Interview: Using Mathematical Optimization to Address the Healthcare Challenges of COVID-19

Date: 4/7/2021

The COVID-19 pandemic has caused major and unprecedented challenges for healthcare systems around the world. Over the past year, public health officials and healthcare industry professionals have found themselves scrambling to answer critical questions like:

• How – with limited resources including PPE, ventilators, ICU beds, and medical personnel – can our healthcare facilities cope with sudden and severe surges in COVID-19 cases and hospitalizations?
• What is the most efficient way to utilize our hospital capacity to treat COVID-19 patients?
• How can we allocate and administer COVID-19 vaccines to the masses in the most effective and equitable manner possible?

To help answer these and other vital questions and make the data-driven decisions on how best to use our scarce healthcare resources to combat the pandemic, governments and healthcare providers have leveraged software applications powered by sophisticated, advanced analytics technologies like machine learning and mathematical optimization.

These applications have been built by some of the brightest minds from both the business and academic worlds. One individual who is at the forefront of this push to develop cutting-edge advanced analytics applications for the healthcare industry is Kimia Ghobadi, who is the John C. Malone Assistant Professor in Civil and Systems Engineering at Johns Hopkins University.

Throughout her career, Professor Ghobadi has been focused on developing data-driven mathematical optimization frameworks for healthcare applications, and many of her projects have been in collaboration with healthcare entities, including the Johns Hopkins Hospital.

Recently we spoke with Professor Ghobadi to find out about her work in building mathematical optimization applications to address COVID-19 challenges and other healthcare problems, and get her insights on the importance and impact of mathematical optimization in our world today.

Gurobi (G): Please tell us about your background and your work.

Kimia Ghobadi (KG): My background is not really traditional – I have jumped around a bit. I studied applied mathematics, computational engineering, and then I did my PhD in industrial engineering and post-doctoral work in management sciences. Now, in my work, I’m focused on civil and systems engineering, primarily in healthcare.

So I’ve had the opportunity to traverse different parts of the field, but the overarching theme of my career has been developing mathematical optimization models and algorithms for healthcare applications.

Since I joined Johns Hopkins University in 2019, I have done a lot of work pertaining to mathematical optimization modeling and data analytics in healthcare operations and medical decision-making. These applications aim to help with decision-making in areas such as vaccine distribution, patient routing, medical personnel and outpatient scheduling, and treatment planning.

G: When you talk about treatment planning, do you mean that doctors are actually using mathematical optimization to figure out the best courses of action to take to treat patients?

KG: Yes. For example, here’s the way it works with treatment planning for radiation therapy for cancer patients: This involves using external beams that come from outside and go through the body of a patient and kill cancerous cells. But you can’t just use one beam, because if you do, it will kill everything in its path and you will end up damaging a lot of healthy organs and tissues – which you don’t want to do. With mathematical optimization, we can figure out exactly how the beams should be spread, what the shape of each beam should be, how long each beam should be radiating from every direction – so that you kill all the cancerous cells and minimize the amount of radiation that hits the healthy surrounding tissue.

If you want to do this sort of treatment planning manually, it can take hours and requires a lot of back and forth between the oncologist and the radiation therapy planners who try to figure out where the beams should go. Or you can just run our mathematical optimization application (which uses the Gurobi Optimizer as its solver) and can generate an optimal treatment plan very rapidly for the given set of criteria.

Of course, there’s always supervision by a doctor who will review the radiation therapy plan generated by mathematical optimization application and confirm it (or change it, if necessary).

G: You mentioned a doctor scheduling application that you worked on. Can you tell us more about that?

KG: I was involved in work on a primary care doctor scheduling application for Massachusetts General Hospital when I was at MIT. The problem was that the medical assistants were feeling overworked and overwhelmed and the hospital was seeing high turnover – and they didn’t know exactly why.

We examined the situation and discovered that the cause of the high turnover was an imbalanced workload. Each medical assistant was working with a few doctors, and these doctors typically would all come in at certain popular times – and the medical assistants were really overwhelmed during those times.

We found that by making minor changes to the times that doctors worked (and they had a lot of commitments – so we had a lot of operational constraints), we could provide the medical assistants with a much more balanced workload.

So we developed a mathematical optimization application (using the Gurobi Optimizer) that could generate optimal schedules for the doctors, residents, and medical assistants, taking into account all the operational constraints including the doctors’ and medical assistants’ preferences as well as clinical considerations.

As a result of the implementation of this application at Massachusetts General Hospital, the workload was better balanced and we anecdotally observed that the amount of turnover among medical assistants dropped – and this made the doctors happier, because they didn’t have to constantly train new medical assistants and learn to work with them. It’s better for patients too to see familiar faces – who are not overwhelmed or overloaded – when they visit.

G: The COVID-19 pandemic has created numerous major healthcare challenges. Can you talk about these challenges and any projects that you have been involved in that use mathematical optimization and other advanced analytics tools to solve pandemic-related problems?

KG: One of the things that happened with COVID-19 is that an imbalance was created. This is partly because the virus is so discriminative. For example, it affects older individuals more, so if you reside in a nursing home, when one person gets it, virtually everybody gets it. Also, there are regions – perhaps with more frontline workers – where the virus spreads more.

Another reason for this imbalance is that there are disparities in access to healthcare, especially in the US, and these disparities have been highlighted by the virus. There are areas with dense populations and not a lot of healthcare capacity. Many of the hospitals in these areas are not well equipped and are constrained in their ICU capacity.

So, to make a long story short, there has been a lot of imbalance in the impact of COVID-19 in different locations – and we started to look at this problem in terms of resource allocation. Generally, the resources that hospitals need (for example, ICUs) are limited, and there has been high demand for these resources.

The question is: How can we better allocate resources to meet demand? It’s not easy to just send medical personnel or equipment like ventilators around to different hospitals. So, we decided that the best way to handle this problem is to redirect patients to different hospitals (with the same or better level of care) if the hospital they were supposed to go to is overwhelmed.

We’ve been working with Johns Hopkins Hospital since November and advising them on patient transfers and capacity management.  We use machine learning and statistical methods to forecast hospital occupancy and capacity and then we use mathematical optimization models (powered by the Gurobi Optimizer) to help the decision-makers in the hospital determine how many patients should go to which hospital, how many beds are needed at each location and for how long, and how the capacity can be managed. In this way, we enable hospital officials to make data-driven decisions and improve efficiency using descriptive, predictive, and prescriptive analytics tools.

G: Thinking about the COVID-19 situation, what do you see as the biggest healthcare challenges that we’re facing today that could and should be addressed with mathematical optimization?

KG: When the pandemic first hit last year, I looked at the problems that the healthcare industry was facing and I thought that mathematical optimization would be the perfect tool to solve many of these problems.

But in reality, a lot of people ended up using heuristics. This is, in part, due to politics, human behavior, complexity, and the tight timelines to build and deploy applications. But I think there’s been a huge missed opportunity – and that mathematical optimization applications could and should be used to tackle many COVID-19 challenges.

For example, many aspects of vaccine distribution could have been handled with mathematical optimization. Mathematical optimization could have told us how to distribute the vaccines and whom to prioritize.

Mathematical optimization could have also helped immensely with supply management, for instance, in PPEs. This is a persistent problem in healthcare and was a problem especially at the beginning of the pandemic when suddenly demand shot up and supplies went down.

Generally speaking, mathematical optimization is extremely effective with resource allocation, and – as healthcare and medical resources such as medical personnel or vaccine quantities are in high demand during the pandemic – mathematical optimization can help us make decisions on how to allocate these resources in the most effective way possible.

G: What do you think would be the additional benefit or value of using mathematical optimization to tackle these and other COVID-19 problems?

KG: A major issue with many data-driven technologies is that the solutions they deliver are not interpretable. You get a solution, but you don’t know why.

With mathematical optimization, you know what the solution is and you know why. Indeed, the interpretability and transparency of solutions is a big benefit of using mathematical optimization. It also allows you to incorporate domain knowledge in the model, for instance, known facts or expert insight about the solution.

Another benefit of using mathematical optimization is its adaptability. If you have a problem with a lot of constraints, priorities, and changing conditions, you can define all these in the optimization model, which is a part of your mathematical optimization application. Once you have all these elements defined in your model, it’s easy to adapt that model to different situations.

Of course, a significant benefit of using mathematical optimization is the guarantees that you get in convex frameworks. You know when you are actually at optimality, or you can determine how close or how far you are from optimality. You don’t have to wonder: Can I really trust this solution or is it garbage? With a heuristic solution, you never know. With machine learning, you can’t always define optimality. You can look at measures of optimality – like area under the curve and false positives – but it’s hard to precisely define and determine optimality with machine learning.

One final point is that mathematical optimization is a prescriptive analytics tool – it can tell you what to do, what decisions to make, and what actions to take. Machine learning – as a mostly predictive analytics tool – often gives you actionable insights, which is very different from decision recommendations.

G: Are mathematical optimization and machine learning complementary technologies?

KG: Absolutely, they are complementary tools. To me, machine learning is like a big knife but maybe a bit of a dull knife. While mathematical optimization is a smaller but sharper knife. There are certain problems where mathematical optimization works very well and can be used to surgically dissect the problem and find a solution. But you can’t use mathematical optimization for everything – it doesn’t apply to everything. But machine learning can apply to almost everything and has a much broader range.

G: Thinking about your career, what would you say is the goal of your research and work?

KG: My department at Johns Hopkins University is civil and systems engineering, and we focus on critical civilization problems that have profound relevance to our world – now and in the future.

We are using engineering and mathematics to solve civilization and societal problems like access to healthcare, resilience and security of our cities, energy infrastructure, and our future habitation in space. We try to solve these problems in a way that’s meaningful, practical, and impactful, while at the same time contributing to the theoretical and scientific research side of things.