New research led by doctors from the University of North Carolina and the Institute of Cancer Research in London shows women who have babies may have a greater risk for breast cancer than women without children.

The study found that risk for breast cancer goes up for 24 years after a woman's last child, peaking at five years after childbirth. The risk starts to fall after 24 years and is at its lowest 35 years out.

Researchers looked at data from nearly 890,000 women of different ages and found the risk continues for more than two decades after childbirth. Dr. David Agus, the director of USC Norris Westside Cancer Center, told "CBS This Morning" the study should change how doctors screen for breast cancer.

"If your last child was at age 35, we may start screening at age 40 instead of classically at age 50 because the risks may go up after five years out. And so it's very important now that doctors ask this question and put the into the history of the patient," Agus said.

Though the results of the study might sound scary, Agus pointed out that because breast cancer is more common later on in life – 50s, 60s and 70s – the decreased risk 30 or more years after childbirth is a good sign.

"So most breast cancer happens 30-plus years out. So if you look cumulatively, it decreases the risk because breast cancer's relatively rare in young women. But this does change our screening criteria and now we're going to ask when was your last child when we determine your risk to determine if you should be screened or not," Agus said.

"I want them [patients] to talk to their doctor and say, listen, I had my last child at an older age so maybe I should be screened earlier because my risk is going to be highest five years out from that point. So the discussion with the doctor is critical to bring in this information."