A quantitative comparison of different group analysis methods in dynamic causal modeling: dependence on noise and inter- subject variability

Introduction The concept of functional integration aims at relating the specific activity of brain regions to context-dependent interactions between neural regions [1]. Dynamic causal modeling or DCM [2] is a recent method that models functional integration. It allows for estimation of regional interactions in addition to direct effects of stimuli on regional activity. Furthermore, interactions between regions can be modulated by the stimulus context. Parameters are estimated in a Bayesian inversion scheme resulting in a multivariate posterior parameter distribution that enables complex inferences on the network connectivity on a single subject level. On a group level, however, several approaches have been proposed: (a) classic random effects (RFX) second level analysis based on the mean parameter estimates ignoring intra-subject variance (e.g. [3]); (b) a more Bayesian-minded approach combining multivariate single subject posterior parameter distributions according to Bayes’ theorem [4,5]; (c) temporal averaging [6]. A Bayesian second level analysis would allow for more complex inferences using e.g. arbitrary thresholds and it avoids the problem of multiple comparisons. Despite all these advantages, Bayesian second level analysis has only been used sporadically in DCM (e.g. [7]) as a product of Gaussian distributions may lead to counterintuitive results if the participating distributions have differing correlation coefficients (see fig. 1). Here we aimed at comparing estimation accuracy of these three averaging methods and their dependence on noise level as well as population heterogeneity based on simulated data.