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

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.

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.

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.

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.