The False Economy of Seeking to Eliminate Delayed Transfers of Care: Some Lessons from Queueing Theory.

BACKGROUND: It is a stated ambition of many healthcare systems to eliminate delayed transfers of care (DTOCs) between acute and step-down community services. OBJECTIVE: This study aims to demonstrate how, counter to intuition, pursual of such a policy is likely to be uneconomical, as it would require large amounts of community capacity to accommodate even the rarest of demand peaks, leaving much capacity unused for much of the time. METHODS: Some standard results from queueing theory-a mathematical discipline for considering the dynamics of queues and queueing systems-are used to provide a model of patient flow from the acute to community setting. While queueing models have a track record of application in healthcare, they have not before been used to address this question. RESULTS: Results show that 'eliminating' DTOCs is a false economy: the additional community costs required are greater than the possible acute cost saving. While a substantial proportion of DTOCs can be attributed to inefficient use of resources, the remainder can be considered economically essential to ensuring cost-efficient service operation. For England's National Health Service (NHS), our modelling estimates annual cost savings of £117m if DTOCs are reduced to the 12% of current levels that can be regarded as economically essential. CONCLUSION: This study discourages the use of 'zero DTOC' targets and instead supports an assessment based on the specific characteristics of the healthcare system considered.

Supporting COVID-19 elective recovery through scalable wait list modelling: Specialty-level application to all hospitals in England.

The recovery of elective waiting lists represents a major challenge and priority for the health services of many countries. In England's National Health Service (NHS), the waiting list has increased by 45% in the two years since the COVID-19 pandemic was declared in March 2020. Long waits associate with worse patient outcomes and can deepen inequalities and lead to additional demands on healthcare resources. Modelling the waiting list can be valuable for both estimating future trajectories and considering alternative capacity allocation strategies. However, there is a deficit within the current literature of scalable solutions that can provide managers and clinicians with hospital and specialty level projections on a routine basis. In this paper, a model representing the key dynamics of the waiting list problem is presented alongside its differential equation based solution. Versatility of the model is demonstrated through its calibration to routine publicly available NHS data. The model has since been used to produce regular monthly projections of the waiting list for every hospital trust and specialty in England.

Modeling the Recovery of Elective Waiting Lists Following COVID-19: Scenario Projections for England.

OBJECTIVES: A significant indirect impact of COVID-19 has been the increasing elective waiting times observed in many countries. In England's National Health Service, the waiting list has grown from 4.4 million in February 2020 to 5.7 million by August 2021. The objective of this study was to estimate the trajectory of future waiting list size and waiting times up to December 2025. METHODS: A scenario analysis was performed using computer simulation and publicly available data as of November 2021. Future demand assumed a phased return of various proportions (0%, 25%, 50%, and 75%) of the estimated 7.1 million referrals "missed" during the pandemic. Future capacity assumed 90%, 100%, and 110% of that provided in the 12 months immediately before the pandemic. RESULTS: As a worst-case scenario, the waiting list would reach 13.6 million (95% confidence interval 12.4-15.6 million) by Autumn 2022, if 75% of missed referrals returned and only 90% of prepandemic capacity could be achieved. The proportion of patients waiting under 18 weeks would reduce from 67.6% in August 2021 to 42.2% (37.4%-46.2%) with the number waiting over 52 weeks reaching 1.6 million (0.8-3.1 million) by Summer 2023. At this time, 29.0% (21.3%-36.8%) of patients would be leaving the waiting list before treatment. Waiting lists would remain pressured under even the most optimistic of scenarios considered, with 18-week performance struggling to maintain 60%. CONCLUSIONS: This study reveals the long-term challenge for the National Health Service in recovering elective waiting lists and potential implications for patient outcomes and experience.

Optimising the balance of acute and intermediate care capacity for the complex discharge pathway: Computer modelling study during COVID-19 recovery in England.

OBJECTIVES: While there has been significant research on the pressures facing acute hospitals during the COVID-19 pandemic, there has been less interest in downstream community services which have also been challenged in meeting demand. This study aimed to estimate the theoretical cost-optimal capacity requirement for 'step down' intermediate care services within a major healthcare system in England, at a time when considerable uncertainty remained regarding vaccination uptake and the easing of societal restrictions. METHODS: Demand for intermediate care was projected using an epidemiological model (for COVID-19 demand) and regressing upon public mobility (for non-COVID-19 demand). These were inputted to a computer simulation model of patient flow from acute discharge readiness to bedded and home-based Discharge to Assess (D2A) intermediate care services. Cost-optimal capacity was defined as that which yielded the lowest total cost of intermediate care provision and corresponding acute discharge delays. RESULTS: Increased intermediate care capacity is likely to bring about lower system-level costs, with the additional D2A investment more than offset by substantial reductions in costly acute discharge delays (leading also to improved patient outcome and experience). Results suggest that completely eliminating acute 'bed blocking' is unlikely economical (requiring large amounts of downstream capacity), and that health systems should instead target an appropriate tolerance based upon the specific characteristics of the pathway. CONCLUSIONS: Computer modelling can be a valuable asset for determining optimal capacity allocation along the complex care pathway. With results supporting a Business Case for increased downstream capacity, this study demonstrates how modelling can be applied in practice and provides a blueprint for use alongside the freely-available model code.

Use of linked patient data to assess the effect of Long-COVID on system-wide healthcare utilisation.

Background: Within the relatively early stages of the COVID-19 pandemic, there had been an awareness of the potential longer-term effects of infection (so called Long-COVID) but little was known of the ongoing demands such patients may place on healthcare services. Objective: To investigate whether COVID-19 illness is associated with increased post-acute healthcare utilisation. Method: Using linked data from primary care, secondary care, mental health and community services, activity volumes were compared across the 3 months preceding and proceeding COVID-19 diagnoses for 7,791 individuals, with a distinction made between whether or not patients were hospitalised for treatment. Differences were assessed against those of a control group containing individuals who had not received a COVID-19 diagnosis. All data were sourced from the authors' healthcare system in South West England. Results: For hospitalised COVID-19 cases, a statistically significant increase in non-elective admissions was identified for males and females <65 years. For non-hospitalised cases, statistically significant increases were identified in GP Doctor and Nurse attendances and GP prescriptions (males and females, all ages); Emergency Department attendances (females <65 years); Mental Health contacts (males and females ≥65 years); and Outpatient consultations (males ≥65 years). Conclusion: There is evidence of an association between positive COVID-19 diagnosis and increased post-acute activity within particular healthcare settings. Linked patient-level data provides information that can be useful to understand ongoing healthcare needs resulting from Long-COVID, and support the configuration of Long-COVID pathways of care.

Modelling the effect of COVID-19 mass vaccination on acute hospital admissions.

BACKGROUND: Managing high levels of acute COVID-19 bed occupancy can affect the quality of care provided to both affected patients and those requiring other hospital services. Mass vaccination has offered a route to reduce societal restrictions while protecting hospitals from being overwhelmed. Yet, early in the mass vaccination effort, the possible impact on future bed pressures remained subject to considerable uncertainty. OBJECTIVE: The aim of this study was to model the effect of vaccination on projections of acute and intensive care bed demand within a 1 million resident healthcare system located in South West England. METHODS: An age-structured epidemiological model of the susceptible-exposed-infectious-recovered type was fitted to local data up to the time of the study, in early March 2021. Model parameters and vaccination scenarios were calibrated through a system-wide multidisciplinary working group, comprising public health intelligence specialists, healthcare planners, epidemiologists and academics. Scenarios assumed incremental relaxations to societal restrictions according to the envisaged UK Government timeline, with all restrictions to be removed by 21 June 2021. RESULTS: Achieving 95% vaccine uptake in adults by 31 July 2021 would not avert the third wave in autumn 2021 but would produce a median peak bed requirement ∼6% (IQR: 1-24%) of that experienced during the second wave (January 2021). A 2-month delay in vaccine rollout would lead to significantly higher peak bed occupancy, at 66% (11-146%) of that of the second wave. If only 75% uptake was achieved (the amount typically associated with vaccination campaigns), then the second wave peak for acute and intensive care beds would be exceeded by 4% and 19%, respectively, an amount which would seriously pressure hospital capacity. CONCLUSION: Modelling influenced decision-making among senior managers in setting COVID-19 bed capacity levels, as well as highlighting the importance of public health in promoting high vaccine uptake among the population. Forecast accuracy has since been supported by actual data collected following the analysis, with observed peak bed occupancy falling comfortably within the inter-quartile range of modelled projections.

Projecting the effect of easing societal restrictions on non-COVID-19 emergency demand in the UK: Statistical inference using public mobility data.

While it is well established that societal restrictions have been effective in reducing COVID-19 emergency demand, evidence also suggests an impact upon emergency demand not directly related to COVID-19 infection. Hospital planning may benefit from a greater understanding of this association and the ability to reliably forecast future levels of non-COVID-19 demand. Activity data for Accident and Emergency (A&E) attendances and emergency admissions were sourced for all hospitals within the Bristol, North Somerset and South Gloucestershire healthcare system. These were regressed upon publicly available mobility data obtained from Google's Community Mobility Reports for the local area. Seasonal trends were controlled for using time series decomposition. The models were used to predict non-COVID-19 emergency demand under the UK Government's plan to sequentially lift all restrictions by 21 June 2021, in addition to three alternative hypothetical relaxation strategies. Rates of public mobility within the local area were shown to account for 77% and 65% of the variance in non-COVID-19 related A&E attendances and emergency admissions respectively. Modelling supports an increase in emergency demand in line with the level and timing of societal restrictions, with significant increases to be expected upon the ending of all legal limits. This study finds that non-COVID-19 emergency demand associates with the level of societal restrictions, with rates of public mobility representing a key determinant. Through predictive modelling, healthcare systems can improve their demand forecasting in effectively managing hospital capacity.

The impact of increased outpatient telehealth during COVID-19: Retrospective analysis of patient survey and routine activity data from a major healthcare system in England.

In response to societal restrictions due to the COVID-19 pandemic, a significant proportion of physical outpatient consultations were replaced with virtual appointments within the Bristol, North Somerset and South Gloucestershire healthcare system. The objective of this study was to assess the impact of this change in informing the potential viability of a longer-term shift to telehealth in the outpatient setting. A retrospective analysis was performed using data from the first COVID-19 wave, comprising 2998 telehealth patient surveys and 143,321 distinct outpatient contacts through both the physical and virtual medium. Four in five specialities showed no significant change in the overall number of consultations per patient during the first wave of the pandemic when telehealth services were widely implemented. Of those surveyed following virtual consultation, more respondents 'preferred' virtual (36.4%) than physical appointments (26.9%) with seven times as many finding them 'less stressful' than 'more stressful'. In combining both patient survey and routine activity data, this study demonstrates the importance of using data from multiple sources to derive useful insight. The results support the potential for telehealth to be rapidly employed across a range of outpatient specialities without negatively affecting patient experience.

Nowcasting for improved management of COVID-19 acute bed capacity

As the second wave of COVID-19 continues to push healthcare services to their limits, rapid and strategic planning has never been more important. Richard M Wood explains how statistical 'nowcasting' can be used to predict bed occupancy rates and help leaders to better manage acute capacity during this ongoing crisis.

The Value of Triage during Periods of Intense COVID-19 Demand: Simulation Modeling Study.

BACKGROUND: During the COVID-19 pandemic, many intensive care units have been overwhelmed by unprecedented levels of demand. Notwithstanding ethical considerations, the prioritization of patients with better prognoses may support a more effective use of available capacity in maximizing aggregate outcomes. This has prompted various proposed triage criteria, although in none of these has an objective assessment been made in terms of impact on number of lives and life-years saved. DESIGN: An open-source computer simulation model was constructed for approximating the intensive care admission and discharge dynamics under triage. The model was calibrated from observational data for 9505 patient admissions to UK intensive care units. To explore triage efficacy under various conditions, scenario analysis was performed using a range of demand trajectories corresponding to differing nonpharmaceutical interventions. RESULTS: Triaging patients at the point of expressed demand had negligible effect on deaths but reduces life-years lost by up to 8.4% (95% confidence interval: 2.6% to 18.7%). Greater value may be possible through "reverse triage", that is, promptly discharging any patient not meeting the criteria if admission cannot otherwise be guaranteed for one who does. Under such policy, life-years lost can be reduced by 11.7% (2.8% to 25.8%), which represents 23.0% (5.4% to 50.1%) of what is operationally feasible with no limit on capacity and in the absence of improved clinical treatments. CONCLUSIONS: The effect of simple triage is limited by a tradeoff between reduced deaths within intensive care (due to improved outcomes) and increased deaths resulting from declined admission (due to lower throughput given the longer lengths of stay of survivors). Improvements can be found through reverse triage, at the expense of potentially complex ethical considerations.

COVID-19 scenario modelling for the mitigation of capacity-dependent deaths in intensive care.

Managing healthcare demand and capacity is especially difficult in the context of the COVID-19 pandemic, where limited intensive care resources can be overwhelmed by a large number of cases requiring admission in a short space of time. If patients are unable to access this specialist resource, then death is a likely outcome. In appreciating these 'capacity-dependent' deaths, this paper reports on the clinically-led development of a stochastic discrete event simulation model designed to capture the key dynamics of the intensive care admissions process for COVID-19 patients. With application to a large public hospital in England during an early stage of the pandemic, the purpose of this study was to estimate the extent to which such capacity-dependent deaths can be mitigated through demand-side initiatives involving non-pharmaceutical interventions and supply-side measures to increase surge capacity. Based on information available at the time, results suggest that total capacity-dependent deaths can be reduced by 75% through a combination of increasing capacity from 45 to 100 beds, reducing length of stay by 25%, and flattening the peak demand to 26 admissions per day. Accounting for the additional 'capacity-independent' deaths, which occur even when appropriate care is available within the intensive care setting, yields an aggregate reduction in total deaths of 30%. The modelling tool, which is freely available and open source, has since been used to support COVID-19 response planning at a number of healthcare systems within the UK National Health Service.