  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.
