Penalized likelihood inference for beta-binomial meta-analysis of proportions of rare events

2026-07-28

AI Summary

This study addresses the finite-sample bias of maximum likelihood estimation (MLE) in meta-analyses of rare events, which arises due to data sparsity and studies reporting zero events. To mitigate this issue, the authors propose a maximum penalized likelihood estimation method within the beta-binomial random-effects model by incorporating a penalty term derived from Jeffreys’ prior. They further develop corresponding Wald-type and profile penalized likelihood confidence intervals. The proposed approach substantially enhances estimation stability and inferential reliability in sparse-data settings. Simulation results demonstrate that, particularly when the number of studies is small or event rates are low, the new method outperforms conventional MLE in terms of convergence, bias, and root mean squared error, while its confidence intervals maintain nominal coverage probabilities effectively.

Abstract

In meta-analyses of proportions, the event of interest is often rare, resulting in sparse event counts and frequent zero-event studies. The beta-binomial model has been used as a flexible random-effects model for pooling overdispersed and rare-event proportions. However, the commonly used maximum likelihood estimator (MLE) may be subject to finite-sample bias, which may be particularly relevant when the number of studies is small or the mean event probability is close to the boundary. In this article, we propose a maximum penalized likelihood estimator for the beta-binomial random-effects model. The proposed estimator is obtained by maximizing the log-likelihood augmented by the Jeffreys-prior penalty, which has shown favorable finite-sample bias and stability properties in a range of sparse-data models. In addition to Wald-type confidence intervals (CIs), we introduce profile penalized likelihood CIs as a potentially more reliable approach to inference in sparse-data settings. A simulation study showed that the proposed estimator generally outperformed the ordinary MLE, particularly in settings with fewer studies or lower event probabilities, in terms of convergence rate, bias, and root mean squared error. Additionally, the profile penalized likelihood CIs effectively maintained coverage close to the nominal level. The proposed method provides a useful alternative to ordinary MLE for meta-analyses of rare-event proportions.

Problem

• rare events
• meta-analysis
• beta-binomial model
• finite-sample bias
• sparse data

Innovation

• penalized likelihood
• beta-binomial model
• rare-event meta-analysis
• Jeffreys prior
• profile confidence interval