-down policies, the availability of resources, or the intensity of the virus-spread. The application of such a baseload is found both in models studying pandemics in general [29, 49] and COVID-19 specifically [26]. This method fails to account for essential characteristics of hospital operations during a pandemic.

Based on the limitations outlined, there is a need for resource allocation models to include and balance both pandemic care and regular care [17, 27, 30]. Balancing the two types of care requires an integrated prediction of both types of care, to subsequently determine the overall impact of different allocation strategies. Secondly, there is a need to model a more comprehensive set of resources, such as staff. Thirdly, there is a need for stochastic and locally-informed parameters and processes to resemble local healthcare practises and clinical variability more closely. Subsequently, this paper aims to answer the question: What is the impact of scarce resource allocation strategies on the ability to treat patients during a pandemic?

This paper is structured as follows. First, the modelling of patient flows and scarce resources is presented in Section 2, alongside an identification and analysis of the required input data. Following the methodology, Section 3 presents the main results of the model, tailored to a large regional hospital in England. Finally, Section 4 discusses the key findings, its implications, and limitations. Directions for further research on scarce resource allocation modelling were provided.

The resource scarcity that hospitals face is time and context-dependent. Scarce resources were defined as: resources which i) are in greater demand than supply now or in the future, ii) are shared between COVID-19 and non-COVID-19 patients, and iii) are predictable in both supply and demand. From a long-list of eight hospital resources (i.e., beds, equipment, staff, PPE, consumables, oxygen, medication, mortuary), two sets of scarce resources were identified based on the definition provided. The definition and choice of scarce resources were co-constructed and validated by managers, planners and clinician leads in Addenbrooke’s hospital. Resources which were scarce but not shared between COVID-19 and non-COVID-19 patients were excluded, as this study aimed to explore the inter-group balancing effects.

First, critical care (CC) beds are used by both COVID-19 and non-COVID-19 patients and are extremely scarce and resource-intensive. CC is defined as the combination of the intensive care unit (ICU) and the high-dependency unit (HDU).

Secondly, the pandemic places extraordinary pressure on CC staff, requiring other staff groups to fulfill the role of CC staff, especially operating theatre staff. Hence, CC and operating theatre staff collectively form a pool of shared and scarce resources, illustrated in Fig. 11. This study focused on operating theatre staff in contrast to nursing staff from other specialties, as operating theatre staff proved to form the outer flexible deployment layer for CC at Addenbrooke’s hospital. It was assumed that all available nursing staff from other wards was already transferred to CC. Although essential to the care of patients, the other resources were assumed to have sufficient capacity. Fig. 1

Staff pool for critical care

This study aimed to integrate COVID-19 with forms of non-COVID-19 care. Whereas emergency department (ED) services continued throughout the pandemic, surgical care saw an inverse relationship with the COVID-19 wave: many surgeries were cancelled to enable increased capacity on CC. Hence, this study focuses on the relationship between COVID-19 and surgical patient streams.

Hospital patient flows are highly variable and unique. Despite the high variation, the majority of COVID-19 patients seem to follow one of two categories of patient flows (see Fig. 2): complicated stay (requiring GW and ICU stay) and uncomplicated stay (requiring GW stay only), based on experiences in Addenbrooke’s Hospital and available literature [51]. Figure 2 displays the patient flows identified by Addenbrooke’s lead infectious disease consultant, based on observed patient flows of 475 COVID-19+ patients. For simplicity, unobserved or unlikely patient flows were excluded. Fig. 2

Identification of COVID-19 patient flows

In parallel, a flow of elective (EL) and emergency (NEL) surgical patients move through the hospital after leaving the operating theatre (OR). Whereas COVID-19 patient flows were modelled using a set of sequential- processes, surgical patient flows were described by a process-network accounting for the variability in clinical needs. Figure 3 presents the network structure of levels-of-care, according to the process-network approach suggested by Devapriya et al. [16]. The network includes additional levels-of-care besides GW, HDU and ICU: the overnight-intensive recovery (OIR) and intermediate-dependency area (IDA). The modelling approach accommodates for all possible flows between all nodes, whilst allowing the transfer probability between certain nodes to be zero. To acknowledge the clinical differences between elective and emergency surgical patients, the network was modelled separately to facilitate different transfer probabilities and LoS. Fig. 3

Identification of surgical patient flows

Three resource allocation strategies were co-constructed with directors of Addenbrooke’s Hospital: i) a proactive cancellation strategy of non-COVID-19 care, ii) a reactive cancellation strategy of non-COVID-19 care, and iii) a ring-fencing strategy of elective surgical care. The strategies reflect different ways of preparation for an uncertain wave, and vary the prioritisation of COVID-19 and elective surgical patients, which hospitals -including Addenbrooke’s Hospital- consider to deploy for a second wave (see Table 1). The first two strategies prioritise COVID-19 over elective surgery but assume different forms of preparation; the pro-active cancellation strategy enables staff training for CC whereas the reactive cancellation assumes staff training is no longer required. The ring-fencing strategy prioritises elective surgical care over COVID-19 care up to a certain threshold to enable life-saving surgery. Table 1

Resource allocation strategies

The resource allocation policies were analysed using a balanced set of key performance indicators (KPIs), based on hospital operations literature [16, 52]. The KPIs evaluated the core concepts: i) how many patients can be admitted to the hospital, ii) how many patients can be provided full treatment, and iii) what was the outcome of these treatments (see Table 2). ‘KPI-3 CC Rejections’ was defined as: the number of patients not being able to capture the appropriate bed or staff required for their level of care on CC [52] within a given time-frame. Rejections were documented separately from direct deaths, as rejections are the result of hospital operations rather than the patient’s clinical characteristics. Table 2

Key performance indicators to evaluate resource allocation strategies

While acknowledging that weighting these KPIs requires ethical considerations, the AggregatedHospitalPerformance measure (AHP) was introduced to compare the strategies using a single metric, by making the following assumptions:

A proportion of elective surgery can be considered life-saving, avoid an -otherwise inevitable- death;

1AHP=ELSurgeriesPerformed∗%LifeSaving+COVID19Admissions−TotalDeaths−CCRejections\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \begin{array}{@{}rcl@{}} AHP &= & EL Surgeries Performed * <percent> Life Saving + \\ && COVID 19 Admissions - \\ && Total Deaths - \\ && CC Rejections \end{array} $$\end{document}

Analysing hospital patient flows and evaluating the consumption of resources requires an approach accounting for different patient flows and variability [12]. This section describes the modelling approach and assumptions.

The collection and processing of the input data is discussed in the subsequent sections, following the patient’s journey: arrival scenarios, hospital patient flows, LoS and resource consumption.

Model validation is performed to evaluate the degree to which the model accurately represents reality [25].

Firstly, black-box testing is the validation of the model output with the actual numbers observed in reality. Black-box testing was performed by comparing the predicted and actual bed occupancy for COVID-19 during the first wave, and by comparing the predicted number of theatres open and the actual number of theatres open.

Secondly, structure-verification testing was applied [25] to validate the structure and processes in the model [52]. More specifically, patient flows, decision nodes and main decision-making heuristics were validated by operational managers and clinicians.

Black-box testing was performed to evaluate the accuracy of model predictions with the actual observations in the hospital. First, black-box testing for COVID-19 bed occupancy was performed over the period March - June 2020, based on actual admissions. Figure 11 illustrates the high accuracy of the model in terms of GW bed occupancy and ICU bed occupancy. Fig. 11

Black-box testing of COVID-19 General Ward (GW) (left) and Intensive Care Unit (ICU) (right) Bed Occupancy

On the other hand, Fig. 12 shows that the model underestimates the total number of operating theatres which can be opened during an in-between-waves context (i.e. June 2020) by 20%. Two assumptions concerning staff requirements explain the discrepancy. Firstly, ‘COVID-19 staffing ratios’ were assumed for all operating theatres (i.e. increased staffing ratios) to account for infection-control regulation. However, in June 2020 several ‘normally-staffed’ theatres were in operation, due to the low prevalence of COVID-19 in the hospital and community. Secondly, the model assumed a COVID-19 consultants rota, requiring more consultants to be present in the hospital during the night, reducing the available capacity for elective theatres. Fig. 12

Black-box testing of Operating Theatre Capacity. CUH: Cambridge University Hospitals, IS: Independent Sector

The simulation model enabled an analysis of the resource allocations strategies. This section presents the in-depth results for the individual strategies, followed by an overall comparison.

A sensitivity analysis was performed to evaluate the robustness of the model and results. More specifically, the underlying assumptions of the proposed AHP-measure were evaluated. The proportion of elective surgeries which can be considered ‘life-saving’ was stretched between 0-100%. Figure 21 shows the sensitivity analysis of performance of the resource allocation strategies in terms of AHP. The null-hypothesis that a ring-fencing strategy outperforms a reactive cancellation strategy was rejected if only less than 7.3% of the elective surgeries can be considered ‘life-saving’ (α = 5%). Otherwise, the ring-fencing strategy prioritising elective surgical care seems superior. Fig. 21

Sensitivity analysis of Aggregate Hospital Performance (AHP)-measure on proportion of surgeries classified as life-saving

This study evaluated the impact of resource allocation strategies on the ability to treat patients. First of all, it can be concluded that a single COVID-19 wave significantly impairs the hospital’s ability to treat patients for 4-5 months. COVID-19 patients have a higher probability of requiring CC (20% vs < 1%), a significantly longer LoS (19 vs 4 days), and a significantly higher probability of dying on CC (36% vs 2.75%) compared to elective surgical patients.

Secondly, a proactive cancellation strategy enables staff training for CC and allows hospitals to prepare for the ‘unknown’ influx of COVID-19 patients. However, this does come at the cost of 11% fewer surgeries compared to a reactive cancellation strategy, while not resulting in fewer death or CC rejections.

Under a reactive cancellation strategy where a staff training period is not required, significantly more surgeries can be performed. As a result, this strategy enables more surgery without seeing increased CC rejections or deaths.

Thirdly, a ring-fencing strategy for operating theatres enables surgical capacity regardless of COVID-19, translating in 2.5-10% more surgeries compared to a reactive strategy for a base case and worst case scenario, respectively. However, CC will be unable to cope with the influx of COVID-19 patients, especially under a worst case scenario; resulting in 50% more CC rejections.

Overall, no strategy outperforms on all aspects. To consolidate the different KPIs, the AHP-measure was introduced. The measure is dependent on the assumptions that all surgery is life-saving surgery during a pandemic, and that not admitting a COVID-19 patient results in death. According to the AHP-measure, a ring-fencing strategy achieves an average AHP improvement of 12% over the other strategies, potentially saving more lives. The increased number of CC rejections under a ring-fencing strategy is outweighed by the vast amount of additional surgeries performed. Such finding importantly goes against the strategy adapted by hospitals worldwide: prioritising COVID-19 patients. The dominance of the ring-fencing strategy in terms of AHP is explained by the fact that COVID-19 is a resource-intense disease; occupying resources for a significant amount of time with a relatively low likelihood of favourable patient outcomes.

Finally, the sensitivity analyses on the AHP-measure showed that only a small proportion of surgeries (> 7.3%) have to be considered ‘life-saving’ to achieve a significant difference between reactive cancellation and ring-fencing strategies in favour of ring-fencing non-COVID-19 surgical care over COVID-19. Further work is required on the life-saving nature of elective surgeries before any conclusive remarks can be made. Furthermore it could be argued that a truly life-saving situation would be treated under emergency surgery, which was outside the remit of this study.

The key findings lead to several implications for hospitals on the modelling of resource utilisation, the preparation for a second wave, and on the allocation of resources during a pandemic. Firstly, the results confirm the need for stochastic and integrated modelling of COVID-19 and non-COVID-19 care. Secondly, resource prediction models should provide predictions on a wider range of resources, including CC nurses and consultants, to enable capacity management on the actual bottlenecks.

Besides the implications for modelling, this study also has implications on the prioritisation of COVID-19 patients. COVID-19 is a resource-intense disease with a relatively low likelihood of a favourable outcome. A significant trade-off exists between COVID-19 and surgical patients. A ring fencing strategy seems to outperform the other strategies as long as more than 7.3% of surgeries are life-saving. In conclusion, this evaluation aids an ethical discussion on the prioritisation of patients and its effects.

Finally, this evaluation demonstrated the need for hospitals to engage in preparation by training staff for CC and improving organisational flexibility. Also, hospitals can engage in resolving bottlenecks, e.g. by recruitment efforts. This will enable hospitals to maximise the number of patients, both COVID-19 and non-COVID-19, they can treat during the pandemic.

This study made several assumptions limiting the accuracy of the model. Firstly, the LoS for surgical patients was not stochastically modelled using probability distributions. Additionally, a patient’s journey was not modelled on an individual’s clinical data and surgical procedure (i.e. patient waiting list database) but based on historical data for every origin-destination combination.

Secondly, even though this evaluation made a first attempt in modelling COVID-19 and non-COVID-19 patients, several patient streams were still approximated using a baseload. Moreover, this study evaluated resources beyond beds, but assumed sufficient capacity for other essential resources, such as ventilators and PPE. Resources such as PPE were extremely scarce during the first wave, and it should be evaluated if these resources will again form a bottleneck.

Finally, the AHP-measure enables a single-currency comparison of strategies but makes fundamental assumptions limiting the validity of the aggregate measure. First of all, even though all surgeries classified as ‘P2’ according to the Royal College of Surgeons of England clinical prioritisation rubric should be performed within 30 days to prevent life altering/threatening consequences [33], those patients do not necessarily die if surgery is postponed. Therefore, this medical classification does not necessarily accurately reflect the ‘proportion of life-saving surgery’. Secondly, not admitting a COVID-19 patient does not necessarily result in death. Hence, it is important that the AHP-measure is considered with some degree of reservations, and that the in-depth KPIs are consulted to evaluate the performance of a strategy comprehensively.

This study is the first in modelling the effect of allocating resources between pandemic and non-pandemic patients. In order to overcome the limitations and continue to explore how patient outcomes can be maximised, several recommendations for future research are proposed.

First of all, new treatments for COVID-19, like remdevesir, have an impact on the patient flow, LoS and patient outcomes. Therefore, research is recommended to evaluate how these treatments will result in reduced resource requirements and increased capacity to treat non-COVID-19 patients. It is expected that new treatments for COVID-19 will reduce the strain on resources and increase the favourability of prioritising COVID-19 care.

Secondly, this study recognised the interdependency of hospital services, such as CC and operating theatres. However, CC and operating theatres are only two areas affected by COVID-19. General wards are similarly impacted and potentially require additional staff during a second wave. Hence, further research is suggested i) to evaluate which areas are most significantly affected and ii) to include these areas in the model, to more comprehensively analyse the impact of resource allocation strategies.

Thirdly, the results of the AHP-measure suggest that COVID-19 is a resource-intensive disease with a relatively low likelihood of a positive outcome, advocating for more life-saving surgery. The AHP-measure requires an ethical evaluation to determine how deaths, rejections, admissions and surgeries can be combined while accounting for factors, such as i) likelihood of positive treatment outcome, ii) resource intensity of treatment, iii) potential harm of postponing treatment.