Multi-subject analyses with dynamic causal modeling

Abstract

Currently, most studies that employ dynamic causal modeling (DCM) use random-effects (RFX) analysis to make group inferences, applying a second-level frequentist test to subjects' parameter estimates. In some instances, however, fixed-effects (FFX) analysis can be more appropriate. Such analyses can be implemented by combining the subjects' posterior densities according to Bayes' theorem either on a multivariate (Bayesian parameter averaging or BPA) or univariate basis (posterior variance weighted averaging or PVWA), or by applying DCM to time-series averaged across subjects beforehand (temporal averaging or TA). While all these FFX approaches have the advantage of allowing for Bayesian inferences on parameters a systematic comparison of their statistical properties has been lacking so far.Based on simulated data generated from a two-region network we examined the effects of signalto-noise ratio (SNR) and population heterogeneity on group-level parameter estimates. Data sets were simulated assuming either a homogeneous large population (N=60) with constant connectivities across subjects or a heterogeneous population with varying parameters. TA showed advantages at lower SNR but is limited in its applicability. Because BPA and PVWA take into account posterior (co)variance structure, they can yield non-intuitive results when only considering posterior means. This problem is relevant for high SNR data, pronounced parameter interdependencies and when FFX assumptions are violated (i.e. inhomogeneous groups). It diminishes with decreasing SNR and is absent for models with independent parameters or when FFX assumptions are appropriate. Group results obtained with these FFX approaches should therefore be interpreted carefully by considering estimates of dependencies among model parameters.

Focusing Attention on the Health Aspects of Foods Changes Value Signals in vmPFC and Improves Dietary Choice

“…Fifth, we used Bayesian parameter averaging (Lee, 1989;Kasess et al, 2010) to estimate the magnitudes and probabilities of each coupling parameter, as well as the magnitudes and effects with which the connections are modulated by different task events or activity in other regions. Briefly, this method uses the estimated posterior densities for each connectivity parameter for each subject, and combines them to obtain a single conditional density for the group by treating the posterior density of the first subject as the prior density for the second subject and continuing this process up to the nth subject.…”

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“…( Kasess et al, 2010;Stephan et al, 2010). Note that the fixed and modulatory parameters were always scale parameters (exponentiated) to ensure positivity as per convention for two-state DCMs, so that the extrinsic connections are always excitatory (Marreiros et al, 2008).…”

Graphical Models of Functional MRI Data for Assessing Brain Connectivity

“…PPC is the abbreviation for partial correlation coefficient; m x is the mean of x, and m y is that of y. This figure is from (Kasess et al, 2010).…”

“…Technically this degrades group analysis to learning a model for a single subject, for which both classical (Heckerman et al, 1995) and Bayesian (Neumann & Lohmann, 2003) approaches have been developed. When the group is homogeneous or inter-subject variability follows certain regular distributions, this approach could increase detection sensitivity, because pooling can build a relatively large data set, and averaging can enhance the signal-to-noise ratio (Kasess et al, 2010). However, when the group becomes more heterogeneous, this approach could lead to undesirable and misleading results (Kasess et al, 2010).…”

“…When the group is homogeneous or inter-subject variability follows certain regular distributions, this approach could increase detection sensitivity, because pooling can build a relatively large data set, and averaging can enhance the signal-to-noise ratio (Kasess et al, 2010). However, when the group becomes more heterogeneous, this approach could lead to undesirable and misleading results (Kasess et al, 2010). Fig.…”