A Capture-Recapture Approach to Enhance Treatment Effect Evaluation in an Observational Cohort

We extend recently proposed design-based capture-recapture (CRC) methods for prevalence estimation among registry participants, in order to enhance treatment effect evaluation among a trial-eligible target population. The so-called ``anchor stream 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 CRC findings. We show that a novel CRC-type estimator derived via multinomial distribution-based maximum-likelihood further exploits the design to deliver benefits in terms of validity and efficiency for comparing the effects of two treatments on a binary outcome. The design also unlocks a direct standardization-type estimator that allows efficient estimation of general means (e.g., for continuous outcomes such as biomarker levels) under a specific treatment. This provides an avenue to compare treatment responses within the target population in a more comprehensive manner. For inference, we recommend using a tailored Bayesian credible interval approach to improve coverage properties in conjunction with the proposed CRC estimator when estimating binary treatment effects, and a bootstrap percentile interval approach for use with continuous outcomes. Simulations demonstrate the validity and efficiency of the proposed estimators under the CRC design. Finally, we present an illustrative data application comparing Anti-S Antibody seropositive response rates for two major Covid-19 vaccines using an observational cohort from Tunisia.