Less than half of children under age 2 years are fully vaccinated against influenza despite a dramatic surge in immunization rates over the past decade, a U.S. study finds.

Among infants aged 6 to 23 months, 45 percent were fully vaccinated in the 2011-2012 flu season. While that far exceeds the 5 percent vaccination rate in the 2002-2003 season, it still leaves many infants and toddlers exposed to a virus that can lead to hospitalizations, pneumonia and even death.

"We are half way there, but that's not good enough," said Dr. Kathryn Edwards, a pediatric vaccine researcher at Vanderbilt University in Nashville, Tennesee, who wasn't involved in the study.

"We know that children less than two years of age have the most influenza infections and have the most complications from influenza infection in any age group, and we have to do a better job of following up with parents to get all of these children vaccinated," Edwards added.

The study by Tammy Santibanez of the U.S. Centers for Disease Control and Prevention in Atlanta and colleagues examined survey data on vaccination rates over 10 flu seasons to see how many children got fully immunized and assess variations based on race and the number of required doses.

Full vaccination coverage in the last year of the study varied by state, ranging from a low of about 24 percent in Mississippi to a high of about 72 percent in Massachusetts, the researchers report in the journal Pediatrics.

For full protection, U.S. children need two doses of vaccine during the first season they receive shots. After that, one dose will suffice in subsequent flu seasons.

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For each year of the study, complete vaccination rates were significantly higher for the children who only needed one dose than for the kids who needed two doses, the study found.

In the last year of the study, among the subset of children who needed two doses and got the first shot, about 64 percent also received the second shot.

Over all 10 flu seasons, black and Hispanic children were less likely to be fully immunized than white kids, the study also found.

One limitation of the study is that the data relies on phone surveys of parents that are then confirmed by immunization providers, a process that might exclude children who live in households without phones or who lack complete vaccination records, the authors note. The CDC didn't respond to requests for comment on the study.

Despite the limitations, the findings suggest that doctors and public health officials still need to do a better job of outreach when it comes to early childhood flu vaccinations, the authors conclude.

It may be very difficult to reach the small minority of parents who simply object to childhood vaccinations, but there are probably another 20 percent of parents who intend to get the shots for their children and simply forget or fail to return for the second dose when needed, said Dr. Paul Offit, an infectious disease specialist at the Children's Hospital of Philadelphia who wasn't involved in the study.

"If the bar is set at two doses, which is what you need the first time you get it, then unfortunately there are going to be some kids who don't end up fully vaccinated even when their parents do bring them in for that first dose," Offit said.

To the extent possible, doctors might try using text messages, emails or phone calls to remind parents when it's time to come in for flu shots, and to give a second round of reminders if that follow-up dose is needed during a baby's first flu season, Edwards said.

"We aren't going to get everybody, but we can get a lot more kids if we can figure out how to make it easier for parents with reminders and with clinic hours that they can actually get to easily, whether it's walk-in hours or nights and weekends," Edwards said. "We can do better."