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This study sought to examine grouped and right-censored (GRC) counts of adolescent marijuana use and estimate its temporal trajectories and sociodemographic disparities over almost half a century. After compiling 46 waves of nationally representative data from the Monitoring the Future (MTF) study from 1976 to 2021 (sample size = 491,348), we utilized an innovative modified Poisson (mixture) approach to analyze past-year marijuana use quantified by GRC counts. The overall reduction in incidence rates of marijuana use was attributable to an almost 40% reduction in the risk of marijuana use (with the proportion of at-risk adolescents at 51.36% in 1979 and 31.53% in 2021). Despite substantial changes over the study period, the recent incidence rates for at-risk individuals were similar to those in the early 1980s. Living in an intact family was a protective factor against adolescent marijuana use over time. The incidence rates of marijuana use among at-risk students, especially those from disadvantaged families, remained high over the study period. The modified Poisson (mixture) approach serves as the preferred tool for modeling GRC responses. It is essential to distinguish among risk, at-risk incidence, and overall incidence when assessing substance use and other risky behaviors. [ABSTRACT FROM AUTHOR]