Parametric coordinate-based meta-analysis: valid effect size meta-analysis of studies with differing statistical thresholds

Abstract

The aim of coordinate-based meta-analysis is to provide valid quantitative summaries of the literature, while taking into account the specificities of neuroimaging data. Neuroimaging findings are usually reported as coordinates of effects surviving multiple comparison correction through statistical thresholding. Different studies may use widely differing censoring thresholds, ranging from strict family-wise corrections to more lenient "uncorrected"p-values. However, standard meta-analysis methods do not take into account these differences, as findings from studies with varying thresholds are treated as though they were equivalent. The present paper details a development in coordinate-based meta-analysis which addresses this limitation. Parametric coordinate-based meta-analysis (PCM) computes valid estimates from thresholded measurements, integrating significant findings with the information generated by subthreshold measurements to produce asymptotically unbiased meta-analytical summaries. The method is validated through simulated data, and demonstrated in a real data meta-analysis of structural differences in grey matter density in depression. PCM demonstrates a sensitivity that is comparable or superior to existing coordinate-based meta-analysis methods, and demonstrates high agreement between its estimates and those obtained from the meta-analysis of unthresholded manual volumetric measurements. PCM constitutes a powerful approach to meta-analysis, able to generate valid and unbiased effect-size summaries of studies with different statistical thresholds, and also allowing the integration of whole brain and region-of-interest studies.