title: Bayesian robustness in meta-analysis for studies with zero responses.
abstract: Statistical meta-analysis is mostly carried out with the help of the random effect normal model, including the case of discrete random variables. We argue that the normal approximation is not always able to adequately capture the underlying uncertainty of the original discrete data. Furthermore, when we examine the influence of the prior distributions considered, in the presence of rare events, the results from this approximation can be very poor. In order to assess the robustness of the quantities of interest in meta-analysis with respect to the choice of priors, this paper proposes an alternative Bayesian model for binomial random variables with several zero responses. Particular attention is paid to the coherence between the prior distributions of the study model parameters and the meta-parameter. Thus, our method introduces a simple way to examine the sensitivity of these quantities to the structure dependence selected for study. For illustrative purposes, an example with real data is analysed, using the proposed Bayesian meta-analysis model for binomial sparse data. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Department of Quantitative Methods and TiDES Institute, University of Las Palmas de GC, Las Palmas de Gran Canaria, 35017, Spain.
authors.forename: F J
authors.initials: FJ
authors.lastname: Vázquez
authors.affiliation: Department of Statistics and O.R., University of Granada, Granada, 18071, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Moreno
authors.affiliation: Department of Quantitative Methods and TiDES Institute, University of Las Palmas de GC, Las Palmas de Gran Canaria, 35017, Spain.
authors.forename: M A
authors.initials: MA
authors.lastname: Negrín
authors.affiliation: Department of Quantitative Methods and TiDES Institute, University of Las Palmas de GC, Las Palmas de Gran Canaria, 35017, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Martel
mesh_terms: D001499:Bayes Theorem; D002986:Clinical Trials as Topic / Q000379:methods*; D003627:Data Interpretation, Statistical; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D035501:Uncertainty
keywords: Bayesian inference; Sarmanov and intrinsic link distribution; noninformative priors; testing on meta-parameters