Estimating the prevalence of problem drug use from drug-related mortality data

Background and Aims
Indirect estimation methods are required for estimating the size of populations where only a portion of individuals are observed directly, such as problem drug users (PDUs). Capture-recapture and multiplier methods are widely used but have been criticised as subject to bias. We propose a new approach to estimating prevalence of PDU from numbers of fatal drug-related poisonings (fDRPs) using linked databases, addressing the key limitations of simplistic ‘mortality multipliers’.

Methods
Our approach requires linkage of data on a large cohort of known PDUs to mortality registers, and summary information about additional fDRPs observed outside of this cohort. We model fDRP rates among the cohort and assume that rates in unobserved PDUs are equal to rates in the cohort during periods out of treatment. Prevalence is estimated in a Bayesian statistical framework, in which we simultaneously fit regression models to fDRP rates and prevalence, allowing both to vary by demographic factors and the former also by treatment status.

Findings
We report a case study analysis, estimating the prevalence of opioid dependence in England in 2008/09, by gender, age group and geographical region. Overall prevalence was estimated as 0.82% (95% credible interval 0.74-0.94%) of 15-64 year olds, which is similar to a published estimate based on capture-recapture analysis.

Conclusions
Our modelling approach estimates prevalence from drug-related mortality data, while addressing the main limitations of simplistic multipliers. This offers an alternative approach for the common situation where available data sources do not meet the strong assumptions required for valid capture-recapture estimation. In a case study analysis, prevalence estimates based on our approach were surprisingly similar to existing capture-recapture estimates but, we argue, are based on a much more objective and justifiable modelling approach.