Bayesian meta-analysis for rare events
Creators: name: Alqasem, Ohud
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 490501
subject: Applied statistics
classificationCode: 490502
subject: Biostatistics
classificationCode: 490508
subject: Statistical data science

description: Meta-analysis can be described as a method for summarising quantitative research results or as a method for estimating the quantitative effect size based on individual investigations. In clinical trials, a meta-analysis determines a drug’s therapy impact, i.e. the difference between the treatment and control groups. Examining the research results from multiple studies simultaneously is more reliable than observing a single study. Comparability of data from constituent studies is crucial to any meta-analysis of randomised trials.

In medication studies, some drugs have rare adverse effects. Due to such infrequent occurrences, a "sparse data" problem arises in meta-analysis studies. As a result of having sparse data, the treatment effects may be indefinable or nil. Using a continuous distribution to approximate a discrete distribution requires a continuity correction by adding a small number to the zero cells of the contingency table to deal with sparse data. In a meta- analysis model, it is essential to account for differences in the design of tested studies regarding quality, sample size, and population. Therefore, fixed-effects or random-effects models are utilised. Fixed effects models presume no inter-study variability; if sample sizes are large, all studies should provide the same conclusions. However, random effect models accommodate for inter- and intra-study variability. They presume that there are differences within each research and between studies. Different statistical methods are utilised to perform a meta-analysis, including the Mantel-Haenszel method, Peto’s method, the DerSimonian and Laird method and the inverse variance method with various continuity corrections under fixed- and random-effects models. Another option for dealing with the rare events problem, boundary estimates of the in-between study variance and the precision of treatment effect estimates is to apply the Bayesian approach for meta-analysis with rare events, which allows for a consistent probabilistic approach to the uncertainty created by the sparse data. To evaluate the treatment effect and the in-between study variance, the normal-normal hierarchical model, the binomial-normal hierarchical model, and the beta-binomial model for risk differences Bayesian models are applied with different prior distributions and parameter specifications. As another approach, the Arc-sine difference is a promising transformation since it deals with the issues of rare events and enhances the estimation of in-between study variance. However, the Arc-sine difference is rarely used in the medical literature. Bayesian models with the truncated normal and truncated gamma prior distributions are implemented to execute Bayesian meta-analysis for estimating the treatment effect and the in-between study variance using the Arc-sine difference.

This research is performed to determine i) the best-performing continuity correction approach in case of the presence of sparse data, ii) if either fixed- or random-effects model is effective when performing meta-analysis with rare events, iii) to what extent different prior distribution choices influence the performance measures in the meta-analysis of rare events and vi) how do Bayesian models alone or in combination with Arc-sine difference deal with rare events in estimating the treatment effect and the in-between study variance. In order to accomplish these objectives, both fixed- and random-effects models, along with a variety of continuity adjustments, are utilised to deal with the presence of sparse data. After that, the frequentist and the Bayesian approaches are contrasted through real-world data of an off-pump coronary artery surgery. Extensive numerical experiments are con- ducted with simulated data. The efficiency of applying Bayesian meta-analysis methods while performing the odds ratio, risk difference and Arc-sine difference as a treatment effect estimator is investigated.

The results show that meta-analysis performance is highly sensitive to settings and approaches such as continuity correction, group imbalance, statistical methodology (fixed- versus random-effects models), and the true level of in-between-study variance. The Arc- sine difference, a novel effect estimate, naturally handles sparse data and is not impacted by the group imbalances. This approach opens up new avenues for investigating the effect estimates. Including it in Bayesian meta-analysis is a non-expensive task of performing a meta-analysis. Furthermore, applying the Arc-sine difference under the Bayesian estimation improves the estimation of in-between-study variance.

Overall, we found an Arc-sine approach is useful for estimating the treatment effect via meta-analysis for rare events. Furthermore, the study showed that combining the Arc- sine difference with the Bayesian technique helps avoid issues related to rare events and achieves a more accurate estimation of the in-between study variance. A Bayesian estimation is a beneficial approach to dealing with complications of the frequentist approaches and attaining a proper estimation of the in-between study variance and the treatment effect. This research assists the investigators in implementing suitable prior distributions to evaluate the treatment effect and the in-between study variance.