It’s not great. From Nelson et al. (2009):
Among those who received a first dose of varicella (n = 16 075), hepatitis A (n = 594 917), and hepatitis B (n = 590 445) vaccine, relatively few completed the series (55%–65% for hepatitis B vaccine and 40%–50% for hepatitis A and varicella vaccines in most age groups). Compliance was lowest among adolescents (35.9%) and Medicaid recipients (29.7%) who received varicella vaccine and among younger adult age groups who received hepatitis A vaccine (25%–35% across those age groups). Even among series completers, there was a relatively long interval of undervaccination between the first and last doses.
On the one hand, these vaccinations didn’t have the public attention of COVID-19 so perhaps compliance would be better. In particular, conditional on someone agreeing to a first COVID-19 vaccine–which will be a selected population given the (unfortunate) politics of the vaccine–perhaps second dose compliance would be higher than those observed in Nelson et al. for other vaccines. Additionally, there is evidence that the COVID-19 vaccines are very effective even after one dose. Nevertheless, this is some concerning historical precedent in the scientific literature.
Hat tip: Marginal Revolution.