  Recently, attention was drawn to the failure of two very large internet-based
probability surveys to correctly estimate COVID-19 vaccine uptake in the United
States in early 2021. Both the Delphi-Facebook CTIS and Census Household Pulse
Survey (HPS) overestimated uptake substantially, by 17 and 14 percentage points
in May 2021, respectively. These surveys had large numbers of respondents but
very low response rates (<10%), thus, non-ignorable nonresponse could have had
substantial impact. Specifically, it is plausible that "anti-vaccine"
individuals were less likely to participate given the topic (impact of the
pandemic on daily life). In this paper we use proxy pattern-mixture models
(PPMMs) to estimate the proportion of adults (18+) who received at least one
dose of a COVID-19 vaccine, using data from the CTIS and HPS, under a
non-ignorable nonresponse assumption. Data from the American Community Survey
provide the necessary population data for the PPMMs. We compare these estimates
to the true benchmark uptake numbers and show that the PPMM could have detected
the direction of the bias and provide meaningful bias bounds. We also use the
PPMM to estimate vaccine hesitancy, a measure for which we do not have a
benchmark truth, and compare to the direct survey estimates.
