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

  • Eric Janssen ORCID logo EMAIL logo and Michael Vuolo
Published/Copyright: October 6, 2025
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Epidemiologic Methods
From the journal Epidemiologic Methods Volume 14 Issue 1

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.

Keywords: capture-recapture; heterogeneity; illicit substances; multilevel model; nationwide estimates; random effects
Corresponding author: Eric Janssen, French Monitoring Centre on Drugs and Drug Addiction (Observatoire Français des Drogues et des Tendances Addictives – OFDT), 69 rue de Varenne, 75007 Paris, France, E-mail: 

Acknowledgments

The authors wish to thank Christophe Palle and Léo Bouthier (OFDT) for updating the data and Thomas Seyler (EUDA) for providing the opportunity to expose a first draft of our research during the PDU Expert Meeting held in Lisbon, May 2019.

  1. Research ethics: The survey was approved by an internal steering committee which acts as the equivalent of an Institutional Review Board, and by the National Data Protection Authority (CNIL, authorization #04-1059).

  2. Informed consent: Informed consent was obtained from all individuals included in this study, or their legal guardians or wards.

  3. Author contributions: EJ: conceptualization, data curation and first draft of the manuscript. MV: conceptualization, methodological assessment and major contribution in writing the final version of the manuscript. All authors read and approved the final manuscript.

  4. Use of Large Language Models, AI and Machine Learning Tools: None to declare.

  5. Conflict of interest: None to declare.

  6. Research funding: This study was supported by the French Monitoring Centre for Drugs and Drug Addictions (OFDT), which provided financial support for conducting the survey and writing this paper. The authors received no financial support for the research, authorship, and/or publication of this article.

  7. Data availability: The datasets generated and/or analysed during the current study are not publicly available. The data contain sensitive information which allows the identification of individuals. It is therefore protected, and access can only be granted with special permission.

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/em-2025-0011).

Received: 2025-03-10
Accepted: 2025-09-24
Published Online: 2025-10-06

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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  2. Research Articles
  3. Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level
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  5. Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
  6. Investigating the association between school substance programs and student substance use: accounting for informative cluster size
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https://doi.org/10.1515/em-2025-0011
Keywords for this article
capture-recapture; heterogeneity; illicit substances; multilevel model; nationwide estimates; random effects

Articles in the same Issue

  1. Causal mediation analysis for difference-in-difference design and panel data
  2. Research Articles
  3. Extending the scope of the capture-recapture experiment: a multilevel approach with random effects to provide reliable estimates at national level
  4. Discrete-time compartmental models with partially observed data: a comparison among frequentist and Bayesian approaches for addressing likelihood intractability
  5. Sensitivity analysis for unmeasured confounding for a joint effect with an application to survey data
  6. Investigating the association between school substance programs and student substance use: accounting for informative cluster size
  7. The quantiles of extreme differences matrix for evaluating discriminant validity
  8. Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions
  9. What if dependent causes of death were independent?
  10. Bot invasion: protecting the integrity of online surveys against spamming
  11. A study of a stochastic model and extinction phenomenon of meningitis epidemic
  12. Understanding the impact of media and latency in information response on the disease propagation: a mathematical model and analysis
  13. Time-varying reproductive number estimation for practical application in structured populations
  14. Perspective
  15. Should we still use pointwise confidence intervals for the Kaplan–Meier estimator?
  16. Leveraging data from multiple sources in epidemiologic research: transportability, dynamic borrowing, external controls, and beyond
  17. Regression calibration for time-to-event outcomes: mitigating bias due to measurement error in real-world endpoints
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