A Bayesian sensitivity study of risk difference in the meta-analysis of binary outcomes from sparse data

Abstract

In most cases, including those of discrete random variables, statistical meta-analysis is carried out using the normal random effect model. The authors argue that normal approximation does not always properly reflect the underlying uncertainty of the original discrete data. Furthermore, in the presence of rare events the results from this approximation can be very poor. This review proposes a Bayesian meta-analysis to address binary outcomes from sparse data and also introduces a simple way to examine the sensitivity of the quantities of interest in the meta-analysis with respect to the structure dependence selected. The findings suggest that for binary outcomes data it is possible to develop a Bayesian procedure, which can be directly applied to sparse data without ad hoc corrections. By choosing a suitable class of linking distributions, the authors found that a Bayesian robustness study can be easily implemented. For illustrative purposes, an example with real data is analyzed using the proposed Bayesian meta-analysis for binomial sparse data.

Keywords:

• Bayesian inference
• intrinsic link distribution
• meta-predictive distribution
• testing on meta-parameters

Financial & competing interests disclosure

The authors were partially supported by Grants ECO2013-47092 (Ministerio de Economía y Competitividad, Spain) and MTM2011-28945 (Ministerio de Ciencia e Innovación, Spain). The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this manuscript.

Key issues

• Bayesian random-effect Normal models should be used with caution for meta-analysis of binomial sparse data.

• A Bayesian sensitivity study for discrete sparse data can be developed choosing a suitable family of linking distributions.

• The intrinsic family of priors shows an appropriated behaviour as a link distribution class.

• When a robust Bayesian approach is adopted, we use ranges of measures for our quantities of interest insted of a unique measure.