Capture-recapture (CRC) surveys are used to estimate the size of a population whose members cannot be enumerated directly. CRC surveys have been used to estimate the number of Coronavirus Disease 2019 (COVID-19) infections, people who use drugs, sex workers, conflict casualties, and trafficking victims. When k-capture samples are obtained, counts of unit captures in subsets of samples are represented naturally by a contingency table in which one element-the number of individuals appearing in none of the samples-remains unobserved. In the absence of additional assumptions, the population size is not identifiable (i.e., point identified). Stringent assumptions about the dependence between samples are often used to achieve point identification. However, real-world CRC surveys often use convenience samples in which the assumed dependence cannot be guaranteed, and population size estimates under these assumptions may lack empirical credibility. In this work, we apply the theory of partial identification to show that weak assumptions or qualitative knowledge about the nature of dependence between samples can be used to characterize a nontrivial confidence set for the true population size. We construct confidence sets under bounds on pairwise capture probabilities using two methods: test inversion bootstrap confidence intervals and profile likelihood confidence intervals. Simulation results demonstrate well-calibrated confidence sets for each method. In an extensive real-world study, we apply the new methodology to the problem of using heterogeneous survey data to estimate the number of people who inject drugs in Brussels, Belgium.
Random-digit dialing (RDD) telephone surveys are challenged by declining response rates and increasing costs. Many surveys that were traditionally conducted via telephone are seeking cost-effective alternatives, such as address-based sampling (ABS) with self-administered web or mail questionnaires. At a fraction of the cost of both telephone and ABS surveys, opt-in web panels are an attractive alternative. The 2019-2020 National Alcohol Survey (NAS) employed three methods: (1) an RDD telephone survey (traditional NAS method); (2) an ABS push-to-web survey; and (3) an opt-in web panel. The study reported here evaluated differences in the three data-collection methods, which we will refer to as "mode effects," on alcohol consumption and health topics. To evaluate mode effects, multivariate regression models were developed predicting these characteristics, and the presence of a mode effect on each outcome was determined by the significance of the three-level effect (RDD-telephone, ABS-web, opt-in web panel) in each model. Those results were then used to adjust for mode effects and produce a "telephone-equivalent" estimate for the ABS and panel data sources. The study found that ABS-web and RDD were similar for most estimates but exhibited differences for sensitive questions including getting drunk and experiencing depression. The opt-in web panel exhibited more differences between it and the other two survey modes. One notable example is the reporting of drinking alcohol at least 3-4 times per week, which was 21 percent for RDD-phone, 24 percent for ABS-web, and 34 percent for opt-in web panel. The regression model adjusts for mode effects, improving comparability with past surveys conducted by telephone; however, the models result in higher variance of the estimates. This method of adjusting for mode effects has broad applications to mode and sample transitions throughout the survey research industry.
Ownership of a bank account is an objective measure and should be relatively easy to elicit via survey questions. Yet, depending on the interview mode, the wording of the question and its placement within the survey may influence respondents' answers. The Health and Retirement Study (HRS) asset module, as administered online to members of the Understanding America Study (UAS), yielded substantially lower rates of reported bank account ownership than either a single question on ownership in the Current Population Survey (CPS) or the full asset module administered to HRS panelists (both interviewer-administered surveys). We designed and implemented an experiment in the UAS comparing the original HRS question eliciting bank account ownership with two alternative versions that were progressively simplified. We document strong evidence that the original question leads to systematic underestimation of bank account ownership. In contrast, the proportion of bank account owners obtained from the simplest alternative version of the question is very similar to the population benchmark estimate. We investigate treatment effect heterogeneity by cognitive ability and financial literacy. We find that questionnaire simplification affects responses of individuals with higher cognitive ability substantially less than those with lower cognitive ability. Our results suggest that high-quality data from surveys start from asking the right questions, which should be as simple and precise as possible and carefully adapted to the mode of interview.
The application of serial principled sampling designs for diagnostic testing is often viewed as an ideal approach to monitoring prevalence and case counts of infectious or chronic diseases. Considering logistics and the need for timeliness and conservation of resources, surveillance efforts can generally benefit from creative designs and accompanying statistical methods to improve the precision of sampling-based estimates and reduce the size of the necessary sample. One option is to augment the analysis with available data from other surveillance streams that identify cases from the population of interest over the same timeframe, but may do so in a highly nonrepresentative manner. We consider monitoring a closed population (e.g., a long-term care facility, patient registry, or community), and encourage the use of capture-recapture methodology to produce an alternative case total estimate to the one obtained by principled sampling. With care in its implementation, even a relatively small simple or stratified random sample not only provides its own valid estimate, but provides the only fully defensible means of justifying a second estimate based on classical capture-recapture methods. We initially propose weighted averaging of the two estimators to achieve greater precision than can be obtained using either alone, and then show how a novel single capture-recapture estimator provides a unified and preferable alternative. We develop a variant on a Dirichlet-multinomial-based credible interval to accompany our hybrid design-based case count estimates, with a view toward improved coverage properties. Finally, we demonstrate the benefits of the approach through simulations designed to mimic an acute infectious disease daily monitoring program or an annual surveillance program to quantify new cases within a fixed patient registry.