How should hospitals manage the backlog of patients awaiting …€¦ · 29-04-2020 · Biomedical Research Centre based at Imperial College Healthcare NHS Trust and Imperial College

How should hospitals manage the backlog of patients awaiting surgery following the COVID-19 pandemic? A demand modelling simulation case study for carotid endarterectomy Mr Guy Martin1*, Dr Jonathan Clarke2*, Mr Sheraz Markar1, Dr Alexander W. Carter3, Mr Sam

Mason1, Mr Sanjay Purkayastha1, Prof Ara Darzi1, Mr James Kinross1, on behalf of the

PanSurg Collaborative1

1 Department of Surgery and Cancer, Imperial College London, UK 2 Centre for Mathematics of Precision Healthcare, Imperial College London, UK 3 Department of Health Policy, London School of Economics & Political Science

* Joint first authors

PanSurg Collaborative:

Ravi Aggarwal, Rabiya Aseem, Piers Boshier, Paris Bratsos, Swathikan Chidambaram,

Emily Deurloo, Simon Dryden, Simon Erridge, Maxwell Flitton, Ayush Kulshreshtha, Max

Denning, Emily Deurloo, Ola Markiewicz, Osama Moussa, Liam Poynter, Simon Rabinowicz,

Ovidiu Serban, Alasdair Scott, Viknesh Sounderajah, Uddhav Vaghela, Leigh Warren,

Jasmine Winter-Beatty, Seema Yalamanchili

Corresponding Author:

Guy Martin

Department of Surgery and Cancer

Imperial College London

10th Floor QEQM Building, St Mary’s Hospital

London, W2 1NY

[email protected]

Conflicts of interest:

All authors declare no support from any organisation for the submitted work; no financial

relationships with any organisations that might have an interest in the submitted work in the

. CC-BY-NC-ND 4.0 International licenseIt is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted May 2, 2020. .https://doi.org/10.1101/2020.04.29.20085183doi: medRxiv preprint

NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.

https://doi.org/10.1101/2020.04.29.20085183

http://creativecommons.org/licenses/by-nc-nd/4.0/

previous three years; no other relationships or activities that could appear to have influenced

the submitted work.

Data Sharing:

All original code and data will be available from the corresponding author upon reasonable

request.

Funding:

The research was supported by the National Institute for Health Research (NIHR)

Biomedical Research Centre based at Imperial College Healthcare NHS Trust and Imperial

College London.



https://doi.org/10.1101/2020.04.29.20085183


Abstract

Background

The COVID-19 pandemic presents unparalleled challenges for the delivery of safe and

effective care. In response, many health systems have chosen to restrict access to surgery

and reallocate resources; the impact on the provision of surgical services has been

profound, with huge numbers of patient now awaiting surgery at the risk of avoidable harm.

The challenge now is how do hospitals transition from the current pandemic mode of

operation back to business as usual, and ensure that all patients receive equitable, timely

and high-quality surgical care during all phases of the public health crisis.

Aims and Methods

This case study takes carotid endarterectomy as a time-sensitive surgical procedure and

simulates 400 compartmental demand modelling scenarios for managing surgical capacity in

the UK for two years following the pandemic.

Results

A total of 7,69 patients will require carotid endarterectomy. In the worst-case scenario, if no

additional capacity is provided on resumption of normal service, the waiting list may never

be cleared, and no patient will receive surgery within the 2-week target; potentially leading to

>1000 avoidable strokes. If surgical capacity is doubled after 1-month of resuming normal

service, it will still take more than 6-months to clear the backlog, and 30.8% of patients will

not undergo surgery within 2-weeks, with an average wait of 20.3 days for the proceeding 2

years.

Conclusions

This case study for carotid endarterectomy has shown that every healthcare system is going

to have to make difficult decisions for balancing human and capital resources against the

needs of patients. It has demonstrated that the timing and size of this effort will critically

influence the ability of these systems to return to their baseline and continue to provide the

highest quality care for all. The failure to sustainably increase surgical capacity early in the

post-COVID-19 period will have significant long-term negative impacts on patients and is

likely to result in avoidable harm.



https://doi.org/10.1101/2020.04.29.20085183


Introduction

The current COVID-19 pandemic is the biggest threat to health in living memory and

presents unparalleled challenges for the delivery of safe and effective care at scale across

all health systems, which have not been considered before. The pandemic has placed

unprecedented pressures on acute healthcare resources and capacity; demand has

overwhelmed even the most developed and well-resourced health systems[1], and difficult

decisions regarding the rationing of care have now been made[2]. In response to the

pandemic, many health systems have chosen to restrict access to surgical procedures and

reallocate resources in order to create additional short-term hospital capacity[3–7]; the

impact on the provision of surgical services has been profound with more than two million

procedures cancelled to date in the UK at a cost of £3bn[8]. Patients will continue to develop

a full range of pathologies as the pandemic progresses, continually contributing to the

demand for post-pandemic surgical services. Ultimately, this will further exacerbate waiting

times, cause preventable morbidity and mortality from surgical disease and adversely affect

quality of life. As healthcare systems attempt to regain the initiative, policy makers and

administrators must now determine how these systems adapt to meet their elective

responsibilities and transition from the current crisis mode of operation back to ‘business as

usual’. The challenge is to manage patient demand for surgery during all phases of the

pandemic whilst ensuring equitable, timely and high-quality care for all. However, no models

currently exist that allow policy makers to develop strategies for achieving this goal.

Stroke is one of the leading causes of death and long-term disability[9], and places a large

burden on health systems, patients and their relatives. The principal cause of stroke is

carotid territory ischaemia, with up to 15% of all cases attributable to significant carotid

artery stenoses[10]. Carotid endarterectomy (CEA) is one of the most studied surgical

procedures, and there is little controversy regarding its benefit in those with moderate to

high-grade stenosis, with up to a 53% relative reduction in stroke risk compared to best

medical therapy alone, and with optimal outcomes seen when surgery is performed within

two weeks of symptoms[11,12]. Whilst there is some evidence for a decline in the number of

procedures performed annually across the world[13,14], carotid endarterectomy remains a

relatively common procedure with approximately 4,000 cases performed annually in the

United Kingdom[15]. National bodies such as The Vascular Society for Great Britain and

Ireland have issued guidance suggesting that surgeons should still try to operate on high risk

patients during the pandemic, but that aggressive best medical therapy may be more

appropriate[16]; the impact of COVID-19 on carotid surgery has been hugely significant.



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This study therefore takes CEA as a case study for an evidence-based time-sensitive

surgical procedure, and then seeks to simulate a range of demand modelling scenarios for

managing surgical capacity after the pandemic has concluded in order to return to business

as usual within the United Kingdom’s National Health Service (NHS). These models provide

valuable insights that are applicable to all surgical procedures and health systems.

Methods Compartmental Demand Model:

A compartmental model was constructed to represent a range of scenarios for increasing

surgical capacity for CEA following total cessation of surgical services in response to the

COVID-19 pandemic. There is no monthly variation in stroke rates[17], and so for the

purposes of the model a constant weekly rate of demand for CEA was assumed based on

the number of procedures performed for symptomatic carotid disease in the United Kingdom

in 2018; equating to 74 cases per week[15]. In addition, it was assumed that at baseline

demand matches system capacity.

Figure 1 shows the components of the model used. Each week, a finite number of patients

from an infinite pool of potential patients are assumed to require carotid endarterectomy.

These patients are added to the list of patients awaiting surgery. Each week, a finite number

of patients are taken from this list and undergo surgery. Patients are selected on a ‘first

come, first served’ basis, and so the patients operated on each week are those that have

waited longest for surgery. In each model it is assumed that no carotid endarterectomies are

performed for three months (13 weeks) due to COVID-19, after which surgery resumes.

Throughout this period, new patients continue to require carotid endarterectomies at a

constant rate of 74 cases per week. In the model it was assumed that once deemed to

require surgery, all patients remained eligible and survived to undergo their procedure

irrespective of delay.

Different scenarios for the capacity to perform carotid endarterectomies were simulated

subject to two distinct parameters; the time taken to return to baseline capacity (TTB) and

the eventual additional capacity reached above pre-COVID-19 capacity (EC). Capacity is

assumed to increase at a constant rate until EC is reached. Models were simulated for the

two years after the initial cessation of surgical services for twenty different TTB values,

ranging from 0 to 19 weeks, and 20 different EC values, ranging from 0% to 100% of



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baseline capacity. Figure 2 illustrates three of the 400 potential capacity scenarios

examined. Model 1 indicates an immediate return to pre-COVID-19 baseline capacity of 74

cases per week (TTB = 0, EC = 100), which thereafter remains constant. Model 2 indicates a

return to pre-COVID-19 baseline capacity at 4 weeks, after which capacity continues to

increase at the same rate to reach 20% above baseline capacity (TTB = 4, EC = 20). Model

3 indicates a slower return to baseline capacity, taking 8 weeks, after which capacity

continues to increase to 40% above baseline capacity (TTB = 8, EC = 40). In each case

once eventual capacity is reached, the number of procedures performed remains constant at

this rate.

The full mathematical model and code is available on request from the authors. All

simulation, analysis and production of figures was conducted using Python V3.6.8 (Python

Software Foundation, www.python.org) using the pandas, numpy, matplotlib and scikit.learn

libraries.

Outcome Measures:

The primary outcome measure reported is the mean waiting time for patients newly requiring

carotid endarterectomy in the two years from the start of the period of cessation of surgery.

The time taken for the waiting list to be eliminated, and the proportion of patients waiting 2

weeks and 12 weeks for surgery are reported as secondary outcome measures. These were

selected based on data derived from the most recent pooled analysis of 6,092 patients with

35,000 years of follow-up that shows maximal benefit from surgery when performed within 2

weeks of symptoms, and no benefit after a wait of more than 12 weeks[11]. Contour plots

were produced using cubic interpolation of scatter points to represents scenarios of equal

values with respect to the above outcome measures.

Results A total of 7,696 patients were assumed to require carotid endarterectomy in the two years

following the start of cessation of surgical services. Where surgical capacity immediately

returns to pre-COVID-19 capacity of 74 cases per week (Mode 1, Figure 2), surgical

capacity equals surgical demand, and therefore waiting lists remain at a constant size of 962



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cases after the resumption of surgery. The waiting list does not reduce, owing to new

demand being equal to the number of cases performed each week.

Figure 3 shows the performance of the 400 models simulated with respect to the average

time waited for surgery, the time taken for the waiting list to be eliminated and the proportion

of patients waiting more than 2 and 12 weeks for surgery is shown.

Figure 3A shows that above an EC of 40%, the average time waited for surgery is primarily

dictated by the TTB, while for EC of less than 20%, EC is more influential with respect to

average waiting time than TTB. For a 20% increase in capacity above baseline, an average

waiting time of 12 weeks can only be achieved if pre-COVID-19 baseline capacity is reached

in fewer than 10 weeks. Where eventual additional capacity is double pre-COVID-19

baseline capacity, if TTB is 8 weeks, patients would on average wait 4 weeks for surgery.

Figure 3B shows the time taken for the additional waiting list to be eroded is more than two

years where capacity is increased above pre-COVID-19 baseline capacity by less than 20%,

unless capacity is returns to baseline in less than 3 weeks. For capacity increases of 10% or

less, the additional waiting list is not eroded completely for at least three years. Even if

capacity is doubled, unless baseline capacity is reached within three months, it would take at

least a year to erode the additional waiting list as a result of cessation of surgical services.

Under all scenarios, the additional waiting list persists for at least 6 months.

Figure 3C shows a 30% increase in capacity above the pre-COVID-19 baseline, coupled

with a TTB of 0 weeks is required for more than 50% of patients to receive a carotid

endarterectomy within 2 weeks in the two years following cessation of services. In scenarios

where pre-COVID-19 baseline capacity is reached after two months following resumption of

surgical services, capacity increases of 60% or more are required to ensure half of patients

receive surgery in less than 2 weeks.

Figure 3D shows where capacity is increased to 20% or more above baseline capacity, 50%

or more of patients receive carotid endarterectomies within 12 weeks. For capacity

increases of less than 20%, the time taken to return to baseline capacity strongly influences

the proportion of patients operated on within 12 weeks.

Discussion



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The cessation of the majority of surgery has had a profound impact on services and will

undoubtedly lead to huge increases in patients awaiting intervention as the incidence of non-

traumatic surgical pathology is unlikely to change as a result of the pandemic. Whilst the

initial priority for policy makers and clinicians was rightly managing the acute phase of the

pandemic, the next, and potentially far bigger challenge is determining how and when

hospitals return to business as usual in what will be a post-pandemic new normal.

This demand modelling scenario has shown that following a 3-month cessation of carotid

endarterectomy surgery, if no additional capacity is provided on resumption of normal

service the waiting list will not be cleared for over 2 years, and the vast majority of patients

would wait >12 weeks for surgery at which point it is of no benefit; exposing them to double

the risk of stroke and resulting in the region of 350-1100 additional strokes[11]. Even if

surgical capacity is doubled after 1-month of resuming normal service it will still take over 6-

months to clear the waiting list backlog, 30.8% of patients will not undergo surgery within the

2-week target, and 11.5% will wait more than 12-weeks with an average wait to surgery of

20.3 days for the proceeding 2 years; resulting in the region of 100-350 additional strokes. It

should also be noted that this modelling technique is not specific to CEA, with delays in

surgery from a post-COVID-19 backlog in cases likely to have a direct impact on patients

across a wide range of diagnoses. Given these sobering figures hospitals must now start to

look forwards and plan for how they can and should manage capacity to ensure they provide

equitable, timely and high-quality care for all in the post-COVID-19 recovery phase.

Increasing capacity to deal with excess demand is not straight forward, with multiple factors

influencing the ability of hospitals to increase the number of surgical procedures performed

and clear the post-COVID-19 backlog.

External factors may include unpredictable changes in the rate of new stroke diagnoses due

to a reduction in the number of patients presenting with acute symptoms during the

pandemic; changes which have already been reported across a range of diagnoses

including in stroke[18,19]. This phenomenon will be of even greater importance in diseases

with more complex referral and treatment patterns such as gastrointestinal cancer where the

majority of patients move between primary care, screening services, diagnostics and

hospitals prior to receiving surgery. Additionally, there are going to be inevitable further

spikes in COVID-19 cases until either a vaccine is developed or herd immunity is

achieved[20]. This will lead to further fluctuations in surgical capacity and successive shut

downs over time; it is therefore it is important to meaningfully catch up when excess capacity



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is possible, and more elegantly decrease surgical capacity without a total shutdown during

future spikes to ensure we are not once again starting from a standstill.

In addition to external factors, multiple internal considerations will also influence the ability to

increase capacity and catch up with a surgical backlog as highlighted in current capacity

planning models[21]. Surgical teams do not operate in isolation, and critical care capacity is

vital to support a wide range of surgical procedures including CEA. The COVID-19 pandemic

has led to a huge increase in demand for critical care capacity that will likely continue into

the medium- and long-term[22,23], and even before the crisis critical care units typically had

occupancy rates of around 80-85%[24,25] with significant variability in the availability of

critical care capacity in relation to surgical activity[26]. Surgical teams can therefore not

depend on predictable levels of critical care availability to support an increase in capacity

and so will need to plan accordingly or modify peri-operative practice. It is not just critical

care capacity that may limit the ability to rapidly expand surgical services. The NHS in

England typically runs at general bed occupancy rates of 90-95%[27], and therefore its

ability to rapidly expand surgical numbers is severely limited without seeking alternative

infrastructure. Potential options could include the use of the private healthcare sector or

transitioning temporary facilities such as the NHS Nightingale Hospitals that were built in

response to the COVID-19 crisis to more permanent facilities geared towards reducing

waiting lists by providing additional capacity. The most important resource for clearing

surgical waiting lists is staff though. Burnout is an increasingly recognised phenomena

across all healthcare workers, and especially in those delivering surgical services[28,29].

Compounding this will be the knock on effects of the huge increases in work intensity, the re-

deployment of staff across different services and the consequences of the sobering 20%

COVID-19 infection rates in healthcare staff[30]. Even if physical capacity is found,

healthcare providers must carefully look after, protect and support their staff to ensure that

the post-COVID-19 response and return to business as usual is both successful and

sustainable; healthcare workers are human, and have limits.

The model presented does have limitations. It assumes all patients remain eligible for

intervention and survive to undergo their procedure irrespective of delay. Within the CEA

cohort there is likely to be in the region of a 10-20% annual dropout rate due to death or

further stroke that makes someone ineligible for surgery, with the greatest risk seen in the

first three months[31,32]. This would act to reduce the number of patients requiring

intervention, and thus the time to return to baseline, but the impact will be minimal;

importantly, the model represents the worst-case scenario for which health systems should

plan for, and act on. In addition, this is a generalised model based on national figures. As



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such, there is a requirement for individual organisations to take into account local factors

such as the direct disruption caused by COVID-19, competing demands of surgical and

supporting services, and wider infrastructure and staffing resource constraints when

designing, modelling and implementing local recovery plans.

To further refine the models and identify contextual solutions, discrete event simulations

could be employed to incorporate probabilistic payoffs on decisions around additional factors

such as mortality rates, the social acceptability of delays and impact of local and national

prioritisation and planning decisions. It is also important to assess the financial and human

capital implications of seeking to increase surgical capacity. To address the avoidable

burden of stroke, the health implications and costs of these policy decisions could be

expressed as incremental gains or losses in quality adjusted life years (QALY). We

recommend that future analyses incorporate these cost indicators, in addition to risk-based

decision aids to help health systems allocate their finite resources to maximise patient

benefit.

The cessation of the majority of global elective surgical services during the Covid-19

pandemic has had a profound impact on patients and healthcare providers. This case study

for carotid endarterectomy has shown that every healthcare system is going to have to make

difficult decisions when balancing human and capital resources against the needs of

patients. It has also demonstrated that the timing and size of this effort will critically influence

the ability of these systems to return to their baseline and continue to provide the highest

quality care for all. The failure to sustainably increase surgical capacity early in the post-

COVID-19 era will have significant long-term negative impacts on patients and is likely to

result in avoidable harm.



https://doi.org/10.1101/2020.04.29.20085183


Figure 1 - schematic of demand model components

Patients awaiting surgery

Patients undergoingsurgery

New patients requiring surgery

Potential Patients

Post-operativePatients



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Figure 2 - three illustrative examples of surgical capacity scenarios varying according

to the time to return to pre-COVID-19 baseline capacity (TTB) and the eventual capacity reached (EC) following complete cessation of surgery for three months.

Model 1) pre-COVID-19 capacity is restarted on day 1 and maintained. Model 2) pre-COVID-19 capacity is reached after 4 weeks and then increases to reach 20% above

baseline. Model 3) pre-COVID-19 capacity is reached after 8 weeks and then increases to reach 40% above baseline



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Figure 3 - contour plots showing the performance of simulation models over varying times to return to baseline capacity (TTB) on the y-axis and the eventual additional capacity reached (EC) on the x-axis for patients requiring surgery within 2 years of the onset of the 3-month cessation of surgery. A) average wait time for patients to

undergo surgery. B) time to clear waiting list and return to baseline. C) proportion of patients undergoing surgery within 2 weeks. D) proportion of patients undergoing

surgery within 12 weeks

A B

C D



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How should hospitals manage the backlog of patients awaiting …€¦ · 29-04-2020 · Biomedical Research Centre based at Imperial College Healthcare NHS Trust and Imperial College