Valuable addition

Mathematical models to improve how hospitals are run

Illustration of a female doctor with a patient, by Harry Campbell

In 2016, Angie Kopetsky was in charge of assessing whether the pediatric outpatient cancer treatment unit at Lucile Packard Children’s Hospital Stanford could take on more patients from elsewhere in the hospital.

She had reviewed historical data showing that the unit, where patients come by appointment for hours-long chemotherapy infusions, was using only 40% of its capacity. But it was also true that activity in the infusion center was very dynamic, with some treatments running longer than scheduled, others shorter, some needing to be canceled for various reasons and others needing to be added at the last minute.

“We knew we couldn’t hit 100% utilization there,” said Kopetsky, executive administrative director of the Bass Center for Childhood Cancer and Blood Diseases at the children’s hospital. “But we wanted to find the sweet spot we should be hitting.”

For help, Kopetsky turned to mathematicians from Stanford’s Management Science and Engineering Department, including graduate student Allison Esho. Esho and her team created computer simulations to identify ways to increase use of the center’s capacity. Based on the simulations, it seemed clear that the center could take on more patients — specifically those who received other types of infusions in beds elsewhere in the hospital — and that doing so would open up those beds for patients recovering from surgery.

But the center’s staff resisted. Patient care manager Merian van Eijk remembers thinking, “We’re full! How can we do this?” Van Eijk, a nurse, had been on the 10-bed unit for 12 years and, at first, the analyses and simulations by Esho didn’t convince her that the center could handle more patients. So van Eijk set about collecting her own data — only to discover that the analyses were right.

“My perception was that we were always busy, but the reality was that it was in a very inefficient way,” she said. “I thought, ‘OK, we’re going to do this, because we need to take care of these patients.’”

Van Eijk said the mathematicians’ work gave her powerful insight and has since proven itself.

Since when do hospitals use advanced mathematical approaches to reorganize internal operations? Most do not. But in 2015 Packard Children’s hired David Scheinker, who has a PhD in mathematics, to apply mathematical, statistical and computational tools to optimize the experience of those who receive care at the hospital and of those who work there. Scheinker, director of systems design and collaborative research for Packard Children’s, and a clinical associate professor of pediatrics, directs Systems Utilization Research For Stanford Medicine, known as SURF. Esho was one of his students and received her PhD in 2018.

Originally focused on the children’s hospital, but now Stanford Health Care as well, Scheinker works closely with various hospital staff, like Kopetsky, who have identified areas where his expertise may be helpful. He then supervises SURF master’s and doctoral students as they use advanced mathematical and computational approaches to chip away at operational problems, fine-tuning staffing levels and improving scheduling efficiency, as well as addressing the challenge of serving more patients without compromising the quality of care.

SURF typically has five to 15 projects going at any one time. In addition to helping the Bass Center adapt to handling more patients, several of the team’s projects have made it possible for families to schedule heart surgeries at Packard Children’s sooner; others have helped ensure appropriate staffing levels for the hospital’s recent expansion and will do the same for the new Stanford Hospital, opening later this year.

“My perception was that we were always busy, but the reality was that it was in a very inefficient way. I thought, ‘OK, we’re going to do this, because we need to take care of these patients.’”

Another project will make better use of data to identify the sickest diabetes patients and provide them with the additional attention they need. Still another will help families understand what to expect during a stay at the children’s hospital.

Essentially, SURF is trying to do for health care what Amazon did for shopping, Kayak did for travel planning and Uber did for getting from point A to point B, Scheinker said. These companies didn’t invent anything. “All they did was design better ways of organizing supply and demand to provide a high-quality experience for consumers and providers,” he said.

Bringing a mathematician on board was “a bit of an experiment,” said Kristin Petersen, vice president of operations, procedures and diagnostic services for Packard Children’s and executive sponsor and director of strategy for SURF.

So far, she said, the experiment has worked: SURF has successfully completed multiple projects at Packard Children’s. Now, at the request of the hospital’s CEO, Paul King, Petersen is working with the SURF team to create a detailed mathematical simulation of ideal patient flow through the hospital. The simulation will help develop a long-term strategy for more efficiently providing high-quality, predictable care for as many patients as possible. “It’s a new, big project,” she said, “and it’s a first for any hospital.”

By building a rich, detailed simulation model of the hospital, Scheinker hopes his team will identify compelling opportunities to redesign care delivery. For significant change to happen, he said, “you need very, very convincing evidence of the benefit to the institution, patients, and doctors and nurses.”

Change is hard

At the Bass Center, even though van Eijk saw the value of the SURF team’s data analysis, others were resistant. The patients whose care would shift to the Bass Center were children and teens who came frequently for infusions, van Eijk said. That would include kids with Crohn’s disease or other rheumatological diseases who required regular one-hour infusions of infliximab to tamp down inflammation, kids with organ transplants who frequently need six-hour immune suppressant infusions, and immunology patients who will need monthly infusions of medication for the rest of their lives.

For years, these patients had received their treatments at the hospital’s short stay unit — a space that was in high demand for other uses, including surgical recovery. Although getting infusion appointments in the short stay space was increasingly challenging, these patients had established relationships with nurses there. They weren’t happy about having to adapt to a new location with unfamiliar staff.

Employees weren’t happy either. The unit’s nurses would miss their patients, and the nurses at the Bass Center would have to learn procedures for treating patients with other categories of illness.

“It was a big deal for us,” said Jill Becchetti, RN, a nurse who had worked at the Bass Center for 15 years. Oncology nurses are highly trained, with national certifications in oncology and bone marrow transplant, she said. “I felt like an expert, and then when those patients came over, I felt like I went back to being a beginner.” It also took a while for the oncology nurses to build connections with the doctors in the other specialties such as gastroenterology, rheumatology and endocrinology, she said.

But the benefits of increasing use of the Bass Center were clear as well. Sending infusion patients there would make more short stay beds available for surgical recovery, allowing the hospital to schedule more operations for more sick kids. In addition, moving patients to the Bass Center would decrease the challenges of scheduling infusion patients around surgical patients’ needs. As things were, van Eijk said, “People were struggling to get their medications.”

It’s all about providing more access to care, Petersen said. “By improving the efficiency of our operations, we can actually get more patients in. There are fewer barriers, and wait times go down.”

“By improving the efficiency of our operations, we can actually get more patients in. There are fewer barriers, and wait times go down.”

In preparation for the influx of new patients, Scheinker and Esho worked closely with the Bass Center team. “I did a lot of shadowing and interviewing of folks to understand their process,” Esho said. Although the unit was open from 7 a.m. to 7 p.m. Mondays through Fridays, she found that relatively few beds were used before 11 a.m. and after 4 p.m. That’s because patients dictated their arrival times, with many of them wanting to come at the same time, Esho said.

With guidance from Kopetsky and other hospital staff, Scheinker and Esho designed simulations to test various alternative scheduling plans as well as options for increasing the clinic’s hours of operation, including adding Saturday hours. The simulations accounted for such constraints as the duration and frequency of infusion appointments, whether the patient’s doctor needed to be on hand, and whether the patient needed lab tests before treatment.

Esho was looking for approaches that were both effective and relatively easy to implement using a clear set of rules.

The simulations helped Scheinker and Esho get buy-in from the Bass Center staff. They showed that adding Saturday hours would spread the burden of adding more patients, and they demonstrated that schedulers could arrange appointments more tightly by filling one room at a time while consistently striving to leave open the largest possible blocks of time rather than carving the day into short, potentially unusable segments.

Using a flow chart Esho provided, Bass Center schedulers encouraged patients to opt for the early and late time slots. For example, because morning hours weren’t as busy as other parts of the day, patients were less likely to have to wait for a bed. Afternoon slots prevented kids from having to miss school, van Eijk said.

“The schedulers are fantastic puzzlers who make it as efficient as possible,” van Eijk said. As a result, the Bass Center is now able to accommodate most of the patients who had traditionally received infusions in the short stay unit. Saturday hours result in fewer parents having to take time off work for their children’s routine infusions. And, the center is now using 64% of its bed space, with fewer spikes in population in the middle of the day and a better ability to accommodate same-day add-ons of patients with urgent needs.

“The schedulers are fantastic puzzlers who make it as efficient as possible.” 

To ensure a smooth transition out of the short stay unit, van Eijk reached out to affected patients and families: “I spoke with every individual family to make it work for them,” she said. And she held in-service trainings to bring her own staff up to speed.

At first, Becchetti said, the families from the short stay unit questioned whether the oncology nurses knew what they were doing. But now, she said, “I think we have won over all of our families. They know that our nurses are just as competent, friendly and skilled as the short stay nurses.”

A teenage boy with Crohn’s disease who had often missed school for appointments was nervous the first time he came to the Bass Center because he didn’t know the nurses, van Eijk recalled. But by his second infusion at the center, he seemed happy with the new location.

“He didn’t have to miss school and he liked the nurses,” she said. “The patients moved over and embraced our unit as much as our nurses embraced them.”

A more predictable day

Surgical scheduling also went under SURF’s microscope. In the past, surgeons at Packard Children’s from any of nine different specialties could pick available date and time slots that most appealed to them and their patients (within windows designated for their specialties), estimate how long the surgery would take, then block it out on the schedule.

Day to day under this system, Scheinker said, “the numbers of planned surgical admissions jump around like crazy.”

During the morning, there might be more staffers than were needed relative to the number of patients, while at midday all of the beds could be occupied at the same time, causing nurses to be stressed. For many reasons, variability could also lead to delays in surgical appointments — essential equipment might be in use in another operating room, post-anesthesia recovery or acute care beds might be full, or urgent cases might bump other patients from the calendar.

“SURF’s work helps us have a more predictable day. There’s this balance we’re trying to achieve, and we can’t do it without the math. Nearly every modern organization does it, but not health care.”

Unlike a manual scheduling system, Scheinker said, the tools he uses, such as machine learning and mathematical optimization, can take variability and uncertainty into account — and plan for it. For example, Scheinker and his team have used machine learning to better predict the time it takes to perform various types of surgery, information now used by schedulers.

In addition, to help guide surgery scheduling and reduce bottlenecks, they created a mathematical model of patient flow through the post-anesthesia care unit, developed a system to ensure that operating rooms were stocked with the correct surgical supplies, and created an electronic system for dealing with cancellations. The new system makes sure operating room slots are filled and equitably selects which surgeries to bump when cancellations are unavoidable.

“SURF’s work helps us have a more predictable day,” said Petersen. “There’s this balance we’re trying to achieve, and we can’t do it without the math. Nearly every modern organization does it, but not health care.”

Data from wearables

Having a mathematician on the team also offers an opportunity to make greater use of data collected from patients’ health-related wearable devices. For example, to stabilize glucose values for Type 1 diabetes patients, parents can capture real-time data from continuous glucose monitors — devices a little bit smaller than an Oreo cookie with a sensor that reads a patient’s glucose level every five minutes. However, only 30% to 35% of Type 1 diabetes patients use the monitors. And for those who do use them, “the data aren’t being leveraged for the best possible care,” Scheinker said.

David Maahs, MD, PhD, professor of pediatric endocrinology at Stanford, hopes that will change with help from SURF. Packard Children’s recently launched a program to start children on the devices in the first week after a diabetes diagnosis. Glucose readings are beamed to cloud storage and then down to a parent’s phone, so he or she can respond to give a child more insulin (if the level is too high) or a snack (if it is too low).

“The monitors improve safety and provide the ability for patients and families to achieve tighter glucose control, which is important for long-term health,” Maahs said.

But in patients’ quarterly visits to the clinic, the data — more than 25,000 readings over the previous 90 days — gets short shrift. “It would be very time-consuming to look at all of the data for all of the patients,” Maahs said. So Scheinker’s team is devising a way to analyze the data and identify patients who need attention from the health care team.

Scheinker’s team has analyzed 2 million hours of glucose data for about 200 patients. Once they can identify which signals merit an alert to a health professional, the hospital can design a new workflow to take advantage of that information as it comes in from patients.

Scheinker envisions a tool that would notify caregivers of, say, the 10 patients most in need of a call on any given week.

“If you have an algorithm trained to recognize: ‘Hey, your patient Jane, who’s done really well before, it looks like her breakfast and dinnertime glucose is really elevated,’ then maybe it’s as easy as the care team making a quick call to chat with the patient,” Scheinker said.

The value of math

Operational change is certainly possible without the help of machine learning and computer simulations, but the math allows better, faster access to information that can enable change. Case in point: Before Scheinker came to Stanford, Andrew Shin, MD, clinical associate professor of pediatric cardiology and now medical director for SURF, used a manual, data-driven approach to determine reasonable goals for such things as the number of days a patient will spend in the intensive care unit and the hospital.

The goals were developed for congenital heart disease surgeries at Packard Children’s and are now taped to patients’ beds. In addition to ensuring transparent communication with families, the project reduced the average length of patient hospital stays — a remarkable success achieved without advanced mathematical modeling.

But because of the labor involved, the approach has been slow to roll out to other surgical procedures. To speed up that process, SURF has developed an automated tool that, in a proof of its worth, successfully and instantaneously reproduced virtually the same goals for six procedures, each of which took Shin’s team four months to identify. Using this tool, the hospital can now more quickly develop goals for other surgical procedures.

Despite SURF’s many successes, Scheinker is under no illusion that change will be easy.

“Health care is notorious for how long it takes to adopt new things, especially if they require people to change their workflows,” he said. Yet current electronic health records make possible the redesigns and improvements that other industries have shown can lead to transparency, efficiency, fewer errors, fewer delays and overall higher quality, Scheinker said.

“That’s the reason a mathematician was hired to do this.”

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Katharine Miller

Katharine Miller is a freelance writer.

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