Driving down many U.S. interstates, you’ve undoubtedly seen a new kind of digital sign advertising local hospitals. “Current wait 5 minutes,” they say, with the wait time updating in real time to reflect the current conditions in the emergency room.
It’s an effective form of advertising, and it gives consumers a sense of transparency about making the choice to go to the ER. Yet if you suddenly start having abdominal pains and head to that nearest ER, don’t be surprised if you end up waiting longer than the sign says. The truth behind these numbers is that they’re often wrong, according to researchers at Stanford who have developed a novel way to improve them.
These results were published in a study in the Manufacturing & Service Operations Management journal by Stanford Graduate School of Business professors Mohsen Bayati and Erica L. Plambeck, along with graduate students Sara Kwasnick and Erjie Ang, and Michael Aratow of the San Mateo Medical Center. Their study looked at the emergency departments of four hospitals – three of which declined to be named and one of which was the San Mateo Medical Center in San Mateo, California – and tested the effectiveness of four methods for estimating wait times using their actual patient data. The most commonly used method proved extremely unreliable in all cases. At SMMC, for example, it was off by as much as an hour and a half for much of the time.
“It turns out that it’s hard to tell people exactly what the wait time will be, because by the time they arrive, things will have changed,” says Bayati, an associate professor of operations, information and technology. “At the same time, there is a lot of uncertainty about how the number is being generated. All of the hospitals do it differently. Our objective was to find a method that is more accurate but is not very complex so all hospitals could adopt it.”
The team’s search for one method to rule them all yielded a new approach they're calling “Q-Lasso.” Drawing on advanced mathematical concepts and an insight from a field of science that started by examining telephone networks in the early 1900s, Q-Lasso was able to cut the margin of error by as much as 33%.
Hurry Up and Wait
The trouble with most wait time estimates, Bayati says, is that the models these systems use are often oversimplified compared to the complicated reality on the ground. One of the most common ways of arriving at a wait time estimate is to simply give a rolling average of the time it took for the last few patients to be seen.
This works well if every patient is the same, they arrive at a steady rate, and all of their ailments take the same amount of time to diagnose and remedy. But that’s rarely the case in the real world — patients come in with a range of different conditions that affect the order they’re seen in, and the rate at which they’re moved through the system is affected by various factors from the number of staff on duty to that staff’s skill level.
Such simple systems also fail at accounting for sudden spikes in demand, even when those spikes are predictable; ERs see an influx of car accident victims, for example, during major commute times.
What’s worse, many of these models assume the wait times for all patients are equal, whether they’re having a heart attack or complaining about an upset stomach. Since critically endangered patients are usually seen instantly, this skews the predicted wait times significantly.
A Better Approach
The researchers realized that no one factor was going to be enough to accurately predict a wait time. They decided to look at a full range of factors, and then use a mathematical model called lasso to determine which were the most predictive at a given time.
This explains the lasso in Q-Lasso. The “Q” comes from queuing theory, a branch of science that seeks to explain how people and things move through lines, and which told the researchers what factors to include in the model. Queuing theory is a well-understood field that started in the early 20th century with efficiency studies on phone lines. Theories from the discipline now find a much wider use, however, addressing problems as diverse as architecting computer networks to dealing with traffic jams efficiently. Drawing from queuing theory, the research team was able to come up with a large number of potential factors to look at, from the obvious to the not so obvious. Lasso would then select the best of them from the data.
For example, the researchers had initially assumed that the number of nurses who were working would be an important criterion for assessing wait time. But the data showed this was mostly irrelevant. The group reasoned that this was because hospitals actually understand when their busy times are and schedule staff accordingly. This means the effect of staffing was already captured more elegantly by other metrics, like what hour of the day it is.
It’s important not to oversell Q-Lasso. The researchers note that even though it proved significantly better than any of the common methods for predicting wait times, it still often missed the mark significantly. In the test hospitals, Q-Lasso was still off between 17 minutes and an hour.
But it does have one crucial advantage: When it’s wrong, it tends to overestimate wait times, rather than underestimate them. This is significant, because these estimates are often used as a form of marketing, and thus the way that patients react to them is almost as important as their accuracy. Waiting for less time than you were expecting is almost always a positive experience.
And a better experience can benefit more than just the hospital’s bottom line, Bayati says.
“If a patient is very satisfied with the service, they’re much more likely to follow the care advice that they receive,” he says. “A good prediction that provides better patient satisfaction benefits everyone.”
It isn’t hard to see how the Q-Lasso technique could be applied to other complicated prediction scenarios, either. It’s a good fit for any complex system with a lot of variability in both the people or things that need to be addressed as well as the providers available to address them. A couple of examples the team gave are passenger boarding and deboarding on airlines, and complicated manufacturing processes.
“We live in a world where people can expect wait time estimates to be very accurate. That’s because for the most part, they work. It’s not hard to predict simple things such as how long it will take for your Uber ride to show up. And in some ways that makes it worse for people when it doesn’t work in a more complicated situation,” says PhD student Kwasnick.
“We think this could help close the gap, to where people’s expectations are more in line with reality in more complicated situations.”