A Capture-Recapture-based Ascertainment Probability Weighting Method for Effect Estimation With Under-ascertained Outcomes

Outcome under-ascertainment, characterized by the incomplete identification or reporting of cases, poses a substantial challenge in epidemiologic research. While capture-recapture methods can estimate unknown case numbers, their role in estimating exposure effects in observational studies is not well established. This paper presents an ascertainment probability weighting framework that integrates capture-recapture and propensity score weighting. We propose a nonparametric estimator of effects on binary outcomes that combines exposure propensity scores with data from two conditionally independent outcome measurements to simultaneously adjust for confounding and under-ascertainment. Demonstrating its practical application, we apply the method to estimate the relationship between health care work and coronavirus disease 2019 testing in a Swedish region. We find that ascertainment probability weighting greatly influences the estimated association compared to conventional inverse probability weighting, underscoring the importance of accounting for under-ascertainment in studies with limited outcome data coverage. We conclude with practical guidelines for the method's implementation, discussing its strengths, limitations, and suitable scenarios for application.