A Capture-Recapture Approach to Facilitate Causal Inference for a Trial-eligible Observational Cohort

Background: We extend recently proposed design-based capture-recapture methods for prevalence estimation among registry participants, in order to support causal inference among a trial-eligible target population. The proposed design for CRC analysis integrates an observational study cohort with a randomized trial involving a small representative study sample, and enhances the generalizability and transportability of the findings. Methods: We develop a novel CRC-type estimator derived via multinomial distribution-based maximum-likelihood that exploits the design to deliver benefits in terms of validity and efficiency for comparing the effects of two treatments on a binary outcome. Additionally, the design enables a direct standardization-type estimator for efficient estimation of general means (e.g., of biomarker levels) under a specific treatment, and for their comparison across treatments. For inference, we propose a tailored Bayesian credible interval approach to improve coverage properties in conjunction with the proposed CRC estimator for binary outcomes, along with a bootstrap percentile interval approach for use in the case of continuous outcomes. Results: Simulations demonstrate the proposed estimators derived from the CRC design. The multinomial-based maximum-likelihood estimator shows benefits in terms of validity and efficiency in treatment effect comparisons, while the direct standardization-type estimator allows comprehensive comparison of treatment effects within the target population. Conclusion: The extended CRC methods provide a useful framework for causal inference in a trial-eligible target population by integrating observational and randomized trial data. The novel estimators enhance the generalizability and transportability of findings, offering efficient and valid tools for treatment effect comparisons on both binary and continuous outcomes.