Sensitivity and Uncertainty Analysis for Two-stream Capture–Recapture Methods in Disease Surveillance

Abstract

Capture–recapture methods are widely applied in estimating the number ($N$) of prevalent or cumulatively incident cases in disease surveillance. Here, we focus the bulk of our attention on the common case in which there are 2 data streams. We propose a sensitivity and uncertainty analysis framework grounded in multinomial distribution-based maximum likelihood, hinging on a key dependence parameter that is typically nonidentifiable but is epidemiologically interpretable. Focusing on the epidemiologically meaningful parameter unlocks appealing data visualizations for sensitivity analysis and provides an intuitively accessible framework for uncertainty analysis designed to leverage the practicing epidemiologist’s understanding of the implementation of the surveillance streams as the basis for assumptions driving estimation of $N$. By illustrating the proposed sensitivity analysis using publicly available HIV surveillance data, we emphasize both the need to admit the lack of information in the observed data and the appeal of incorporating expert opinion about the key dependence parameter. The proposed uncertainty analysis is a simulation-based approach designed to more realistically acknowledge variability in the estimated $N$ associated with uncertainty in an expert’s opinion about the nonidentifiable parameter, together with the statistical uncertainty. We demonstrate how such an approach can also facilitate an appealing general interval estimation procedure to accompany capture–recapture methods. Simulation studies illustrate the reliable performance of the proposed approach for quantifying uncertainties in estimating $N$ in various contexts. Finally, we demonstrate how the recommended paradigm has the potential to be directly extended for application to data from >2 surveillance streams.