If you beat cancer when you were a kid, you’re not out of the danger zone yet. Childhood cancer survivors older than 40 have a higher risk of developing new cancers, according to a new study published in this week’s Journal of the American Medical Association.

The study looked at nearly 18,000 British children diagnosed with cancer before the age of 15 and followed them for an average of 25 years. Survivors’ risk of getting new cancers was 4 times that of people in the general public with similar age, sex, and other characteristics, but who didn’t have cancer as children.

Doctors have long known that people who had cancer as kids are more likely to get deadly new cancers as adults. but there hadn’t been much research about risks in this group past the age of 40, when everyone’s risk of cancer starts to creep up, says study leader Raoul C. Reulen, Ph.D., of the University of Birmingham in the United Kingdom.

Beyond age 40, the most common new cancers for childhood survivors occurred in the digestive tract or reproductive and urinary systems. Treatment for the original cancer, such as radiation to the pelvis, along with unlucky genetics, could be to blame, the researchers suggest. (Related from MensHealth.com: 8 Ways to Beat Any Type of Cancer.)

Reulen notes that most survivors’ risk of getting a new cancer is still fairly low—86 percent hadn’t developed any new cancers by age 60.

What should you do if you had cancer as a kid? Here’s Reulen’s recommendation: If you received high-dose radiation or had childhood cancers with a genetic component (such a retinoblastoma, a cancer that affects the eye), work with your doctor to keep a closer watch for new cancers. Extra screening could be the key to catching new cancers early—and saving your life. Learn how to recognize the signs of these 6 Cancers that Strike Men.

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