Monitoring Drug Use Using Bayesian Acceptance Sampling: The Illinois Experiment

Abstract

Bayesian acceptance sampling was used to monitor illegal drug use in a population of probationers. The study utilizes an economic model of drug testing based on single-sample, single-attribute acceptance sampling. This approach reduces from 100% the amount of testing which must be done to monitor the use of illegal drugs in the population and provides a decision rule, vis-à-vis a sampling plan, that specifies under what sampling outcome the entire population must be tested. The objective is to minimize the expected total cost of a drug testing program while ensuring that the proportion of users in the population is not increasing over time. A field study of the acceptance sampling approach was conducted using probationers assigned to Intensive Drug Supervision Programs in six Illinois counties. The degree to which drug testing results were reported to probation officers was controlled during the experiment. Counties were assigned to receive: no feedback of drug-test results; random proportion of feedback using Bayesian acceptance sampling plans; and 100% feedback—the status quo situation. Results show that those counties using acceptance sampling could have reduced the number of drug tests performed without increasing drug use. In those counties with no feedback, there was an upward trend over time in the proportion testing positive for drug use. Acceptance sampling-based drug testing programs are now being implemented by Illinois probation offices.