Zero-Inflated Binomial Model for Meta-Analysis and Safety-Signal Detection

Background: Meta-analysis of related trials can provide an overall measure of safety-signal accounting for variability across studies. In addition to an overall measure, researchers may often be interested in study-specific measures to assess safety of the product. Likelihood ratio tests (LRT) methods serve this purpose by identifying studies that appear to show a safety concern. In this paper, we present a Bayesian approach. Despite having good statistical properties, the LRT methods may not be suitable for the meta-analysis of randomized controlled trials (RCTs) when there are several studies with zero events in at least one arm.

Methods: In this article, we describe a Bayesian framework using a Zero-inflated binomial model with spike-and-slab parameterization for the treatment effects. In addition to providing an overall meta-analytic estimate, this method provides posterior probability of a safety-signal for each study.

Results: We illustrate the approach using two published data sets comprising several randomized controlled trials (RCTs) each and compare the model performance for different choices of priors for treatment effect.

Discussion: The proposed Bayesian methodological framework is useful to identify potential signal for single adverse event and to determine overall meta-analytic estimate of the magnitude of the signal. Practitioners may consider this approach as an alternative to the frequentist's LRT approach discussed in Jung et al. (J Biopharm Stat 31:47-54, 2020) when there are zero events in either the treatment arm or the control arm. In the future, this approach can be further extended to accommodate multiple adverse events.