Appropriate analyses of bimodal substance use frequency outcomes: a mixture model approach

Background: In addiction research, outcome measures are often characterized by bimodal distributions. One mode can be for individuals with low substance use and the other mode for individuals with high substance use. Applying standard statistical procedures to bimodal data may result in invalid inference. Mixture models are appropriate for bimodal data because they assume that the sampled population is composed of several underlying subpopulations.Objectives: To introduce a novel mixture modeling approach to analyze bimodal substance use frequency data.Methods: We reviewed existing models used to analyze substance use frequency outcomes and developed multiple alternative variants of a finite mixture model. We applied all methods to data from a randomized controlled study in which 30-day alcohol abstinence was the primary outcome. Study data included 73 individuals (38 men and 35 women). Models were implemented in the software packages SAS, Stata, and Stan.Results: Shortcomings of existing approaches include: 1) inability to model outcomes with multiple modes, 2) invalid statistical inferences, including anti-conservative p-values, 3) sensitivity of results to the arbitrary choice to model days of substance use versus days of substance abstention, and 4) generation of predictions outside the range of common substance use frequency outcomes. Our mixture model variants avoided all of these shortcomings.Conclusions: Standard models of substance use frequency outcomes can be problematic, sometimes overstating treatment effectiveness. The mixture models developed improve the analysis of bimodal substance use frequency.