Background: The Copas parametric model is aimed at exploring the potential impact of publication bias via sensitivity analysis, by making assumptions regarding the probability of publication of individual studies related to the standard error of their effect sizes (Copas and Shi). Review authors often have prior knowledge about the extent of selection in the set of studies included in a meta-analysis. However, a Bayesian implementation of the Copas model has not been studied yet.
Objectives: To present a Bayesian selection model for publication bias and to extend it to the case of multiple-treatments meta-analysis.
Methods: We explored various models corresponding to the shape of the association between precision and probability of publication. We used a dataset of antidepressant studies submitted to the US regulatory agency (Food and Drug Administration), according to Turner and colleagues (Turner et al.). We took advantage of the greater flexibility offered in the Bayesian context to incorporate in the model prior information on the extent and strength of selection. To derive prior distributions, we used both external data and an elicitation process of expert opinion.
Results: The Copas model assumes a likelihood approach which requires strong assumptions for the model to be identified and a sensitivity analysis is employed. Bayesian implementation using informative priors provides a solution to this problem by explaining adequately the selection process and giving clear-cut results. Extension of the model for multiple-treatments meta-analysis allows incorporation of comparison-specific priors beliefs and thus allowed a flexible class of models to be fit.
Conclusions: A Bayesian framework utilizing expert opinion provided a powerful and easily understood approach.
Copas JB, Shi JQ. A sensitivity analysis for publication bias in systematic reviews. Stat Methods Med Res. 2001;10(4):251 -65.
Turner EH, Matthews AM, Linardatos E, Tell RA, Rosenthal R. Selective publication of antidepressant trials and its influence on apparent efficacy. N Engl J Med. 2008;358(3):252 -60.