Urn models and vaccine efficacy estimation

Carlos M. Hernández-Suárez, Carlos Castillo-Chavez

Research output: Contribution to journalReview articlepeer-review

11 Scopus citations


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 (C) 2000 John Wiley and Sons, Ltd.

Original languageEnglish (US)
Pages (from-to)827-835
Number of pages9
JournalStatistics in Medicine
Issue number6
StatePublished - Mar 30 2000
Externally publishedYes

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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