Use of power-law analysis to predict abuse or diversion of prescribed medications: proof-of-concept mathematical exploration.

Objective: To conduct a proof-of-concept study comparing Lorenz-curve analysis (LCA) with power-law (exponential function) analysis (PLA), by applying segmented regression modeling to 1-year prescription claims data for three medications-alprazolam, opioids, and gabapentin-to predict abuse and/or diversion using power-law zone (PLZ) classification.

Results: In 1-year baseline observation, patients classified into the top PLZ groups (PLGs) were demographically and diagnostically similar to those in Lorenz-1 (top 1% of utilizers) and Lorenz-25 (top 25%). For prediction of follow-up (6-month post-baseline) Lorenz-1 use of alprazolam and opioids (i.