2026/07/28 by Kotaro Sasaki, Hisashi Noma
Mathematics · #stat.ME
13 pages
arxiv created 2026/07/29 · arxiv updated 2026/07/30
Meta-analyses of proportions often involve sparse event counts and 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 ordinary maximum likelihood estimator (MLE) may suffer from finite-sample bias when few studies are available or the mean event probability is close to the boundary. In this article, we propose a maximum penalized likelihood estimator based on the Jeffreys-prior penalty, which has shown favorable finite-sample bias and stability properties in sparse-data models. We also develop Wald-type and profile penalized likelihood confidence intervals (CIs). In a simulation study, the proposed estimator generally achieved higher convergence rates, lower bias, and lower root mean squared error than the ordinary MLE, particularly with fewer studies or lower event probabilities. Additionally, the profile penalized likelihood CIs maintained coverage close to the nominal level. The proposed method provides a useful alternative for meta-analyses of rare-event proportions.