In a study published in the New England Journal of Medicine, the researchers looked at the records of more than 407,000 children from every state and found that younger children in the same grouping of students had a 30 percent higher risk for an ADHD diagnosis than older students.

It said this variation may be explained by experts labeling children as having attention-deficit/hyperactivity disorder when they are simply displaying behavior consistent with their age.

“Our findings suggest the possibility that large numbers of kids are being overdiagnosed and overtreated for ADHD because they happen to be relatively immature compared to their older classmates in the early years of elementary school,” said Timothy Layton, the study’s lead author and an assistant professor of health-care policy at the Blavatnik Institute at Harvard Medical School.

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ADHD is a brain-based medical disorder that affects the behavior of people across age, gender, intelligence and socioeconomic lines. Children with ADHD may daydream a lot, talk too much, fidget, frequently forget and lose things, act impulsively, display risk-taking behavior and have trouble making transitions.

According to the Centers for Disease Control and Prevention, “the percent of children estimated to have ADHD has changed over time and its measurement can vary.” The American Psychiatric Association stated in its 2013 Diagnostic and Statistical Manual of Mental Disorders that 5 percent of children have ADHD, but other studies have found higher rates in community samples. It is also believed that while ADHD may be overdiagnosed in some populations, it is underdiagnosed in others.

The authors of the new paper, titled “Attention Deficit-Hyperactivity Disorder and Month of School Enrollment,” reached their conclusions after analyzing records from a large insurance database.

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The Harvard researchers knew that most states have arbitrary age cutoffs for entry into public school, usually Sept. 1, and as a result, one child can start school at the same time as another who is nearly a year older. A child who was born in August could begin school and be in a class with children up to a year older because their birthdays are in September. That means the September-born child had a lot more time to develop socially.

“As children grow older, small differences in age equalize and dissipate over time, but behaviorally speaking, the difference between a 6-year-old and a 7-year-old could be quite pronounced,” study senior author Anupam Jena, an associate professor of health-care policy at Harvard Medical School, said in a statement. “A normal behavior may appear anomalous relative to the child’s peer group.”

The researchers compared the rate of ADHD diagnosis among children born in August with that among children born in September between 2007 and 2009 (and followed until the end of 2015). They also compared the rate in states requiring children to be 5 years old by Sept. 1 for enrollment in kindergarten and states without that requirement.

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They found that in states with a Sept. 1 enrollment cutoff, August-born children had a 30 percent greater chance of an ADHD diagnosis than September-born children. No such differences were observed between children born in August and September in states with cutoff dates other than Sept. 1 for school enrollment, the report says.