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FLAME - Multi-Level Modelling for Group Analysis

FMRI studies are typically used to address questions about activation effects in populations of subjects. This involves a multi-subject and/or multi-session approach where data are analysed in such a way as to allow for hypothesis tests at the group level [19]. In order to be able to generate results that accurately extend to the wider population, we need to account for the fact that these limited samples from the population are random quantities with associated random effects variances. We can formulate the problem of group statistics hierarchically [3]; the different levels of the hierachy could be separate GLMs at within-session level, within-subject-cross-session level and cross-subject level.

In [17] the hierarchical model is approached using all time-series data as input to a single ``all-in-one'' analysis. However, in neuro-imaging, where the human and computational costs involved in data analysis are relatively high, it is desirable to be able to make top-level inferences using the results of separate lower-level analyses without the need to re-analyse the lower-level data, an approach commonly referred to as the summary statistics approach to FMRI analysis [19]. In [3] we showed that top-level inference using the ``split-level summary statistics'' approach can be made exactly equivalent to an all-in-one approach if we feed up the correct summary statistics (in particular, the covariances from lower levels). It was demonstrated that by taking into account lower-level covariances and heterogeneity, a substantial increase in higher-level z-statistic is possible. Another reason for wanting to carry up lower-level covariances to higher-level analyses is that it is not then necessary for lower-level design matrices to be identical (i.e., ``balanced designs'' - for example having the same number of time points or event timings).

The investigations covered in [3] assume that all variance components are known; taking this work further, in [39], using a fully Bayesian approach, we show the split-level model equivalence taking into account that the variance components are unknown.

There are three main contributions presented in [39]. Firstly, ``reference priors'' were introduced to neuro-imaging; due to the typically small numbers of sessions or subjects in neuro-imaging the choice of prior is critical. Secondly, two practical inference techniques were developed for multi-level hierarchies: a fast approach using maximum a posterior estimates and a slower, more accurate approach using Markov Chain Monte Carlo (MCMC). Thirdly, it was shown that we can infer on the top-level of multi-level hierarchies by inferring on the split levels separately and passing summary statistics (multivariate non-central t-distributions) between them. The use of the lower-level covariance information contained in these summary statistics overcomes the ``negative variance'' problem experienced using previous approaches to split-level analyses [19].

This research has been implemented as FLAME (FMRIB's Local Analysis of Mixed Effects), the higher-level modelling tool used inside FEAT. One additional advantage of using FLAME is that it is easy to model and estimate different variances for different groups of subjects in the model. For example, an unpaired two-group comparison (e.g. between controls and patients) can be analysed with separate estimates of variance for each group.


next up previous
Next: FEAT - A Complete Up: Functional MRI Analysis Research Previous: FILM - Voxelwise Timeseries
Stephen Smith 2005-02-25