Alternative Capture-Recapture Point and Interval Estimators Based on Two Surveillance Streams

The capture-recapture approach is a common and potentially useful paradigm for estimating the total number (N) of cases or deaths via multiple registries in epidemiological studies. Using data on childhood deaths from two sources in a Sierra Leone chiefdom collected by the Child Health and Mortality Prevention Surveillance (CHAMPS) project team as a motivating example, we consider point and interval estimation in the two-capture case. We focus primarily on closed population scenarios under what we term and clarify as the LP conditions, i.e., assumptions that make the well-known Lincoln-Petersen (LP) and Chapman estimators valid. We clarify the unverifiable nature of assumptions about a key population-level parameter (akin to a relative risk of capture) implicitly made by popular alternatives such as loglinear models and the estimator of Chao (Biometrics. 43:783–791, 1987). We argue that the LP conditions remain the most central and useful given the possibility to defend them within strata of judiciously chosen covariates and/or to ensure them by design. We then propose two new multinomial distribution-based estimators that are valid under those conditions. The first adjusts for typical (mean) bias and provides a potentially preferable alternative to the Chapman estimator. The second targets reduced median bias, which is generally overlooked as a performance criterion in the capture-recapture setting. Finally, we develop an approach geared toward improved confidence intervals in this setting that utilizes refinements to the posterior distribution of the proposed mean bias-adjusted estimand within a Bayesian credible interval strategy. The proposed point and interval estimators are evaluated in comparison with others through simulation studies.