Understanding need - full abstract

Using mathematics to inform where specialist children’s retrieval teams should be located across England and Wales

Christina Pagel(1), Padmanabhan Ramnarayan(2), Sarah Seaton(3), Enoch Kung(1)
(1)University College London, (2)Great Ormond Street Hospital, (3)University of Leicester

Background: In England and Wales, specialist retrieval teams (PICRTs) transport critically ill children from district general hospitals (DGHs) to one of 24 Paediatric Intensive Care Units (PICUs). There are currently 11 PICRT locations in England and Wales, each staffed with one to three teams. Reaching the bedside of a critically ill child within three hours of agreeing the child requires intensive care (“time to bedside”) is a key target for PICRTs, but it is only achieved about 90% of the time.  Reaching the bedside can take longer during winter when demand for PICRT services typically doubles for about two months due to unavailability of teams. Could the time to bedside for retrieval teams be reduced by changing the number and location of PICRTs?

We sought to inform the allocation and location of PICRTs across England and Wales using mathematical optimisation methods.

Methods: We developed a location allocation optimisation framework to help inform decisions on the optimal number of locations for PICRTs, where those locations should be, which local hospitals each location serves and how many teams should staff each location. Our framework allows for variable journey times, and incorporates queuing theory by considering the time spent waiting for a PICRT to become available (if all teams are busy when a request for transport is received).  Incorporating waiting times into the framework necessarily introduces feedback loops that result in non-linear equations. We used heuristic optimisation methods and a genetic algorithm to solve instances of the framework given specific inputs.

The inputs to the framework are: number of desired locations; demand for PICRT services from each local hospital; number of teams at each location.

The outputs of the framework are: the optimal locations for each PICRT service, the allocation of local hospitals to each location; the overall average time to bedside; the average waiting time for a team to become available for transport; the overall percentage of patient demand reached within 3 hours.

We worked with clinical collaborators to define a plausible set of scenarios to test using the optimisation framework.

Results: The scenarios developed with clinicians that we tested using the framework were:

  • Varying the number of locations from 6 to 14

  • Varying the total number of teams available across locations from 11 to 22

  • Using average historical non-winter (March – October) demand

  • Using average historical winter (November – February) demand

  • Increasing demand by 5% a year for 10 years to model future increases

There are several configurations of services that have similar performance in terms of meeting the national three hour target. However, for the same number of teams, fewer locations staffed with more teams had better performance than more locations with fewer teams. This is because reduction in waiting times due to greater team availability at a single location saves more time in the long run than slightly shorter journey times achieved with more locations. Our results also showed that certain locations would benefit from an extra team during the winter surge. For configurations where the three hour target is met, how to balance number and location of PICRTs in the context of current services and budget provision needs to be decided by clinical teams and commissioners. 

Implications: Mathematical location-allocation methods are very useful in informing decisions on how to organise specialised services, but need to be undertaken in close collaboration with the clinical community.


National Institute for Health Research Health Services and Delivery Research Programme (15/136/45)


Department of Health disclaimer

The views and opinions expressed therein are those of the authors and do not necessarily reflect those of the HSDR Programme, NIHR, NHS or the Department of Health.


Understanding the individual characteristics that drive health and social care utilisation – using a linked dataset across five settings of care for adult residents of Barking and Dagenham

Jenny Shand(1), Steve Morris(2), Manuel Gomes(1)
(1)University College London, (2)University of Cambridge

Background: Better integration across all settings of care is a core ambition of the NHS to address the changing needs of an ageing population and achieve efficiency gains. This study created a novel individual level data resource to explore the use of health and social care services across five care settings, to evaluate the factors associated with this use, and the extent to which these factors vary by setting of care for residents of Barking and Dagenham (B&D) in 2016/17.

Methodology: A two-part regression model to calculate the combined effect of the probability of service use and the level of service use if there was one across a wide range of co-variates overall and by setting of care, for each of hospital, primary care, community care, mental health and social care.

Results: 114,393 adults (age 19 and above) who lived in B&D between 1st April 2016 and 31st March 2017 were included in the analysis. Those that died or moved out in year were excluded. The following co-variates were associated with increased odds of having a service cost and increased mean total cost:

Socio-demographic variables: Increasing age, female (2.63OR, CI 2.50 2.70, increase in adjusted mean cost £669) non-white ethnicity, having a carer (1.68OR, CI 1.01 2.82, £1,189)

Health variables: Being an ex-smoker (1.32OR, CI 1.24 1.40, £174) or a smoker (1.93OR, CI 1.83 2.03, change in mean not significant), being obese (1.45OR 1.37 1.53, £176) or morbidly obese (1.51OR 1.32 1.72, £526), Presence of more than one long term condition, presence of any of the 16 long-term conditions

Household variables: Being in a household in receipt of Employment Support Allowance (1.60OR, CI 1.44 1.77, £1,634), Income Support (1.32OR, CI 1.16 1.49, £884) and standard housing benefit (1.25OR, CI 1.18 1.33, £315).

There were similar findings for each setting with regards to age (with the exception of mental health), the presence of any of the long-term conditions, and being in a household in receipt of Employment Support Allowance. The individual conditions that had the highest odds and highest adjusted means were different for different settings of care.

Implications: Policy for promotion of integrated care tends to focus on small groups of people who have complex care needs; however, there are other communities for whom integration can also be important. The narrative on integration has promoted a shift from disease-based models of care to population-based models that reflect the wider needs of individuals. Our findings on, for example, employment support allowance and living alone, support this shift; however, given the strong association with individual diseases and service use across all settings of care, disease-based planning remains important. In addition, identifying the settings most dominant in the service use profile for different conditions may help better target interventions.

Large, linked datasets, such as the one considered in this study, provide extensive opportunities to improve our understanding of service user patterns and the wider determinants of health. 

Predicting crisis in the delivery of emergency care in acute trusts using administrative and open source data: a longitudinal study

Violeta Balinskaite, Alex Bottle, Paul Aylin
Imperial College London

Background: Hospitals around the world face increasing demand for both planned and unplanned (emergency) services. During recent winters, acute hospitals trusts in England experienced extreme pressures and were advised to cancel/delay outpatient appointments and defer non-urgent surgery. In our study, we defined an episode of organisational crisis within an acute trust based on a combination of two performance characteristics: 4-hour target and A&E diverts. A 4-hour target was selected because it is often used as a barometer for the overall performance of the NHS, is a proxy for inpatient flow and is highly correlated with inpatient occupancy. A&E diverts are used only as an action of last resort and hence show the trust’s ability to meet demands. This study aimed to create a predictive model for estimating the probability of a crisis in the delivery of emergency care in acute hospital trusts leading to A&E diverts and four-hour A&E breaches. 

Methods: A retrospective longitudinal study using data from 131 acute hospital trusts collected over three winter periods: 5 December 2016 – 12 March 2017, 20 November – 4 March 2018, 3 December 2018 – 3 March 2019. We applied advanced statistical (mixed modelling analysis, generalised estimating equation [GEE]) and novel machine learning (boosted multivariate trees) methods to create the prediction model. To assess the results of each model a leave-one-out cross-validation technique (LOOCV) and c-statistic (pooled) were used. 

Results: During the study period, almost 49% (64) of trusts had an episode of crisis at least once with an average of 17 episodes of crisis per week. The median daily number of admissions was 271, of which 39.4% were emergency. Over 94% of daily A&E attendances were at Type 1 departments (a consultant-led 24-hour service with full resuscitation facilities and designated accommodation), of which 27.7 % were admitted. In all models, the number of previous A&E diverts were the most significant for predicting the episode of crisis in the delivery of emergency care occurring the following week. For each additional period during which there were A&E diverts, there is 48.7% (mixed-effects) and 77.5% (GEE) increased risk for the episode of a crisis occurring the following week. Model performance for GEE and mixed-effects  was similar (c-statistic 0.75 vs 0.74), and the boosted multivariate trees method outperformed latter methods (c-statistic 0.86).

Implications: Using routinely collected administrative data we were able to predict two weeks in advance an episode of crisis in the delivery of emergency care in acute hospital trusts. A fundamental limitation is the limited time period of, and information on, the Winter Daily Situation Reports dataset, which restricted our analysis. However, we still believe that this study is a step forward to create a model for predicting an episode of failure within a trust, and, when applied to local real-time data, could assist trusts in predicting emergency care crises, allowing them to mitigate or even prevent their occurrence.

Diabetes Severity SCOre (DISSCO) improves hospitalisation and mortality prediction: model development and validation in 139,626 people with T2DM

Salwa Zghebi(1), Mamas Mamas(2), Darren Ashcroft(1), Chris Salisbury(3), Christian Mallen(2), Carolyn Chew-Graham(2), David Reeves(1), Harm Van marwijk(4), Nadeem Qureshi(5), Stephen Weng(5), Tim Holt(6), Iain Buchan(7), Niels Peek(1), Martin Rutter(1), Evangelos Kontopantelis(1)
(1)University of Manchester, (2)Keele University, (3)University of Bristol, (4)University of Brighton, (5)University of Nottingham, (6)University of Oxford, (7)University of Liverpool

Background: Type 2 diabetes (T2DM) prevalence is increasing worldwide. But, a validated and clinically applicable T2DM severity measure derived from medical data is lacking. We  aimed to: 1) develop and validate a disease severity score (DISSCO) in T2DM patients using electronic health data, 2) evaluate the score's association with risks of hospitalisation and mortality, assessing if it provides additional risk information to sociodemographic factors and HbA1c.

Methods: We used primary and secondary care data held by the UK CPRD. We included patients with T2DM from March 2007 to March 2017, aged ≥35 years, registered in 400 general practices in England. The study cohort was randomly divided to a training cohort (N= 111,748, 80%) to develop the severity tool, and validation cohort (N=27,878, 20%). We developed baseline and longitudinal severity scores using 34 diabetes-related and cardiovascular (CV) domains. The primary outcome was all-cause mortality. Secondary outcomes were first hospitalisation due to any cause, diabetes (including hypoglycaemia), or due to CV disease or procedures.

Results: Patients aged (mean±SD) 63±12 years, 45% female, 83% White, 18% from deprived areas, baseline HbA1c 62±22 mmol/mol. DISSCO ranged between 0-22. Overall, 27,362 (20%) people died, and 99,951 (72%) had ≥1 hospitalisation during follow-up. Cox models (adjusted for age, gender, race, deprivation, and HbA1c) showed that a 1-unit increase in baseline DISSCO was associated with significantly higher risks for mortality (HR: 1.14, 95%CI: 1.13; 1.15, an AUROC=0.77), and CV hospitalisation (HR: 1.45, 95%CI: 1.44; 1.46, AUROC=0.76). The addition of DISSCO to demographic variables improved the predictive value of survival models outperforming the added value of HbA1c for mortality (AUROC improved from 0.76 to 0.77) and CV hospitalisation (AUROC from 0.70 to 0.76). Compared to DISSCO, HbA1c was a weaker predictor for all outcomes but hypoglycaemia hospitalisation, based on AUROC. Findings were consistent in the validation cohort.

Implications: Higher T2DM severity score are associated with higher risks for hospital admissions and mortality. The new severity score had higher predictive value than the proxy used in clinical practice, HbA1c. This reproducible algorithm can be useful to practitioners, help stratify clinical care of T2DM patients and inform funding allocation to health services.


Assessing the severity of cardiovascular disease in people with coronary heart disease (CHD): a retrospective cohort study using the UK Clinical Practice Research Datalink

Salwa Zghebi(1), Mamas Mamas(2), Darren Ashcroft(1), Martin Rutter(1), Harm Van marwijk(3), Chris Salisbury(4), Christian Mallen(2), Carolyn Chew-Graham(2), Nadeem Qureshi(5), Stephen Weng(5), Tim Holt(6), Iain Buchan(7), Niels Peek(1), Sally Giles(1), David Reeves(1), Evangelos Kontopantelis(1)
(1)University of Manchester, (2)Keele University, (3)University of Brighton, (4)University of Bristol, (5)University of Nottingham, (6)University of Oxford, (7)University of Liverpool

Introduction: CHD is the most common cardiovascular (CV) disease and caused ~9.5m deaths worldwide in 2016. Nearly 2.3m people have CHD in the UK. We aimed to: i) develop/validate CV severity scores in people with CHD using routinely-collected EHRs; ii) evaluate its association with risks of all-cause and cause-specific hospitalisation and mortality.


Methods: Using Clinical Practice Research Datalink (CPRD), we extracted data for people with CHD, and modelled baseline and longitudinal scores across 20 severity domains. We used Cox regression models and competing risk regressions to evaluate the association between severity and 1-year all-cause mortality and 1-year hospitalisations after controlling for age, gender, ethnicity, and deprivation.


Results: We identified 213,088 patients with CHD from 398 English practices.  Baseline severity scores ranged between 0-10, mean(±SD) 1.5±1.2. Overall, 49,918 (23%) patients died, and 173,204 (81%) patients had ≥1 hospitalisation during 9.4years of follow-up. A 1-unit increase in baseline severity score was associated with significantly 41% increased risk for all-cause mortality (95%CI: 37%-45%, AUROC=0.83). In competing risk regressions, a 1-unit increase in score was associated with 28% any-cause hospitalisation (27%-29%, AIC=992,096), and 39% CV/diabetes hospitalisation (37%-40%, AIC=699,635). The new score improved the models' predictive value for all outcomes when added to socio-demographic variables.


Implications: A higher CHD severity score is associated with increased risks of hospital admissions and mortality. This reproducible scoring tool based on routinely-collected data could support practitioners to provide better clinical management of CHD in primary care with wider implications on individual patient and population healthcare.