The study from Sam Houston State University found that when compared to parents who did not use substances, parents who used alcohol, marijuana, and drugs were significantly more likely to have children who used those same drugs.
Specifically, the odds of children's alcohol use were five times higher if their parents used alcohol; the odds of children's marijuana use were two times higher if their parents used marijuana; and the odds of children's other drug use were two times higher if their parent used other drugs.
"If a parent uses drugs, will their children grow up and use drugs? When did the parent use and when did their children use? There appears to be an intergenerational relationship," said Dr Kelly Knight from the College Criminal Justice.
The study examined the patterns of substance use by families over a 27-year period.
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The analysis was based on 655 parents and 1,227 offspring from 1977 to 2004.
The study suggests that if substance use can be curtailed in adolescence, it may help to curb its prevalence in future generations.
The study also helps pinpoint the use of different illicit substances over the span of a lifetime, including its emergence in adolescence and when that use may decline.
For example, marijuana and other drug use is most prevalent in adolescence and generally declines before or at age 24, researchers said.
Alcohol use continues to increase throughout adolescence and young adulthood, and then remains relatively steady over the lifetime, they said.