title: The importance of distribution-choice in modeling substance use data: a comparison of negative binomial, beta binomial, and zero-inflated distributions.
abstract: BACKGROUND
  It is important to correctly understand the associations among addiction to multiple drugs and between co-occurring substance use and psychiatric disorders. Substance-specific outcomes (e.g. number of days used cannabis) have distributional characteristics which range widely depending on the substance and the sample being evaluated.
  
  
  OBJECTIVE
  We recommend a four-part strategy for determining the appropriate distribution for modeling substance use data. We demonstrate this strategy by comparing the model fit and resulting inferences from applying four different distributions to model use of substances that range greatly in the prevalence and frequency of their use.
  
  
  METHODS
  Using Timeline Followback (TLFB) data from a previously-published study, we used negative binomial, beta-binomial and their zero-inflated counterparts to model proportion of days during treatment of cannabis, cigarettes, alcohol, and opioid use. The fit for each distribution was evaluated with statistical model selection criteria, visual plots and a comparison of the resulting inferences.
  
  
  RESULTS
  We demonstrate the feasibility and utility of modeling each substance individually and show that no single distribution provides the best fit for all substances. Inferences regarding use of each substance and associations with important clinical variables were not consistent across models and differed by substance.
  
  
  CONCLUSIONS
  Thus, the distribution chosen for modeling substance use must be carefully selected and evaluated because it may impact the resulting conclusions. Furthermore, the common procedure of aggregating use across different substances may not be ideal.
authors.affiliation: a Department of Biostatistics and Informatics , and.
authors.forename: Brandie
authors.initials: B
authors.lastname: Wagner
authors.affiliation: b Department of Psychiatry , University of Colorado , Aurora , CO , USA.
authors.forename: Paula
authors.initials: P
authors.lastname: Riggs
authors.affiliation: a Department of Biostatistics and Informatics , and.|b Department of Psychiatry , University of Colorado , Aurora , CO , USA.
authors.forename: Susan
authors.initials: S
authors.lastname: Mikulich-Gilbertson
mesh_terms: D000293:Adolescent; D017831:Diagnosis, Dual (Psychiatry) / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D008297:Male; D001523:Mental Disorders / Q000150:complications* / Q000453:epidemiology*; D015233:Models, Statistical; D016008:Statistical Distributions; D019966:Substance-Related Disorders / Q000150:complications* / Q000453:epidemiology*; D055815:Young Adult
keywords: Beta binomial; Timeline Followback; negative binomial; substance use; zero inflated