Saving lives with maths

Innovative mathematical modelling is delivering improved cancer outcomes, ambulance response times, and a new NHS contact service.

Scenes of queuing chaos in a Mumbai hospital in the mid-1990s set one Cardiff University mathematician on a unique journey.

Without an effective queuing or scheduling system, or indeed any data to inform decision-making, patients in need of emergency healthcare were left waiting in pain, leaving healthcare professionals frustrated and overworked.

Little did Professor Paul Harper know that this experience would lead him, and his research team, on a mission to apply mathematical modelling to help fix and improve vital NHS services, both in Wales and in other parts of the UK.

“Going to Mumbai for the summer of 1996 for my MSc project was the first time I realised the potential use of mathematical modelling to deliver better health services,” recalls Professor Harper.

“When you come out of the classroom for the first time and encounter the real world – in my case, to help support the response to the HIV crisis – you see how you can apply your academic knowledge and make change.”

Fast forward some 25 years, and Harper and his team have worked on a wide range of healthcare improvement projects, including transforming cancer services in Wales, increasing the efficiency of the London Ambulance Service, and helping to design the Wales NHS 111 service.

Improving cancer outcomes

As the Mumbai experience showed, emergency healthcare requires accurate demand forecasting to ensure the effective deployment of both medical resources and patients to the correct service.

Closer to home, with the onset of devolution, policymakers in Wales knew it had a serious problem with cancer survival outcomes. At the time, the five-year cancer survival rates in Wales were poor compared to other developed nations.

The key to the problem was the existence of two established diagnosis and treatment pathways for cancer.

When a patient’s GP saw obvious red-flag cancer symptoms, the patient entered the ‘urgent’ pathway, and treatment was required to start within 62 days. When symptoms were present which could indicate either cancer or some other condition, patients entered the ‘non-urgent’ pathway, for which a treatment deadline was only set once cancer was confirmed through diagnostic tests.

This complicated cancer statistics. It also inaccurately recorded the waiting time of patients on the ‘non-urgent’ pathway, who could be waiting for months before cancer was confirmed and a treatment deadline was imposed.

However, while knowing there was a problem, NHS managers had no real idea how to solve it, and sought the advice of Professor Harper and his team.

“I remember the approach quite clearly. It was December, and I had a call from the Wales Cancer Network to meet at the University,” recalls Professor Harper. “We had already been working on cancer, and the research we’d already undertaken showed that modelling patient pathways could help unblock critical bottlenecks in care delivery.”

The meeting saw his team embark on a mission to establish what level of resource would be required to implement a Single Cancer Pathway (SCP) in Wales.

‘A bowl of spaghetti’

The existing system, in Professor Harper’s view, was like a “bowl of spaghetti”, with patients coming through in different routes with different diagnostic tests, and not necessarily getting the diagnostics they needed, or in the most efficient sequence to avoid delays. The key to unravelling the spaghetti, and ensuring patients got the quickest decision about whether it was cancer or not, was reducing the number of different pathways and determining the required resourcing needs.

This is where Professor Harper’s research and expertise proved vital. His group was able to model the resources needed to meet the proposed SCP waiting time targets and to determine optimal diagnostic pathways.

This involved analysis of more than 6,000 cancer referrals, across 10 different types of cancer, for 30 defined categories of diagnostic tests. Their report identified the need for a 20% increase in diagnostic resources to meet proposed treatment timescales, and indicated that a rollout of “rapid diagnostic hubs” would help achieve the project’s goals.

The findings were used to advise Vaughan Gething, then Welsh Government Minister for Health and Social Services. He released £3m of funding to provide the operational and diagnostic support required to transition to the Single Cancer Pathway in line with Professor Harper’s modelling.

“As a result of our research contribution, Wales was the first UK nation to introduce a single waiting time target for cancer patients. The SCP changed the diagnosis and treatment pathway for the approximately 60% of cancer patients in Wales who would previously have been placed on the ‘non-urgent’ suspected cancer pathway.

“Ultimately, it was about getting the patient and right resources in the right place at the right time,” adds Professor Harper.

London Ambulance service

The dilemmas faced by the London Ambulance service were similar to those faced by NHS Wales.

The London Ambulance Trust is responsible for responding to urgent and emergency medical situations within the UK’s busiest ambulance service.

Every year, it receives 1.9m 999 calls and responds to over 1.2m incidents. The efficient allocation of support and frontline staff is essential to avoiding unnecessary burden on emergency departments.

It wasn’t running as efficiently as it could have been until the research team worked closely with the London Ambulance Service Forecasting and Planning team.

“The head of their Analytics team studied for their PhD with us, which led to us developing this relationship,” says Professor Harper. “Ambulance services routinely collect detailed data on all 999 calls, including timings and locations of incidents. With such data we can create accurate geospatial forecasts of the peaks and troughs of demands in the Ambulance Service.”

Professor Harper explains further: “In essence, we deploy analytical methods on the large volumes of data to try and make sense of it, and provide the ambulance service with enhanced understanding on the types of calls you’re getting, where they’re coming from, and when you might expect them.

“With this detailed understanding, you can then roster or shift profile more intelligently, to operationally deploy staff and ambulance vehicles in the most effective manner, as well as making better strategic decisions on both capacity and how to optimally allocate crew and vehicles to ambulance bases in order to minimise patient waiting times for an ambulance, and to improve patient outcomes and survival.”

Using their modelling, the team was able to use the data to help London Ambulance Service develop a forecasting suite that predicts resource requirements as far as 14 days in advance, which enabled informed and proactive decisions about staffing.

In financial terms, the team was able to assist in saving vital resources. Annual contract negotiations for the London Ambulance Service, costing some £370m, were previously based on unconfirmed estimates and previous averages of demand.

By working with us, the London Ambulance Service Finance and Planning team improved the offering of the financial year forecasting. It allowed for operational planning to occur much further in advance, with recommended flex for seasonal demands, and allowed the Service to agree to contracts which didn’t eat into budgets unnecessarily.

A crucial element, in Professor Harper’s view, was “making more effective use of agency spend”. Increased assurance around demand and performance enabled the more effective use of approximately £10m of staff overtime per annum.

This included budget savings in lower-demand periods that could instead be used at times of greater pressure, ultimately resulting in a more equitable and safe delivery of service to patients.

Designing and launching the NHS 111 Service

With its growing reputation for providing solutions to some of the NHS’s longstanding problems, in 2015, NHS Wales again commissioned Professor Harper’s group. This time, the team was asked to analyse national NHS Direct and out-of-Hours data to model a proposed 111 service across Wales.

The service sought to combine the functionalities of the NHS Direct call-centres with the out-of-Hours GP phone service, and differs from other national 111 services by employing a greater proportion of clinical staff.

The University team evaluated different ways of providing the complex new service, and forecast the ideal staffing size and skills required to support it.

“Again, this task was about better understanding demand and capacity, and optimising service design,” says Professor Harper.

The team’s analysis found that an effective combined service required increased staffing of nurses and call-handlers, but revealed that fewer GPs could be used in the service. The analysis also provided information about resource allocation, and predicted impact on service delivery, to the 111 project.

Their recommendations were implemented in a 2016 pilot launch across the Abertawe Bro Morgannwg, Hywel Dda, and Powys Health Board areas.

Within six months, in the Abertawe Bro Morgannwg Health Board, the service received 71,853 calls: 404 calls per day at the weekend and 802 calls per day on bank holidays, and resulted in 1,343 fewer hospital emergency visits and 1,291 (29%) fewer ambulance callouts.

By avoiding unnecessary emergency journeys, savings of £642,120 were generated over the six-month monitoring period. Based on the success of the pilot schemes, the Welsh Government announced in 2018 that the service would be expanded to the entire population of Wales.

Headset resting on a laptop in a call centre — The team’s analysis found that an effective combined service required increased staffing of nurses and call-handlers but revealed that fewer GPs could be used in the service.

Shaping future decisions

The group has a well-established track record in helping to improve outcomes and save lives.

As Professor Harper reflects on his team’s successes, it becomes clear that the journey has many pathways. The pandemic saw their work become even more vital in solving live problems.

Decision-makers faced many unprecedented issues during the onset of lockdown. In a university context, there was a major issue with the impact of students moving from their university halls of residence to their permanent home addresses.

Using data from the university’s asymptomatic COVID-19 testing service, the team modelled secondary infection numbers if students returned home. They created a new online app to estimate secondary infections for a specific region, considering local values for returning student numbers and prevalence of COVID-19.

“There was evidence that encouraging students to return to their permanent home address from university residences during the Welsh fire-break in Autumn 2020 would create greater risks than encouraging students to remain located close to their university of study,” Professor Harper explains.

“There were also projected risks for an anticipated 1 million UK university students returning home for the 2020 Christmas vacation – effectively spreading it all over the country again. It was a very real public health risk.”

Ultimately, this helped formulate Welsh Government messaging for students not to return home during the firebreak, and also helped inform decision-making in the months that followed.

Despite these many achievements, Professor Harper is concerned that there can be a reluctance for organisations to make informed decisions based on data and modelling.

“We now have so much data – but it still isn’t always used intelligently, so that we can pinpoint when things aren’t quite working as well as they could be in the health service. Using data and modelling is vital to effectively adjust services and make the changes necessary to deliver excellent patient care.

“The key is the willingness to adapt and change. I’m optimistic that as more parts of the NHS see the tangible results that come from modelling, the more we will see a shift to this approach.”