Revisiting multi-subject random effects in fMRI: advocating prevalence estimation

Random effect analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation within the study group since in order to be significant, an activation has to be larger than the inter-subject variability. Indeed, detected regions are smaller when using random effect analysis versus fixed effects. The statistical assumptions behind the classic random effect model are that the effect in each location is normally distributed over subjects, and "activation" refers to a non-null mean effect. We argue that this model is unrealistic compared to the true population variability, where due to function-anatomy inconsistencies and registration anomalies, some of the subjects are active and some are not at each brain location. We propose a Gaussian-mixture-random-effect that amortizes between-subject spatial disagreement and quantifies it using the prevalence of activation at each location. We present a formal definition and an estimation procedure of this prevalence. The end result of the proposed analysis is a map of the prevalence at locations with significant activation, highlighting activation regions that are common over many brains. Prevalence estimation has several desirable properties: (a) It is more informative than the typical active/inactive paradigm. (b) In contrast to the usual display of p-values in activated regions - which trivially converge to 0 for large sample sizes - prevalence estimates converge to the true prevalence.