An Optimal Learning Model for State-Level Optimization of Naloxone Kit Allocation with Non-Convex Response Rates

Abstract

Although intended to treat pain, opioids have recently emerged at the forefront of national health concerns, contributing to over 47,000 reported overdose deaths in 2017 (“Provisional Drug Overdose Death Counts”, 2018). In many cases, however, an overdose can be reversed if a witness quickly administers naloxone, an opioid antagonist, to the victim. Access to this life-saving drug has greatly increased in recent years through pharmacy standing orders, naloxone distribution and training programs, and philanthropic donation of naloxone kits to at-risk populations. Unfortunately, the cost of the drug, about $75 for two doses, presents a major barrier to widespread access, especially in context of state governments’ tight budgets. This thesis provides a mathematical framework for how a state government would allocate a limited budget for naloxone kits among its counties to maximize the number of reported community overdose reversals over a finite horizon. Simulating data from a logistic curve representation of the relationship between the number or value of distributed naloxone kits and the number of reported community overdose reversals, the sequential decision model implements a backward dynamic program and Bayesian updating to search for an optimal allocation and learning policy.