Urn models and vaccine efficacy estimation.
We derive the distribution of the number of infections among unvaccinated and vaccinated individuals for model 1 (leaky) and model 2 (all/nothing) vaccines, assuming random mixing of a homogeneous population. For all/nothing vaccines, we show that the distribution of the number of infected vaccinated individuals conditioning on n observed infections follows a hypergeometric distribution, and the vaccine efficacy estimate (VE) can be derived from the usual estimate of the total population size in a capture-recapture sampling program. For leaky vaccines, we show that the number of vaccinated infected follows a distribution that was first derived by Wallenius. We found that the current point estimates of VE for each model perform very well, but the urn model construction presented here provides a strong framework for estimation and hypothesis testing on the parameters, and can be applied when the available data are a sample of the population. Since the method does not require an underlying transmission model, it can be applied to estimate the VE for non-contagious diseases.
Hernández-Suárez
C M
CM
CGIC - Universidad de Colima, Apdo. Postal 25, Colima, 28045 México.
Castillo-Chavez
C
C
D000293:Adolescent; D000328:Adult; D002648:Child; D004196:Disease Outbreaks; D006801:Humans; D008457:Measles / Q000517:prevention & control / Q000635:transmission; D008458:Measles Vaccine / Q000008:administration & dosage; D008875:Middle Aged; D015233:Models, Statistical; D014611:Vaccination / Q000706:statistics & numerical data*
D008458:Measles Vaccine