Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level

Abstract Objectives This study investigates the use of multilevel models within capture-recapture experiments, a common procedure to estimate the size of an elusive population, accounting for random effects to accurately calculate the probabilities of being observed. Methods We review single data-source capture-recapture estimators. We provide a general framework to account for random effects to accurately calculate the probabilities of being observed and apply the method to estimate the number of powder cocaine, crack cocaine, heroin users and people who inject drugs in France in 2019. Using two-level, random-intercepts logistic regression models that account for both individual and center factors, we conduct the calculations once with fixed effects only, and once with predicted center-level random effects. Results There are substantial differences between estimates based on fixed-effects only predictions and fixed and random effects combined, reflecting the influence of the treatment center-level. The application of multilevel modelling in capture-recapture allows the researcher to include individual and contextual information, and provide estimates at a large geographical scale. Conclusions Multilevel capture-recapture modelling offers a credible alternative to estimate the size of elusive populations in large geographical settings. The influence of higher-level clusters in capture-recapture studies using multilevel modelling should be explicitly considered in future studies.