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A note on the distribution of the number of vaccinated infected under non‐random mixing conditions
Author(s) -
HernándezSuárez Carlos M.
Publication year - 2001
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/sim.824
Subject(s) - mixing (physics) , hypergeometric distribution , mathematics , statistics , distribution (mathematics) , hypergeometric function , estimation , vaccination , medicine , econometrics , virology , physics , mathematical analysis , management , quantum mechanics , economics
Abstract A common situation in vaccine efficacy (VE) estimation is dealing with non‐randomly mixing populations, which may subject vaccinated and unvaccinated individuals to a different infection pressure. These conditions may lead to a bias in VE estimates. The derivation of the statistical distribution of the number of vaccinated and infected out of a sample of n infections in a VE trial is essential to develop estimates and their properties. For randomly mixing populations, it has been shown recently that this follows a hypergeometric distribution for ‘all/nothing’ vaccines, whereas it is a non‐central hypergeometric distribution for ‘leaky’ ones. Here it is shown that these distributions still hold under non‐random mixing conditions, provided that mixing preferences and contact rates are independent of vaccination status. These conditions are met when vaccine and placebo are randomized. Copyright © 2001 John Wiley & Sons, Ltd.