When you overhear a person five spots ahead of you at the coffee shop ordering a mocha light decaf no whip one pump, it might be enough to make you abandon your place in line and walk out of the store. But what if the context is different, and what’s at stake isn’t a handcrafted drink, but your health — or even life itself?

The factors influencing people who face this dilemma are analyzed in “Waiting Patiently: An Empirical Study of Queue Abandonment in an Emergency Department” by Christian Terwiesch, Wharton operations and information management professor, and University of Wisconsin-Madison professor Robert J. Batt, a recent Wharton doctoral graduate. Knowing what compels emergency room visitors to wait — or bail — is a key piece of information that has been missing from the equation, despite its critical consequences, says Terwiesch.

“That decision-making process is really an important aspect [of] any type of service, because when a customer leaves without service, you have lost revenue,” he notes. “But in the case of health care, this is really undesirable, because a patient who has left without being seen has revealed himself as being somewhat sick but is now going home because of poor service, and who knows what will happen at home? That chest pain might be more serious than a pulled muscle.”

The study grew out of Terwiesch’s professional interest and expertise in operations management, and a desire to give something back after having been a patient himself in emergency departments. The authors used detailed data from 180,000 patient visits to a big-city, major health system emergency department. Queue abandonment, also called reneging, is a poorly understood aspect of human behavior, the study notes. But what Terwiesch and Batt were able to show is that abandonment is not only influenced by wait time, but also by the length of the line and observable queue flows during the wait — in other words, the patient is making a spontaneous calculation of hope.

What’s particularly interesting about emergency rooms is the fact that patients’ decisions about their waiting time are based on observed circumstances, even though a lot of important evidence is missing or misleading. In an emergency department waiting area, available information is more complete than patients typically receive while on hold to a call center, but less complete than what is observable in a grocery store line.

For instance, emergency patients who bring themselves in (as opposed to those arriving by ambulance) are assigned a triage Emergency Severity Index [ESI] ranking from one (most severe) to five (least) that determines how quickly they are seen. A patient doesn’t know the other patients’ ESI levels, and typically doesn’t know his or her own. This makes it difficult to see a light at the end of the tunnel, or at least guess its distance accurately.

Assessing Human Stock and Flow

The study theorizes that patients observe and consider two factors: stock variables and flow variables. Stock variables are the number of patients in the waiting room, the number with a higher priority (since some more serious illnesses are obvious) and the number of patients with a later arrival time. Flow variables are the rate at which the queue is depleted, the rate of new arrivals and the number of patients served in the last hour ahead of earlier-arriving patients.

Using timestamp data from more than 150,000 patient visits, the authors were able to form four key conclusions. First, for patients of moderate severity, observing an additional patient in the queue increases the probability of abandonment by a half a percentage point. Second, the observed flow in and out of the waiting room has an effect on abandonment, with arrivals leading to increased abandonment, and departures leading to a decrease. Third, patients do make inferences about the condition of other patients (flawed though these assessments may be), with the observation of a more-sick additional arrival leading to an increase in abandonment by one percentage point, and the arrival of a less-sick one having no effect.

Finally, the study showed that early initiation of a task such as diagnostic testing reduces the probability of abandonment by 1.8 percentage points — even though administering a test has no effect on the overall wait time.

Terwiesch, who is also a senior fellow at Penn’s Leonard Davis Institute for Health Economics, says that although he expected patients would be sensitive to being “jumped” — i.e., experiencing an increase in the number of people in the line because another patient is served before them — the severity of the reaction was news to him. “I think we knew that patients weren’t entirely rational, but we were surprised by the dynamics of people coming in after you and being served ahead of you. That had a strong impact on people’s desires to stay or go. It influenced not just happiness, but how people made a decision that is potentially life-or-death by a little thing like someone coming in after them.”

As for passing on acquired wisdom to potential emergency room patients, Terwiesch has this to offer: “I think with this notion of looking at the number of people ahead of you and getting a sense of what speed the ED is moving, you can form a pretty good estimate of your wait time. That’s my operations management answer. My health care answer is, stay there … because until you get an answer, everything else is putting your life at risk.”

Even knowing your triage score does not necessarily support sound judgment. Patients with an urgent score are usually seen very quickly. But those who are less sick can be seen quickly, too, since sometimes hospitals operate a separate fast-track system staffed by nurse practitioners that functions apart from the rest of the emergency department. “The middle ones are the tricky ones. If they give you a three, those people need to wait long. So bring an iPad and download three good movies,” says Terwiesch.

The study takes no position on whether hospitals should divulge more information to patients. If a hospital believes that patients “cannot accurately assess their need for treatment, then the hospital may withhold information,” the researchers write. “The position of the American College of Emergency Physicians is that providing queue information might have ‘unintended consequences’ and lead to patients who need care leaving without treatment.”

For the particular hospital participating in this study, the desire is to minimize abandonment, fulfilling “a sense of duty to serve anyone seeking care,” according to the study. Soon, however, hospitals across the U.S. will have reason to be interested in this analysis. The Centers for Medicare & Medicaid Services is about to begin requiring hospitals to report emergency department performance measures such as median wait times, median lengths of stay and left-without-being-seen percentages. “Eventually, target values will be established and hospitals will be reimbursed based on their performance relative to the targets. Thus, hospitals will be looking to reduce abandonment at least to the target levels,” the study states.

Further, even though the study homed in on emergency department queues, many conclusions translate to other sectors, Terwiesch says. “Absolutely, [it is relevant] anywhere you have waiting going on that is visible, where one customer looks at the other customer trying to get a sense of the speed at which things are moving — supermarkets, retail banking, amusement parks, all of these places where our brain is trying to make sense of a complex waiting decision, whether we are happy or not, where understanding the environment and how people come to their decision is critical.”

Changing the System

The study, which has been submitted to the journal Management Science, promises to affect change in the real-life emergency waiting room setting. It has been presented to top management and clinicians at the hospital at which it was conducted (Terwiesch prefers not to publicly name the medical center yet). The next step is working with medical staff to determine a credible system for forecasting wait times. Once that has been established, solutions will be proposed, and — pending analysis by an independent review board — experiments will be tried. “We are going to go back to [the hospital], and we are going to change their process,” says Terwiesch.

Among the possibilities, he adds, are: “Making the waiting room more pleasant by taking the uncertainty out of it — this notion of sharing the forecast. [Another] thing you can do is go further upstream, and before patients get to the ED, have a billboard on the [expressway] saying the waiting time is 35 minutes. You can also articulate to patients the rewards of waiting. If you can help them appreciate the benefits of staying as opposed to the cost of leaving, you could really move the needle, because there are patients you really don’t want to leave.”

The study even raises the possibility — although it in no way endorses the idea — of a placebo test. Patients who begin receiving medical attention (even if the outcome is, unbeknownst to them, irrelevant to their care) feel more invested in the experience and are less likely to bail. “There is a sense that now I can’t leave anymore, a commitment from the patient to stay in the process,” he says.

Whatever the method, the goal is the same: to make the waiting patient more patient. This leads to greatly reducing the chances of a seriously ill person leaving untreated and suffering even more serious consequences after getting home.

“You can imagine a buzzer kind of system like the one at restaurants where you are told that it’s about an hour wait, and when it buzzes, come back and we will serve you. That is a way of easing the waiting time — you know, [for example, that you could] go have a coffee at Starbucks — and it will be more pleasant.”