title: A note on the distribution of the number of vaccinated infected under non-random mixing conditions.
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.
authors: Universidad de Colima, Facultad de Ciencias, Apartado Postal 25, Colima, 28000, Mexico. cmh2@cgic.ucol.mx
authors: C M
authors: CM
authors: Hernández-Suárez
mesh_terms: D006801:Humans; D018448:Models, Immunological; D014611:Vaccination / Q000592:standards*; D014612:Vaccines / Q000276:immunology* / Q000592:standards
chemical_list: D014612:Vaccines