Stephanie Sorrentino developed a close relationship with her neonatologist following the birth of her son, Nicholas, who was born after only 25 weeks’ gestation. She came to count on Dr. Edith McCarthy’s attentiveness and compassion during her baby’s 4 1/2-month stay at the hospital. So when Dr. McCarthy founded her own pediatric practice, Ms. Sorrentino didn’t hesitate to choose her as Nicholas’s doctor.

“It’s very frustrating having a son with so many needs,” Ms. Sorrentino said. “I needed a doctor who would spend the time; I knew she would know what Nicholas would need as a preemie.”

Dr. McCarthy is one of a growing number of doctors who are opening practices focused on caring for babies born prior to 37 weeks of gestation throughout their childhood. With premature babies accounting for about 1% of all births in America, an increasing body of research shows that they can face long-term medical difficulties, including chronic lung disease, asthma, diabetes, and behavioral issues. Learning disabilities such as attention deficit hyperactivity disorder also are common in children born at a low birth weight.

“Some of what we’re doing here is uncharted territory,” Dr. McCarthy, who left New York University Langone Medical Center just over a year ago to found Care Intensive Pediatrics, said.

Dr. McCarthy’s practice specializes in providing in-house care to deal with all of the medical and developmental problems faced by preemie babies as they grow older. About a quarter of her patients also work with outside specialists and occupational therapists. “I think of myself sort of as the gatekeeper,” she said.

A handful of new studies have brought to the fore medical risks to preemies in infancy and later in life. According to a recent study from the Université Pierre et Marie Curie in Paris, nearly half of all babies born before 33 weeks’ gestation require specialized health service at age 5. Of those children who seek special care, 20% suffer from various behavioral problems. The study, which compared 1,817 children born between 22 and 32 gestational weeks to 667 full-term children, found that the very preterm children scored significantly lower on a measure of cognitive ability, the mental composite processing scale, according to a summary in New Scientist magazine.

“Disability occurs in 60% of survivors born at 26 weeks, and in 30% of those born at 31 weeks,” an assistant professor in obstetrics and gynecology at Duke University, Dr. Geeta Swamy, said in an introduction to her study of the long-term health effects of preterm birth. Dr. Swamy’s study, published in the March issue of the Journal of the American Medical Association, focused on 1.2 million single births in Norway, 5% of which were preterm.

For her part, Dr. McCarthy said she is working to protect her patients from these difficulties. With about 60 families in her practice — she is aiming to expand to 100 families — roughly 75% have former premature infants. Among the steps she is taking to provide emotional assistance is distributing her cell phone number to every patient.

“They’re pretty savvy parents because their kids have come close to dying in the hospital,” Dr. McCarthy said, adding, “Parents of premature babies are more protective of their kids.” As for handing out her cell phone number, “I like the immediate access they have to me,” she said.

The need for this kind of specialized care for preterm babies is important, said Dr. Karen Hendricks-Munoz, the chief of neonatology at NYU Langone Medical Center, who worked with Dr. McCarthy before she launched her own practice.

“The smaller you are, the greater the risk for neurological delay,” Dr. Hendricks-Munoz said. “Parents need extra support” that this kind of practice can provide, she added.

Not all doctors support Dr. McCarthy’s model, however. A neonatologist at Lenox Hill Hospital who founded its follow-up program for premature babies in 1989, Dr. Annamarie Greco, said a practice like Dr. McCarthy’s doesn’t necessarily provide the best solution.

Because some patients still use outside specialists and occupational therapy, “I don’t know if it’s taking care of the issue of fragmentation of care unless all care is truly in one place,” she said.

Dr. Greco’s program, run in conjunction with general pediatric care, assists families in their transition from the neonatal intensive care unit, helping them “navigate the system of specialty intervention.”

To Dr. McCarthy, however, follow-up programs are insufficient because they focus only on development. “It’s not comprehensive pediatric care,” she said, adding that many pediatricians are reluctant to work with these children “because they don’t have the time, the patience. It takes a lot of coordination.”

She added, “Certainly they’re a high-risk population, but that is why I want to do it.”