When too many patients arrive at a hospital’s emergency department in too short a time, that can mean bad news for the later-arriving patients. To stave off any potential problems, the administrator can ask the local emergency medical services to divert incoming ambulances to less-crowded hospitals nearby until things ease up. In theory, an effective diversion program should reduce overcrowding and delays in local clusters of hospitals. But experience has shown that the process does not always work. Rather than improving healthcare delivery, hospital executives complain, diversion often impairs it.

A study by Itai Gurvich, assistant professor of managerial economics and decision sciences at the Kellogg School of Management, and Sarang Deo, an assistant professor at the Indian School of Business, provides one explanation for the failures. The study also suggests one possible way to overcome the problem. “Ambulance diversion can be beneficial but its benefits can be compromised by the lack of coordination or regulation,” Gurvich says. “But partial, non-intrusive regulation is possible that would recover much of the lost benefit.”

Many hospital administrators have already given up on ambulance diversion, with no apparent ill effects. “Numerous papers in the emergency medicine literature indicate that waiting times don’t go up when diversion is banned,” Gurvich points out. “This culminated in a complete—and permanent—ban on ambulance diversions in Massachusetts in January 2009. Other states are going in that direction. And when experiments stopped diversion for three weeks in certain counties elsewhere, patients’ waiting times didn’t increase.”

Continual State of Flux 

Analyzing diversion decisions is complicated for several reasons. First, any emergency department operates in a continual state of flux. Its fixed numbers of beds and medical staff must serve a fluctuating number of patients brought in from different distances and suffering from conditions of varying severities. And the ability to move patients who need further on-site care out of the emergency department can be compromised by the temporary lack of beds in the hospital’s regular wards. Just as important, there are no standard rules to determine when administrators should call for ambulance diversion. Each individual shift leader in each emergency department makes her or his own decision, based on a database that shows the state of neighboring hospitals’ emergency departments. Financial considerations also play a role; hospitals don’t want to turn away patients without good reason. And of course, any diversion decision can affect more than one other hospital.

“Even with two hospitals, the underlying dynamics of the ambulance and patient flows are very complicated,” Gurvich says. “It is very hard to characterize precisely and explicitly the effect of a given diversion decision on, say, patients’ waiting times. As a result, it is very hard to identify the best or optimal diversion decisions.”

A Non-cooperative Game 

Given that complexity, Gurvich and Dao used a combination of queuing theory and so-called “static non-cooperative games” in their analysis. “This is the simplest form of a game, where each player—in our case each emergency department—makes a decision—in our case a crowding threshold for diversion—and implements this decision,” Gurvich explains. “Each player has its own objective function. It is non-cooperative in the sense that the players do not agree in advance or try to coordinate their decisions. Rather, each makes his own decisions while taking into account possible reactions of the other players.”

“If one could fully coordinate ambulance transports one could use diversion effectively to spread demand in a network of emergency departments so as not to have one department with excess capacity at the same time that another one nearby experiences long waiting times.” — Itai Gurvich

Application of the game to just two hospitals revealed what Gurvich and Deo call “the existence of a defensive equilibrium in which both EDs (emergency departments) choose a threshold of zero, ambulances are not diverted at all and consequently, the potential benefits of pooling are not realized.” In this situation, one emergency department declares a diversion to avoid being swamped by ambulances diverted from the other department, a sort of defensive posture. “Hospital A might think that, because hospital B is overusing diversion, too many ambulances that were supposed to go to B will go to A,” Gurvich says. “To protect against such surge in demand, hospital A might also declare diversion. By being preemptive in this way, emergency departments might be overusing diversion.”

One explanation for the emergence of defensive equilibrium and the resulting ineffectiveness of ambulance diversion is the lack of coordination among neighboring hospitals. “If one could fully coordinate ambulance transports,” Gurvich explains, “one could use diversion effectively to spread demand in a network of emergency departments so as not to have one department with excess capacity at the same time that another one nearby experiences long waiting times.”

A Simpler Policy 

That solution, of course, would mean the appointment of an administrator to oversee a group of neighboring hospitals and emergency medical services. But the game devised by Gurvich and Deo suggests a simple coordination mechanism that does not require significant outside intervention and yet serves to prevent the emergence of defensive equilibrium. The suggested policy allows emergency departments to declare diversion only when they have no available beds. “We don’t want them to overreact,” Gurvich states. “They should go on diversion only when they’re really crowded.”

The two researchers expand on that solution in their paper. “When there are available beds in one ED simultaneously with queued patients at the other, this policy routes all the ‘routable’ patients to the ED with available beds and thus recovers most of the pooling benefits. In addition to its being easier to implement than the true social optimum… it reduces the expected waiting times of both EDs.”

“Ambulance diversion, if done in a coordinated manner across emergency departments, has a potential value of reducing waiting time,” Gurvich says. “In the absence of coordination, the non-cooperative equilibrium might be such that all potential benefit is lost. And the policymaker can obtain much of the benefit with simple coordination mechanisms like no bed reservation—that is, not allowing ambulances to be diverted from emergency departments that have unused beds.”

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