Recalibrating single-study effect sizes using hierarchical Bayesian models - Cao, Zhipeng; McCabe, Matthew; Callas, Peter; Cupertino, Renata B.; Ottino-González, Jonatan; Murphy, Alistair; Pancholi, Devarshi; Schwab, Nathan; Catherine, Orr; Hutchison, Kent; Cousijn, Janna; Dagher, Alain; et al. (Frontiers in Neuroimaging, 2023)
Despite growing concerns about effect sizes being commonly inflated in small neuroimaging studies, no study has yet addressed how to recalibrate effect size estimates for small samples.Here, we propose a hierarchical Bayesian model to adjust the magnitude of single-study effect sizes while incorporating a tailored estimation of sampling variance. First, we estimated the effect sizes of case-control differences on brain structural features between individuals who were dependent on alcohol, nicotine, cocaine, methamphetamine, or cannabis and nondependent participants for 21 individual studies (Total cases: 903; Total controls: 996). Then, the studyspecific effect sizes were modeled using a hierarchical Bayesian approach in which the parameters of the study-specific effect size distributions were sampled from a higher-order overarching distribution. The posterior distribution of the overarching and study-specific parameters was approximated using the Gibbs sampling method. The results showed shrinkage of the posterior distribution of the study-specific estimates towards the overarching estimates given the original effect sizes observed in individual studies. Differences between the original effect sizes (i.e., Cohen's d) and the point estimate of the posterior distribution ranged from 0 to 0.97. The magnitude of adjustment was negatively correlated with the sample size (r=-0.27, p<0.001) and positively correlated with empirically estimated sampling variance (r=0.40, p<0.001), suggesting studies with smaller samples and larger sampling variance tended to have greater adjustments.The present work demonstrates the utility of the hierarchical Bayesian model in recalibrating single-study effect sizes using information obtained from similar studies. Thus, Bayesian utilization of existing knowledge can be an alternative approach to improve the effect size estimation of individual studies.