Teenagers with family members in the military are more likely to contemplate suicide if their relatives are sent into combat overseas on multiple deployments, according to a new study published on Monday.

The study, carried out by researchers at the University of Southern California and published in the Journal of Adolescent Health, found a link between multiple deployments of parents or siblings and a series of mental health problems, including thoughts of suicide, in teens.

It adds to a growing body of evidence that more than a decade of conflict in Afghanistan and Iraq has taken its toll not only on returning troops but also their families.

Previous studies have used data on children and adolescents already getting treatment, or from those within military camps, making any comparison with other children difficult.

However, the researchers were able to draw on health data collected in schools for the first time in 2011 in California, a state with a large military population. They added questions of their own to seventh, ninth and 11th graders about military background and the history of deployment in families in order to get a state-wide picture.

They found that deployment was the "strongest predictor" of adolescent mental health issues and that those who experienced more family deployments were more likely to report symptoms of depression and thoughts of suicide.

Julie Cederbaum, assistant professor at the school of social work at the University of Southern California, said: "It is not just military kids – it is military kids who have experienced deployment. This experience of repeated deployment seems to be the trigger. We know thats been more common during recent wars. We know there are stressors when a parent leaves, there can be loss of communication, then there's a time lapse of nine months to a year. By no means all the parents who return from war have problems. But it's an adjustment."

Up to 28.5% of young people in the US have reported feeling sad or hopeless almost every day for two weeks during the last 12 months, and more than 15% report seriously contemplating suicide, according to the Centers for Disease Control and Prevention.

The report's findings, published on Monday, suggest that although military-connected teens had similar mental health problems as others, when deployment was taken into account, the results were significantly different. Those with a parent or sibling deployed were 40% more likely to report feeling sad or hopeless for more than two weeks in the past 12 months. For those with a parent or sibling who had been deployed twice overseas, the percentage jumped to 56%.

The study also found higher rates of suicidal "ideation" among those teens with military connections and more than one deployment. Ninth and 11th graders with a parent or sibling involved in two deployments were 34% more likely to have suicidal thoughts than their peers without military connections. In previous studies, 15% of teens overall have been found to have had suicidal thoughts.

They also found that girls were more likely than boys to report poorer well-being, a finding that echoed previous studies and was thought to reflect differences in roles and responsibilities at home.

The study's authors said there was a need to increase mental health screening among all adolescents, particularly among those in military-connected families experiencing deployments.