Bayes' Theorem to estimate population prevalence from Alcohol Use Disorders Identification Test (AUDIT) scores

The aim in this methodological paper is to demonstrate, using Bayes' Theorem, an approach to estimating the difference in prevalence of a disorder in two groups whose test scores are obtained, illustrated with data from a college student trial where 12-month outcomes are reported for the Alcohol Use Disorders Identification Test (AUDIT).

Using known population prevalence as a background probability and diagnostic accuracy information for the AUDIT scale, we calculated the post-test probability of alcohol abuse or dependence for study participants. The difference in post-test probability between the study intervention and control groups indicates the effectiveness of the intervention to reduce alcohol use disorder rates.

In the illustrative analysis, at 12-month follow-up there was a mean AUDIT score difference of 2.2 points between the intervention and control groups: an effect size of unclear policy relevance. Using Bayes' Theorem, the post-test probability mean difference between the two groups was 9% (95% confidence interval 3-14%). Interpreted as a prevalence reduction, this is evaluated more easily by policy makers and clinicians.

Important information on the probable differences in real world prevalence and impact of prevention and treatment programmes can be produced by applying Bayes' Theorem to studies where diagnostic outcome measures are used. However, the usefulness of this approach relies upon good information on the accuracy of such diagnostic measures for target conditions.