AUTHOR=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 , Foxe John J. , Goudriaan Anna E. , Hester Robert , Li Chiang-Shan R. , Thompson Wesley K. , Morales Angelica M. , London Edythe D. , Lorenzetti Valentina , Luijten Maartje , Martin-Santos Rocio , Momenan Reza , Paulus Martin P. , Schmaal Lianne , Sinha Rajita , Solowij Nadia , Stein Dan J. , Stein Elliot A. , Uhlmann Anne , van Holst Ruth J. , Veltman Dick J. , Wiers Reinout W. , Yücel Murat , Zhang Sheng , Conrod Patricia , Mackey Scott , Garavan Hugh ,  The ENIGMA Addiction Working Group 

TITLE=Recalibrating single-study effect sizes using hierarchical Bayesian models

JOURNAL=Frontiers in Neuroimaging

VOLUME=Volume 2 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/neuroimaging/articles/10.3389/fnimg.2023.1138193

DOI=10.3389/fnimg.2023.1138193

ISSN=2813-1193

ABSTRACT=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.