# A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

Stéphane Laurent; Catherine Legrand

ESAIM: Probability and Statistics (2012)

- Volume: 16, page 375-398
- ISSN: 1292-8100

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topLaurent, Stéphane, and Legrand, Catherine. "A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials." ESAIM: Probability and Statistics 16 (2012): 375-398. <http://eudml.org/doc/273609>.

@article{Laurent2012,

abstract = {In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions $(\lambda S)$x1d4ab;(λS) and $(\mu T)$x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. 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 φ is the parameter of interest. We also define a family of reference priors with partial information on μ while remaining uninformative about φ. We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals for φ enjoy attractive frequentist properties when using reference priors, a typical property of reference priors.},

author = {Laurent, Stéphane, Legrand, Catherine},

journal = {ESAIM: Probability and Statistics},

keywords = {Poisson rates; relative risk; vaccine efficacy; partial immunity model; semi-conjugate family; reference prior; Jeffreys’ prior; frequentist coverage; beta prime distribution; beta-negative binomial distribution; Jeffreys prior},

language = {eng},

pages = {375-398},

publisher = {EDP-Sciences},

title = {A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials},

url = {http://eudml.org/doc/273609},

volume = {16},

year = {2012},

}

TY - JOUR

AU - Laurent, Stéphane

AU - Legrand, Catherine

TI - A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

JO - ESAIM: Probability and Statistics

PY - 2012

PB - EDP-Sciences

VL - 16

SP - 375

EP - 398

AB - In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions $(\lambda S)$x1d4ab;(λS) and $(\mu T)$x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. 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 φ is the parameter of interest. We also define a family of reference priors with partial information on μ while remaining uninformative about φ. We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals for φ enjoy attractive frequentist properties when using reference priors, a typical property of reference priors.

LA - eng

KW - Poisson rates; relative risk; vaccine efficacy; partial immunity model; semi-conjugate family; reference prior; Jeffreys’ prior; frequentist coverage; beta prime distribution; beta-negative binomial distribution; Jeffreys prior

UR - http://eudml.org/doc/273609

ER -

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