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Urn models and vaccine efficacy estimation
Author(s) -
HernándezSuárez Carlos M.,
CastilloChavez Carlos
Publication year - 2000
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(20000330)19:6<827::aid-sim382>3.0.co;2-b
Subject(s) - statistics , estimation , population , mixing (physics) , hypergeometric distribution , point estimation , distribution (mathematics) , homogeneous , mathematics , epidemic model , econometrics , medicine , physics , combinatorics , mathematical analysis , management , environmental health , quantum mechanics , economics
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. Copyright © 2000 John Wiley & Sons, Ltd.