Many leveled ordinal models for frequency of alcohol and drug use.

Background: The numbers of days people consume alcohol and other drugs over a fixed interval, such as 28 days, are often collected in surveys of substance use. The presence of an upper bound on these variables can result in response distributions with "ceiling effects." Also, if some peoples' substance use behaviors are characterized by weekly patterns of use, summaries of substance days-of-use over longer periods can exhibit multiple modes. Objective: To highlight advantages of ordinal models with a separate level for each distinct survey response, for bounded, and potentially multimodal, count data. Methods: We fitted a Bayesian proportional odds ordinal model to longitudinal cannabis days-of-use reported by 443 individuals who used illicit drugs (206 female, 214 male, 23 non-binary). We specified an ordinal level for each unique response to allow the exact numeric distribution implied by the predicted ordinal response to be inferred. We then compared the fit of the proportional odds model with binomial, negative binomial, hurdle negative binomial and beta-binomial models. Results: Posterior predictive checks and the leave one out information criterion both suggested that the proportional odds model gave a better fit to the cannabis days-of-use data than the other models. Cannabis use among the target population declined during the COVID-19 pandemic in Australia, with the odds of a member of the population exceeding any specified frequency of cannabis use in Wave 4 estimated to be 73% lower than in Wave 1 (median odds ratio 0.27, 90% credible interval 0.19, 0.38). Conclusion: Ordinal models can be suitable for complex count data.