Statistical Analysis of Past-Year Marijuana use in U.S. General Population: A Negative Binomial Regression Model

Abstract

Marijuana is the most frequently reported illicit substance in the United States. However, limited studies have delved into the analysis of marijuana use as a count variable, in which the distribution often exhibits overdispersion and notable occurrences of zero values. This study encompassed a total of 58,034 individuals, with12,528 having reported marijuana use in the past year from the 2021 National Surveys on Drug Use and Health data. Marijuana use was measured by number of days used in the past year. Three distributions were compared including normal distribution, Poisson, and Negative Binomial (NB) distributions. The Akaike information criterion (AIC), corrected AIC (AICC), consistent AIC (CAIC), and the Bayesian information criterion (BIC) statistics were used to select the best distribution. The overall prevalence of past-year marijuana use was 21.6%. The NB regression model proved to be the best with lowest AIC, AICC, CAIC, and BIC values compared with linear and Poisson models. According to the NB model, African American and age 18–64 years were associated with increased days of marijuana use, whereas, females, rural living, Asian and Hispanic were associated with decreased days of marijuana use. The findings can guide healthcare providers when screening for marijuana use in general population.