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In this paper, we advocate and expand upon a previously described monitoring strategy for efficient and robust estimation of disease prevalence and case numbers within closed and enumerated populations such as schools, workplaces, or retirement communities. The proposed design relies largely on voluntary testing, which is notoriously biased (e.g. in the case of coronavirus disease 2019) due to nonrepresentative sampling. The approach yields unbiased and comparatively precise estimates with no assumptions about factors underlying selection of individuals for voluntary testing, building on the strength of what can be a small random sampling component. This component enables the use of a recently proposed "anchor stream" estimator, a well-calibrated alternative to classical capture-recapture (CRC) estimators based on 2 data streams. We show that this estimator is equivalent to a direct standardization based on "capture," that is, selection (or not) by the voluntary testing program, made possible by means of a key parameter identified by design. This equivalency simultaneously allows for novel 2-stream CRC-like estimation of general mean values (e.g. means of continuous variables like antibody levels or biomarkers). For inference, we propose adaptations of Bayesian credible intervals when estimating case counts and bootstrapping when estimating means of continuous variables. We use simulations to demonstrate significant precision benefits relative to random sampling alone. [ABSTRACT FROM AUTHOR]