Recapture or precapture? Fallibility of standard capture-recapture methods in the presence of referrals between sources.

Capture-recapture methods, largely developed in ecology, are now commonly used in epidemiology to adjust for incomplete registries and to estimate the size of difficult-to-reach populations such as problem drug users. Overlapping lists of individuals in the target population, taken from administrative data sources, are considered analogous to overlapping "captures" of animals. Log-linear models, incorporating interaction terms to account for dependencies between sources, are used to predict the number of unobserved individuals and, hence, the total population size. A standard assumption to ensure parameter identifiability is that the highest-order interaction term is 0. We demonstrate that, when individuals are referred directly between sources, this assumption will often be violated, and the standard modeling approach may lead to seriously biased estimates. We refer to such individuals as having been "precaptured," rather than truly recaptured. Although sometimes an alternative identifiable log-linear model could accommodate the referral structure, this will not always be the case. Further, multiple plausible models may fit the data equally well but provide widely varying estimates of the population size. We demonstrate an alternative modeling approach, based on an interpretable parameterization and driven by careful consideration of the relationships between the sources, and we make recommendations for capture-recapture in practice.