People who survive a heart attack are at much higher risk of sudden cardiac death in the next 30 days, researchers have found.

The findings, which appeared in the Nov. 5 Journal of the American Medical Association, suggest that doctors need to closely supervise patients in the month after a heart attack, and that patients also need to be alert to signs of trouble.

“The first month after a heart attack can be envisioned as a period of healing with heart tissue remodeling, which conceptually is associated with a propensity to experience sudden death,” one of the authors, Dr. Véronique L. Roger of the Mayo Clinic in Rochester, Minn., said in an e-mail message.

The researchers, led by Dr. A. Selcuk Adabag of the Veterans Affairs Medical Center in Minneapolis, followed the health of almost 3,000 people who had a heart attack from 1979 to 2005.

In the first 30 days, they found, the rate of sudden cardiac death was 1.2 percent, about four times the risk that would have been expected in the general population, once age and sex were taken into account.

But the rate improved greatly over the following 11 months, dropping to a level lower than that usually seen in the general population.

In fact, over all, the study found big improvements in the rate of sudden cardiac death for heart attack patients in the past three decades. The decline, the researchers said, was more than 40 percent. They attributed that to improved treatment for people who have just had a heart attack.