Refining capture-recapture methods to estimate case counts in a finite population setting

TL;DR

This paper refines capture-recapture methods for estimating case counts in finite populations, especially when data streams are non-representative, by incorporating finite population corrections and demonstrating improved precision through simulations and real data application.

Contribution

It introduces finite population correction techniques for capture-recapture estimators in finite, closed populations with non-representative data streams, enhancing estimation accuracy.

Findings

FPC adjustments improve estimator precision significantly.

Simulation results show better performance with FPC methods.

Application to cancer recurrence data demonstrates practical utility.

Abstract

In this paper, we expand upon and refine a monitoring strategy proposed for surveillance of diseases in finite, closed populations. This monitoring strategy consists of augmenting an arbitrarily non-representative data stream (such as a voluntary flu testing program) with a random sample (referred to as an "anchor stream"). This design allows for the use of traditional capture-recapture (CRC) estimators, as well as recently proposed anchor stream estimators that more efficiently utilize the data. Here, we focus on a particularly common situation in which the first data stream only records positive test results, while the anchor stream documents both positives and negatives. Due to the non-representative nature of the first data stream, along with the fact that inference is being performed on a finite, closed population, there are standard and non-standard finite population effects at play. Here, we propose two methods of incorporating finite population corrections (FPCs) for inference, along with an FPC-adjusted Bayesian credible interval. We compare these approaches with existing methods through simulation and demonstrate that the FPC adjustments can lead to considerable gains in precision. Finally, we provide a real data example by applying these methods to estimating the breast cancer recurrence count among Metro Atlanta-area patients in the Georgia Cancer Registry-based Cancer Recurrence Information and Surveillance Program (CRISP) database.