Variable Inclusion Strategies for Effective Quota Sampling and Propensity Modeling: An Application to SARS-COV-2 Infection Prevalence Estimation

Public health policymakers must make crucial decisions rapidly during a pandemic. In such situations, accurate measurements from health surveys are essential. As a consequence of limited time and resource constraints, it may be infeasible to implement a probability-based sample that yields high response rates. An alternative approach is to select a quota sample from a large pool of volunteers, with the quota sample selection based on the census distributions of available—often demographic—variables, also known as quota variables. In practice, however, census data may only contain a subset of the required predictor variables. Thus, the realized quota sample can be adjusted by propensity score pseudoweighting using a “reference” probability-based survey that contains more predictor variables. Motivated by the SARS-CoV-2 serosurvey (a quota sample conducted in 2020 by the National Institutes of Health), we identify the condition under which the quota variables can be ignored in constructing the propensity model but still produce nearly unbiased estimation of population means. We conduct limited simulations to evaluate the bias and variance reduction properties of alternative weighting strategies for quota sample estimates under three propensity models that account for varying sets of predictors and degrees of correlation among the predictor sets and then apply our findings to the empirical data.