Article (Scientific journals)
A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials
Laurent, Stéphane; Legrand, Catherine
2011In ESAIM: Probability and Statistics
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Keywords :
Bayesian inference; Reference priors; Intrinsic loss
Abstract :
[en] In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions and we are interested in performing statistical inference on the ratio of the two incidence rates, called the relative risk in vaccine efficacy trials, in which context x and y are the numbers of cases in the vaccine and the control groups respectively. In this paper we start by defining a natural semi-conjugate family of prior distributions for this model, allowing straightforward computation of the posterior inference. Following theory on reference priors, we define the reference prior for the partial immunity model when the relative risk is the parameter of interest. We also define a family of reference priors with partial information on the incidence rate of the unvaccinated population while remaining uninformative about the relative risk . We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals enjoy attractive frequentist properties when using reference priors, a typical property of reference priors.
Disciplines :
Mathematics
Author, co-author :
Laurent, Stéphane ;  Université Catholique de Louvain - UCL
Legrand, Catherine;  Université Catholique de Louvain - UCL
Language :
English
Title :
A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials
Publication date :
2011
Journal title :
ESAIM: Probability and Statistics
ISSN :
1292-8100
eISSN :
1262-3318
Publisher :
EDP Sciences, France
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
IAP research network
Available on ORBi :
since 26 November 2010

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