Each year, more than half a million Americans run 26.2 miles down city streets in one of the country’s 1,100 marathons. The chafing and exhaustion induced by all those miles is well-known, but a new study suggests marathons can take a toll even on those who aren’t running in them.

A study published Thursday in the New England Journal of Medicine finds that the death rate from heart attacks rises 15 percent on the day of marathons, largely because of delays caused by road closures.

The authors, led by Harvard Medical School’s Anupam Jena, analyzed the death rate for Medicare patients hospitalized for cardiac arrest and heart attacks on marathon days in 11 cities, compared to non-marathon days. For example, they looked at the Monday of the Boston marathon, compared with the death rate for the five previous and five following Mondays. Then, they compared it to the death rate in a nearby city that wasn’t affected by marathon-related road closures.

It turns out that for every 100 people who have a heart attack or cardiac arrest, an additional four people die if they happen to have it on the day of the marathon.

It took about four minutes longer to reach the hospital by ambulance on marathon days. But the study authors suspect the real reason for the heightened mortality is the delays patients encountered when they tried to drive themselves to the hospital—as about a quarter of them opted to do. In those cases, it can take 30-to-40 minutes longer to reach the hospital on a day with marathon road closures, Jena estimates.

Jena acknowledged that we don’t know, for a fact, that those people died because it took them too long to reach the hospital, but that explanation seems most likely. Heart attacks are rather random, so there’s nothing special about the people who went to the hospital on the day of the marathon. Jena and his team also ruled out the idea that people might have gone to different hospitals, or were actually running in the race itself, or that hospitals were clogged with out-of-towners. None of those things explained the overall trend: If the roads are closed, chest pains are worse news than usual.

The findings likely apply to other events that cause road closures, like parades or big concerts. The answer, of course, is not to stop having those events. (“They bring a great deal of civic pride and joy,” Jena said.) Instead, he suggests, city planners could work to improve the re-routing of ambulances on days with major road closures. And they could put the word out: If there’s a marathon that day, don’t try to drive yourself to the hospital in an emergency. Just call an ambulance.