TY - JOUR
T1 - Urn models and vaccine efficacy estimation
AU - Hernández-Suárez, Carlos M.
AU - Castillo-Chavez, Carlos
PY - 2000/3/30
Y1 - 2000/3/30
N2 - 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.
AB - 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.
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U2 - 10.1002/(SICI)1097-0258(20000330)19:6<827::AID-SIM382>3.0.CO;2-B
DO - 10.1002/(SICI)1097-0258(20000330)19:6<827::AID-SIM382>3.0.CO;2-B
M3 - Review article
C2 - 10734286
AN - SCOPUS:0343238292
SN - 0277-6715
VL - 19
SP - 827
EP - 835
JO - Statistics in Medicine
JF - Statistics in Medicine
IS - 6
ER -