Explaining “U-Shaped†Distributions of Population Substance Use with a Simple Computational Approach

Background : “U-shaped†distributions of past 30-day substance use frequencies are pervasive, yet no established model explains this phenomenon. Using probability functions to describe these distributions yields unintuitive, atheoretical results. This study introduces a simple computational model of individual-level, longitudinal substance use patterns to understand how cross-sectional U-shaped distributions emerge in populations. Model : Each independent computational object transitions between two states: not using a substance (“N†), or using a substance (“U†). The model has two key components: (1) each object has a unique risk factor probability governing the transition from N to U, and a unique protective factor probability governing the transition from U to N; (2) an object’s current decision to use or not use is influenced by its prior decisions (i.e., “path dependence†). Three modeler input parameters control these two components. Analysis : First, the model is fit to empirical cross-sectional distributions of past 30-day use frequencies for ten substances (e.g., alcohol, cannabis, tobacco, etc.) from the U.S. National Survey on Drug Use and Health. Next, combinations of values of the model’s three inputs are tested to determine the conditions that produce U-shaped distributions. Finally, supplemental testing explored structural variations of the original model to assess whether simpler or alternative configurations are also capable of generating U-shaped distributions. Results : The model effectively reproduced the U-shaped distributions observed in empirical data across all substances. Path dependence emerged as a critical feature for generating U-shaped distributions, independent of the specific distribution shapes used for assigning transition probabilities. However, results also indicated that neither of the model's two key components are required for generating U-shaped distributions. Conclusion : This study demonstrates how a simple, theoretically-grounded computational model of individual-level substance use patterns can help substance use researchers understand the emergence of population-level, cross-sectional U-shaped distributions of substance use.