Publication bias – when non-significant results (from smaller studies) become underrepresented in the literature - results in an overestimation of average effect sizes. Several statistical methods have been developed to detect and describe publication bias, and to provide adjusted average effect sizes. However, these approaches generally oversimplify reality. Here, a novel Bayesian model is developed which can explicitly model changes in publication bias with covariates leading to a better understanding of the sampling procedure of publication bias, and more realistic adjusted effect sizes. This new approach is applied to simulated data and to empirical data from a recent meta-analysis of associations between fluctuating asymmetry and health and quality in humans.
The Markov Chain Monte Carlo showed rapid convergence. The simulations showed that the new approach detects associations between publication bias and sample size and provides unbiased average effect sizes. The estimated average effect size for the empirical dataset was close to those reported using other methods. The level of publication bias dropped rapidly when sample sizes approached 150 individuals. Posterior predictive checks showed an overall appropriate model fit.
The new model proposed here allows an objective analysis of how the selection process due to publication bias changes with covariates. The exploration of the performance of this new approach indicated advantages over existing methods. It can thus be concluded that the model provides an innovative way to detect and study publication bias and reaches more realistic adjusted effect sizes.