To provide estimates for how different treatment pathways for the management of severe aortic stenosis (AS) may affect National Health Service (NHS) England waiting list duration and associated mortality.
We constructed a mathematical model of the excess waiting list and found the closed-form analytic solution to that model. From published data, we calculated estimates for how the strategies listed under Interventions may affect the time to clear the backlog of patients waiting for treatment and the associated waiting list mortality.
The NHS in England.
Estimated patients with AS in England.
(1) Increasing the capacity for the treatment of severe AS, (2) converting proportions of cases from surgery to transcatheter aortic valve implantation and (3) a combination of these two.
In a capacitated system, clearing the backlog by returning to pre-COVID-19 capacity is not possible. A conversion rate of 50% would clear the backlog within 666 (533–848) days with 1419 (597–2189) deaths while waiting during this time. A 20% capacity increase would require 535 (434–666) days, with an associated mortality of 1172 (466–1859). A combination of converting 40% cases and increasing capacity by 20% would clear the backlog within a year (343 (281–410) days) with 784 (292–1324) deaths while awaiting treatment.
A strategy change to the management of severe AS is required to reduce the NHS backlog and waiting list deaths during the post-COVID-19 ‘recovery’ period. However, plausible adaptations will still incur a substantial wait to treatment and many hundreds dying while waiting.
Our model provides a good basis from which to alleviate a time-critical health system problem when data gathering is likely to result in a greater number of deaths.
Offering transcatheter aortic valve implantation to some surgical aortic valve replacement patients in what might be considered suboptimal per-patient treatment in ideal conditions could result in better target population-based outcomes.
The assumption that the entire NHS can be modelled as a single entity with a single waiting list is a limitation of this study.
We recognise that the waiting numbers used in our study are only estimates because we do not know how many patients with AS died due to COVID-19 infection.
The COVID-19 pandemic has led to the reorganisation of healthcare services to limit the transmission of the virus and deal with the sequelae of infection. This reorganisation had a detrimental effect on cardiovascular services, with reductions in hospitalisations for acute cardiovascular events and the deferral of all but the most urgent interventional procedures and operations.
Aortic stenosis (AS) is the most common form of valvular heart disease. Once stenosis is severe, symptoms follow and the prognosis is poor, with 50% mortality within 2 years of symptom onset.
There was a large decline in TAVI and SAVR procedural activity to treat severe AS during the COVID-19 pandemic.
In this study, we used mathematical methods to examine the extent to which additional capacity to provide treatment of severe AS should be created to clear the backlog and minimise deaths of people on the waiting list.
Data from the UK TAVR registry and National Institute for Cardiovascular Outcomes Research National Adult Cardiac Surgery Audit between 2017 and 2020 have previously been extracted to estimate an excess waiting list size (
We took 1 year mortality (
Patients on the waiting list for treatment of severe AS were represented as a dynamical system (
Dynamical system model of the waiting list length. SAVR, surgical aortic valve replacement; TAVI, transcatheter aortic valve implantation.
To this model, we introduced capacity in surplus to the 2018/2019 performance and called this capacity
These assumptions were brought together to give an estimated time (see
and associated mortality (
Using
We investigated three types of capacity increase: (1) a general increase in the capacity to provide SAVR and TAVI, which could be facilitated by an increased number of procedures per list, additional lists and prioritisation of care pathways and staffing to treat severe AS; (2) extra capacity created by treating some patients with TAVI who would routinely have SAVR; (3) a combination of a general increase in capacity and the conversion of a proportion of cases from SAVR to TAVI. During the COVID-19 pandemic, TAVI was performed in patients usually referred for surgery, with no difference in short-term outcomes compared with historical reference groups.
We assumed that the duration of a SAVR would routinely be between 2 and 4 hours and a TAVI between 1 and 2 hours.
We completed additional sensitivity analyses for how the conversion of SAVR to TAVI could affect the principal outcomes, including if three SAVR operations could be routinely completed in a day and four to five TAVI procedures per day (presuming increasing uptake of a minimalist TAVI approach without general anaesthesia enabling more rapid procedure time).
Patients and the public were not involved in the conduct of this study.
In the pre-COVID-19 period, the routine capacity for treatment of severe AS was set to cover the normal incident rate. That is, clearing the backlog by returning to pre-COVID-19 capacity is not possible. As a result, mortality on the excess waiting list at 1 year is estimated to be more than 1500, putting a strong emphasis on the need for change.
Time to clear backlog (left) and the resulting deaths (right) with associated 95% reference range as a function of daily percentage increase in capacity, with uncertainty from mortality and the initial waiting list. The x-axis is truncated at 5% for visualisation and clarity.
The conversion of a proportion of cases from surgery to TAVI provides a modest improvement in estimates of time to clear the backlog and mortality on the waiting list. With the conversion of 30% of SAVR operations to TAVI procedures, without the creation of additional capacity in the system, we estimated that it would take 975 (741–1284) days to clear the backlog and there would be 1914 (923–2809) deaths on the waiting list. Even with a conversion of 50% of SAVR operations to TAVI procedures, the estimated backlog would be cleared within 666 (533–848) days with 1419 (597–2189) deaths. For the highest conversion ratio that we considered (2:4), at a 50% rate of conversion, we estimated the backlog to be cleared in 384 (330–462) days with 871 (314–1426) deaths. While this result is improved, we consider a 2:4 conversion ratio the highest reasonable ratio in the short term, and is unlikely to be achieved at every centre immediately. It is also worth noting that even if this was achieved, the backlog would still take over a year to clear.
Mean time to clear backlog (left) and the resulting deaths (right) as a function of daily percentage increase in capacity (y-axis) and percentage of surgical aortic valve replacement (SAVR) converted to transcatheter aortic valve implantation (TAVI) (x-axis) (presented in two different forms). (A) Isoclines of constant mean clearance-time going from half a year (blue) to 2 years (purple) in half-year increments. (B) Isoclines of constant mean mortality after clearing the backlog from 500 people (blue) to 2000 (purple) in 500-person increments. (C) Heatmap of different combinations of conversion and daily capacity increases and how long the backlog would take to clear on average, in days. (D) Heatmap of different combinations of conversion and daily capacity increases and how many people would die, on average.
Sensitivity analyses where the number of TAVI procedures that could be completed within the same time as SAVR was altered (TAVI to SAVR: 4 to 3, 4 to 2, 5 to 3) support these findings (
In this study, using dynamical system modelling, we provide estimates for how changes to treatment pathways for patients with severe AS may affect the time taken to clear the backlog and minimise mortality on the waiting list in the NHS of England. Without providing at least 20% total additional capacity for the interventional treatment of AS, we estimated there would be more than 1000 deaths on the waiting list over a period of nearly 1.5 years. A conversion of cases from SAVR to TAVI would expedite the clearance of the backlog, but even converting half the cases to TAVI would still result in over 1400 deaths over a period of almost 2 years. A combination of converting 40% of cases usually planned for SAVR to TAVI and creating 20% additional capacity for procedures (through measures such as extra lists) would clear the excess backlog within 1 year, with 784 deaths.
Our study has several strengths. First, in a time-critical clinical situation of many unknowns, our use of novel mathematical models provides plausible estimates on which to base health services planning, and provides an exemplar that may be used in service delivery in other conditions in the postpandemic landscape. Given the high event rate among this population, waiting for more contemporary data to be collected may well not provide enough time to institute system changes to prevent deaths. Second, we also provide specific estimates for how the conversion of cases to TAVI from surgery may affect waiting lists and associated mortality, which can inform local multi-disciplinary team (MDT) discussions. Third, our model can act as a basis for a clinical and cost–benefit analysis to evaluate different ways to increase capacity and define the optimal strategy at each centre. For each centre, the most effective combination of converting SAVR to TAVI and provision or prioritisation of treatment of severe AS can be generated.
We recognise the limitations inherent in modelling a complex situation. First, we represent the NHS in England as a single entity. As such, we implicitly assume that population and capacity are distributed evenly throughout the country by treatment centre capacity. If the distribution of waiting list patients deviates significantly from the distribution of treatment centres weighted by capacity, the time it would take to clear the waiting list, and thus the mortality rate would be higher. Second, we have not attempted to calculate how many patients with AS may have died in the COVID-19 pandemic, which could have reduced the numbers of deaths on the waiting list and the duration of the waiting list because of an underestimation of ‘abandonment’ from the model. Third, our assumed mortality rate may differ at a centre-level due to prioritising clinically more vulnerable patients on the waiting list. Fourth, a centre-level analysis could account for the different practices in each treatment centre and identify strategies that work best for each centre. Fifth, our estimates from converting cases from SAVR to TAVI do not include postprocedural factors such as the requirement for intensive care capacity, hospital stay and further procedures because these rely on multiple centre-specific factors. Finally, it has been shown that rapid growth in the demand for TAVI can overwhelm current capacity,
A previous study used a mathematical model to quantify the cumulative cardiac surgical backlog (including coronary artery bypass grafting surgery, valve replacement and transcatheter aortic and mitral valve replacements) in two centres based on the projected pandemic duration in the USA.
The results of our study highlight concerns pertaining to the deferral of non-emergency treatment for severe AS during the ‘recovery period’ of COVID-19. Severe AS is a progressive condition with valve replacement the only available treatment improving prognosis.
Nonetheless, planning should prioritise patients at the highest risk from a deferral of treatment. Mortality on the waiting list for AS has been reported to be as high as 14%.
To help planning, we provide an app (
In this study, we found that without a combination of increased capacity for treatment of patients with severe AS and an expansion in the use of TAVI, there would be many potentially avoidable deaths during the post-COVID-19 recovery period. Our study findings and accompanying app may help inform the planning of cardiac services.
We want to thank all the participants of the V-KEMS Study Group on ‘Modelling Solutions to the Impact of COVID-19 on Cardiovascular Waiting Lists’ that took place on February 2-4, 2021, for thought-provoking discussions. Our special thanks to Clare Merritt (Newton Gateway to Mathematics), whose help extended beyond the workshop and was crucial in completing this work, and to Alan Champneys who brought the group together in the first place. BG is supported by the NIHR Bristol Biomedical Research Centre at the University of Bristol and University Hospitals Bristol and Weston NHS Foundation Trust. JHFR is part-supported by the NIHR Cambridge Biomedical Research Centre, the British Heart Foundation, HEFCE, the EPSRC Cambridge Centre for Mathematics of Information in Healthcare and the Wellcome Trust.
@Dr_R_Nadarajah, @sunlouise1, @jhfrudd, @mmamas1973, @FeryalErhun
MM proposed the initial workshop and designed the research question. MM, CPG, RN, BG and JHFR all helped to run said workshop as clinical experts. All members but KC and FE were involved in conceptualisation in the initial workshop. CPS, HJ, KJS and FE designed the model with clinical guidance from MM, CPG, RN, BG and JHFR. CPS performed data analysis. CPS, RN and FE drafted the initial manuscript. MM, CPG, BG, JHFR, NH, SL, LaSc, MS, LoSu, JW-M, KC provided critical interpretation and revision of the manuscript. All authors approved the final manuscript. FE acts as the guarantor for the overall content.
This study was part funded by EPSRC Cambridge Centre for Mathematics of Information in Healthcare, grant number EP/T017961/1. None of the study funding sources had an impact on the design, data analysis, writing of or decision to publish this paper.
BG acknowledges grants not related to this project from the David Telling Charitable Trust, and the Biotechnology and Biological Sciences Research Council, he additionally declared Associate Editorship of Anesthesia Journal, and being the chair DMSC for the COPIA Trial. All other authors confirm that they have no competing interests to declare.
Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.
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Data sharing not applicable as no datasets generated and/or analysed for this study.
Not applicable.