A BAYESIAN FRAMEWORK FOR THE RATIO OF TWO POISSON RATES IN THE CONTEXT OF VACCINE EFFICACY TRIALS

作者：Laurent Stephane^*; Legrand Catherine

来源：ESAIM: Probability and Statistics , 2012, 16: 375-398.

DOI：10.1051/ps/2010018

• Poisson rates
• relative risk
• vaccine efficacy
• partial immunity model
• semi-conjugate family
• reference prior
• Jeffreys%26apos
• prior
• frequentist coverage
• beta prime distribution
• beta-negative binomial distribution

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions P(lambda S) and P(mu T) and we are interested in performing statistical inference on the ratio phi = lambda/mu 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, phi is called the relative risk and the statistical model is called %26apos;partial immunity model%26apos;. 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 phi is the parameter of interest. We also define a family of reference priors with partial information on mu while remaining uninformative about phi. We notice that these priors belong to the semi-conjugate family. We then demonstrate using numerical examples that Bayesian credible intervals for phi enjoy attractive frequentist properties when using reference priors, a typical property of reference priors.

• 出版日期2012-9