An equation for early postdischarge visits

Queuing theory helped one hospital fit heart failure patients into a clinic soon after discharge.


In 2015, clinicians at Northwestern were having trouble getting their heart failure patients seen within a week of discharge, and they knew they weren't alone. “Both the American College of Cardiology and the American Heart Association promulgate seven-day discharge clinic visits as a best practice for care of hospitalized heart failure patients, but we know that national rates of arrival to a seven-day discharge clinic are really dismal,” said R. Kannan Mutharasan, MD, an assistant professor of cardiology at Northwestern.

Knowing that postdischarge visits can reduce readmission risk and that their hospital was participating in a payment model that rewards avoiding admissions (CMS's Bundled Payments for Care Initiative), Dr. Mutharasan and medical colleagues partnered with their school of management to develop a solution based on queuing theory.

How it works

“Queuing theory is the study of waiting times,” said Dr. Mutharasan. “Let's just say on a given day, you have five clinic slots and on an average day, you discharge four people from the hospital, but then, one day you discharge 10 people from the hospital. You only have one extra slot to burn off that extra demand, so it takes about a week or two to catch up to that. Until you do that, no one is getting in within seven days.”

The Northwestern team used queuing theory calculations to determine how many appointments would be needed to accommodate the hospital's usual volume of departing heart failure patients within a week or two of discharge. “There was already money set aside for a nurse practitioner [full-time equivalent] to help take care of heart failure patients both on the inpatient and outpatient sides,” noted Dr. Mutharasan. Using this extra clinician time, they added another 15 visits per week to the existing 32.


Before the intervention, 23% of heart failure patients had a visit scheduled within a week after discharge and 43% had a visit within two weeks. After a month on the new schedule, 53% were seen in a week and 93% were seen in two weeks. Clinic utilization dropped from 97% to 84%, according to results published by Circulation: Cardiovascular Quality and Outcomes in July.

“Traditionally, clinic metrics are driven by things like utilization rate and how full schedules are. . . . The financial incentive is to make sure that there aren't any empty slots and make sure that all the capacity that is available is utilized so that you minimize the overhead,” said Dr. Mutharasan. “When you're thinking about intentionally designing a discharge clinic, the thing that you have to be willing to do is to leave empty slots to allow for the variability.”


The project leaders would have liked to see even higher percentages of patients visiting the clinic soon after discharge, but obstacles included some patients declining early clinic appointments and others moving outside the health system for outpatient care.

In addition, it took time to get the word out to hospital staff that appointments were available. “Even though we're always very interested in trying to get heart failure patients in within seven days, discharging teams, knowing that seven days was all but impossible to obtain, would sort of instruct patients [otherwise],” he said.

How others benefit

For any postdischarge clinics interested in following this example, the Northwestern team has shared their calculator online. “Anyone can go in and plug in their numbers for their average demand and their goal ability to schedule patients in clinic and come up with their own model,” said Dr. Mutharasan. “I think it's generalizable to any situation where you have a variable discharge demand for a condition, like heart failure, [chronic obstructive pulmonary disease], maybe uncontrolled hypertension, maybe [chronic kidney disease].”

Next steps

In addition to continuing to work on increasing post-discharge visits, the researchers plan to analyze the financial impact of the extra slots. “That money we believe comes back to the health care system if we prevent readmissions, which are very expensive. Tying everything together in a financial model is very interesting to us,” said Dr. Mutharasan.

There's also the question of whether the goal for seeing patients after discharge should be moved even earlier. “Even though within seven days is what the national societies recommend, the peak day that patients readmit after a heart failure hospitalization is actually day three,” he said. “A two- or three-day discharge appointment might be ideal.”