Problem drug use prevalence estimation revisited: heterogeneity in capture-recapture and the role of external evidence

Background and aims: Capture-recapture (CRC) analysis is recommended for estimating the prevalence of problem drug use or people who inject drugs (PWID). We aim to demonstrate how naive application of CRC can lead to highly misleading results, and to suggest how the problems might be overcome.

Methods: We present a case study of estimating the prevalence of PWID in Bristol, UK, applying CRC to lists in contact with three services. We assess: (i) sensitivity of results to different versions of the dominant (treatment) list: specifically, to inclusion of non-incident cases and of those who were referred directly from one of the other services; (ii) the impact of accounting for a novel covariate, housing instability; and (iii) consistency of CRC estimates with drug-related mortality data. We then incorporate formally the drug-related mortality data and lower bounds for prevalence alongside the CRC into a single coherent model.

Results: Five of 11 models fitted the full data equally well but generated widely varying prevalence estimates, from 2740 [95% confidence interval (CI) = 2670, 2840] to 6890 (95% CI = 3740, 17680). Results were highly sensitive to inclusion of non-incident cases, demonstrating the presence of considerable heterogeneity, and were sensitive to a lesser extent to inclusion of direct referrals. A reduced data set including only incident cases and excluding referrals could be fitted by simpler models, and led to much greater consistency in estimates. Accounting for housing stability improved model fit considerably more than did the standard covariates of age and gender. External data provided validation of results and aided model selection, generating a final estimate of the number of PWID in Bristol in 2011 of 2770 [95% credible interval (Cr-I) = 2570, 3110] or 0.9% (95% Cr-I = 0.9, 1.0%) of the population aged 15-64 years.

Conclusions: Steps can be taken to reduce bias in capture-recapture analysis, including: careful consideration of data sources, reduction of lists to less heterogeneous subsamples, use of covariates and formal incorporation of external data.