Written evidence submitted by by Prof Alan Champneys FIMA (University of Bristol) and Prof Christine Currie (University of Southampton) (CBP00174)


Principally, this evidence is in response to the following question in the call for evidence:



It also relates in a secondary way to the following questions

Exec Summary


A workshop was held between mathematical scientists from across the UK with stakeholders from across the NHS to address the question of the effect of the COVID-19 Pandemic on treatment waiting lists for the specific specialism of Cardiovascular medicine. This evidence summarises conclusions that have arisen in subsequent, as yet unpublished, work. Our over-arching conclusion is that data must be collected more efficiently in a centralised way and fed into optimisation and scenario-planning to enable sound investment decisions both at a local and national level. The problem is more nuanced than simply that of clearing a backlog by investing money. Like most conditions, cardiovascular diseases are typically chronic rather than acute, so we need to take account of the evolution of a patient’s state of health while on the waiting list and the possibility that the optimal result may be achieved by providing an otherwise sub-optimal treatment sooner. Increasing resources, e.g. by hiring more consultants or providing extra bed spaces, typically has a significant time lag.   Crucially, there are numerous feedback loops: e.g. every patient not treated is likely to develop more serious conditions whose treatment will clog up further NHS resources; clearing backlogs through enforced overtime of clinicians may harm recruitment and retention; prioritisation of the most sick may lead to a the mildly ill becoming sicker, and a steady state to be reached of worse quality of life for all.    Our expertise in mathematical modelling, and experience in modelling waiting lists for cardiovascular disease in particular, forces us to conclude that a reasonable strategy to clear backlogs requires joined up mathematical modelling using techniques from operational research, such as discrete-event simulation, systems dynamics and constrained optimisation. Our overall recommendation is that patient health is likely to be optimised by the use of mathematical modelling and scenario planning via a collaboration between the NHS and the UK mathematical sciences and operational research community. Only then can rational decisions be made on the level of investment required, and the optimal way to use this fixed resource between specialisms and regions.



1. Expertise of and outputs from Virtual Study Group on cardiovascular waiting lists


1.1 V-KEMS is a virtual centre that was formed in March 2019 to combine the expertise of the UK mathematical sciences academic community to users to address challenges from society, business and the third sector that are either long-standing or have arisen as a result of the COVID-19 pandemic. It is run as a collaboration between the three leading bodies in the UK that co-ordinate knowledge exchange with the mathematical sciences; the International Centre for Mathematical Sciences, the Isaac Newton Institute (through its Newton Gateway to Mathematics) and the Knowledge Transfer Network.


1.2 Following discussions with clinicians, the effect of the pandemic on hospital waiting lists was prioritised as a topic to be facilitated by VKEMS. The particular case of cardiovascular disease chosen as these tend to represent a particularly self-contained set of conditions and yet are one of the leading causes of death in the UK.


1.3 The virtual study group (a kind of brainstorming or “hackathon”) was held on 2nd – 4th February 2021 and has been followed up with subsequent research.


1.4 A full list of participants at the VKEMS study group is as follows. Mathematical scientists: Jess Enright (University of Glasgow), Feryal Erhun (Cambridge Judge Business School), Rebecca Hoyle (University of Southampton), Pietro Lio (University of Cambridge), Marion Penn (University of Southampton), William Pettersson (University of Glasgow), Yang Zhou (University of Bath), Nick Holliman (Newcastle University), Houyuan Jiang (University of Cambridge), Sara Lombardo (Loughborough University), Lars Schewe (University of Edinburgh), Kieran Sharkey (University

of Liverpool), Matteo Sommacal (Northumbria University), Christian Stickels (University of

Liverpool), Alan Champneys (University of Bristol), Christine Currie (University of

Southampton), Alex Heib (University of Southampton), Lucy Morgan (Lancaster University), Matt Butchers (KTN) and Clare Merritt (Newton Gateway to Mathematics), Leila Finikarides (Winton

Centre for Risk and Evidence Communication). Clinicians: Chris Gale (University of Leeds - Professor of Cardiovascular Medicine), Ben Gibbison (University of Bristol - Consultant Senior Lecturer in Cardiac Anaesthesia and Intensive Care), Prof Mamas Mamas (Keele University - Professor of Cardiology), Dr Ramesh Nadarajah (University of Leeds - British Heart Foundation Clinical Research Fellow) and Dr Jianhua Wu (University of Leeds - Associate Professor), Dr James Rudd (University of Cambridge Honorary Consultant in Cardiology), Jonathan Weir McCall (University of Cambridge - Honorary Consultant in Cardiothoracic Imaging), Charlotte King (NHS England - Analyst), Louise Sun (University of Ottawa Heart Institute) and Mike Woodall (NHS Midlands and Lancashire Commissioning Support Unit).



1.5. A report of the study group is available at https://gateway.newton.ac.uk/sites/default/files/asset/doc/2103/Modelling%20Solutions%20to%20the%20Impact%20of%20COVID-19%20on%20Cardiovascular%20Waiting%20Lists.pdf

The report considers three exemplar case studies for which data was available. Further work on each has happened subject to the study group and forms the subject of each of the next sections.


2. Case study I: the national picture on the delivery of elective cardiovascular appointments


2.1 This challenge concerns the overarching state of the delivery of elective cardiovascular procedures and outpatient consultations at the national level, as a result of the pandemic and how this plays out at regional or local (single NHS trust) levels.


2.2 Evidence from various data sets in the published literature suggests the situation is complex with many appointments and procedures being cancelled, but waiting lists for many conditions not increasing as a result of the 2020 lockdowns. A rational explanation is because of patients not presenting to primary care with mild symptoms. This suggests that such patients are more likely to present as a later emergency admission, and/or to require more complex procedures.


2.3 Several attempts have been identified to model waiting lists post-pandemic using techniques from operational research. These include the reference https://www.tandfonline.com/doi/full/10.1080/17477778.2020.1764876 by Richard Wood on “Modelling the impact of COVID-19 on elective waiting times, Journal of Simulation (2020) using discrete event simulation. Also, the software tool on work of Mike Woodall at the NHS Midlands and Lancashire Commissioning Support Unit which uses a systems dynamics approach.


2.4 Using charity funding to the Bristol Heart Institute, we have started to use the data collected for the study group to build our own open-source systems dynamics model. Preliminary results suggest the existence of several feedback loops. One feedback loop is the lowering of staff morale if overworking is required, which is likely to lead to a recruitment and retention crisis. Another is the diversion of resources towards emergency admissions because of missed appointments causing further lengthening of waiting lists. Finally, treating the most sick patients first prioritisation of the most sick may lead to a the mildly ill becoming sicker, and a steady state to be reached in which the hospital is always treating the most sick who have a worse prognosis. A steady state where the less sick is likely to lead to procedures that create greater benefit in terms of patient quality adjusted life years (QALYs).


2.5 We are planning to run all kinds of what-if scenarios through this national-level model to determine which of these constraints and feedback loops lead to the rate determining step if the backlog were to be cleared.


2.6 We are also researching how to define a suitable utility or objective function. A simple objective of most rapidly clearing a backlog, or even of maximising QALYs, would likely lead to an “optimal solution” where the most sick are not treated, so that they leave the waiting list through death. This would clearly not be optimal.



3. Case study II: modelling optimal treatment for a single procedure


3.1. The case study involves optimisation of delivery of an exemplar cardiovascular procedure - aortic stenosis. This is a particularly well-defined data-set and for which missed early intervention can lead to serious adverse outcomes (death) over the course of one or two years.


3.2. There are two kinds of procedures, a minimally invasive TAVI and an open heart surgery. NICE guidelines favour each procedure for different patients depending on their age and severity of their valve problem. Given that valve disorders are progressive, a less optimal procedure that could be delivered more rapidly may actually be in a patient’s benefit and may clear the backlog quicker.


3.3  Three separate groups from the University of Liverpool, the University of Edinburgh and the have been considering this as a problem in optimisation theory. Preliminary outcomes from all three lead to the same conclusion. Given a data stream of patients at trust level, and knowledge of the current state of waiting lists, and available clinical resource, a decision support tool can aid clinicians and bed planners to make optimal decisions in real time, which will improve patient benefit and optimally reduce the waiting list.



4. Case Study III: Modelling optimal treatment of a particular disease 


4.1 Chronic heart failure (CHF) is loosely defined as ongoing poor heart function leading eventually to death by the heart ceasing to pump blood. There are many causes of CHF; for example, age, high blood pressure, and the result of damage after a heart attack, otherwise known as a Myocardial Infarction (MI). Expert clinicians cite median life expectancy post CHF diagnosis to be 5 years. CHF diagnosis is confirmed using an echocardiogram (echo), an ultra-sound scan for the heart which can be performed by consultant cardiologists or specially trained medical staff at heart clinics.


4.2  The important aspect of the model was to base it on real data. This was collected after from collaboration with the Leeds hospital trust. During the Covid-19 pandemic the number of people diagnosed with CHF fell and from July to November 2020 the number of GP referrals were at 20% of pre-pandemic levels and the number of diagnostic echo tests from April and May 2020 were 31% of the number conducted in the same months of 2019.


4.3  We built a discrete-event computer simulation model of CHF patients’ progression through the health system that explicitly includes modelling of waiting lists for echocardiogram tests, identified as the bottleneck in the pathway. Results are still preliminary but show that a reduction in echocardiogram capacity during the pandemic, if unmitigated, leads to a permanent increased number on the waiting lists and more patients seeking emergency care through hospitals.


4.4. The preliminary finding of this study based on the Leeds data were compared through expert elicitation with the Universities Bristol Hospital Trust. There, there is no shortage of echocardiogram capacity.


4.5. This contrast suggests that a ‘one-size fits all’ to clearing the backlog is not optimal. It is crucial that bottlenecks are identified at the level of individual trusts.








5. Recommendations


5.1. There is a need for joined up mathematical modelling and “what-if” scenario planning at a national and regional level. This must be supported by clear and straightforward processes for accessing necessary data.


5.2 A joined up approach across NHS digital, the Department of Health, individual Hospital Trusts and Care Commissioning Groups will enable best practice to be shared and avoid reinventing the wheel.


5.3 Mathematical modelling, in particular the use of operational research, provides a valuable tool in identifying optimal strategies for reducing the backlog in the NHS.


Sept 2021