Nonprobability follow-up sample analysis: an application to SARS-CoV-2 infection prevalence estimation

Public health policy makers are faced with making crucial decisions rapidly during infectious disease outbreaks such as that caused by SARS-CoV-2. Ideally, rapidly deployed representative health surveys could provide needed data for such decisions. Under the constraints of a limited timeframe and resources, it may be infeasible to implement random based (probability) sampling that yields a population representative survey sample with high response rates. As an alternative, a volunteer (nonprobability) sample is often collected using outreach methods such as social media and web surveys. Compared to a probability sample, a nonprobability sample is subject to selection bias. In addition, when participants are followed longitudinally nonresponse often occurs at later follow up timepoints. As a result, estimates of cross-sectional parameters at later timepoints will be subject to selection bias and nonresponse bias. In this paper, we create kernel-weighted pseudoweights (KW) for the baseline survey participants and construct nonresponse-adjusted kw (kwNR) for respondents at each follow-visit to estimate the population mean at the follow-up visits. We develop Taylor Linearization variance estimation that accounts for variability due to estimating both pseudoweights and the nonresponse adjustments. Simulations are conducted to evaluate the proposed kwNR-weighted estimates. We investigate covariate effects on each of the following: baseline sample participation propensity, follow-up response propensity and the mean of the outcome. We apply the proposed kwNR-weighted methods to the SARS-Cov-2 antibody seropositivity longitudinal study, which begins with a baseline survey early in the pandemic, and collects data at six- and twelve-month post baseline follow-ups.