The coordinate-based meta-analysis of neuroimaging data

Abstract

Neuroimaging meta-analysis is an area of growing interest in statistics. The special characteristics of neuroimaging data render classical meta-analysis methods inapplicable and therefore new methods have been developed. We review existing methodologies, explaining the benefits and drawbacks of each. A demonstration on a real dataset of emotion studies is included. We discuss some still-open problems in the field to highlight the need for future research.

Keywords: functional magnetic resonance imaging; meta-analysis; neuroimaging.

Fig 1

An average brain in MNI space. Note the directional labels at the edge of each panel: P for Posterior, A for Anterior, S for Superior, I for Inferior, L for Left and R for Right. The origin approximately corresponds to an anatomical structure known as the anterior commissure.

Fig 2

Realisation of the BHICP model for 3 studies. At level 3 (top) latent population centres (grey, z) lie. At level 2 (middle) we have centres of multiple foci (black). These come either directly from population centres (squares, y_i) or from background noise (triangles, y_i∅). Level 1 (bottom) contains the data (x_i). These are multiple (red, ${\mathbf{x}}_i^1$) or singleton (green, ${\mathbf{x}}_i^0$) foci. Singletons come either directly from population centres (dots, ${\mathbf{x}}_{i\xi }^0$) or from a background Poisson process (asterisks, ${\mathbf{x}}_{i\varnothing }^0$).

Fig 3

Results of the simulation study. Power properties of the ALE algorithm are plotted against the proportion of valid studies p. Top left: probability that at least one center is detected. Top right: probability that all 8 centers are detected. Bottom left: mean number of centers detected. Bottom right: mean voxel-wise true positive rate.

Fig 4

Results of the simulation study. Power properties of the ALE algorithm are plotted against the total number of valid studies Ip. Top left: probability that at least one center is detected. Top right: probability that all 8 centers are detected. Bottom left: mean number of centers detected. Bottom right: mean voxel-wise true positive rate.

Fig 5

Qualitative comparison of the CBMA methods in regions of high clustering of foci. Column 1 is the MKDA statistic m(v), column 2 is the ALE statistic ℓ(v), column 3 is the SDM statistic s(v), and column 4 is the study activation center intensity ${\sum }_{i=1}^I[{\lambda }_i^0(v)+{\rho }_i(v)]$ for the BHICP. Rows 1–3 correspond to axial slices z = −22, z = −16 and z = −2, respectively. Note that differences in brain shapes across methods are simply due to different masks used by the various algorithms.

Fig 6

Power properties against the proportion of valid studies p, using the MKDA (left panel) and SDM (right panel) kernels. Top left (both panels): probability that at least one center is detected. Top right (both panels): probability that all 8 centers are detected. Bottom left (both panels): mean number of centers detected. Bottom right (both panels): mean voxel-wise true positive rate.

Fig 7

Power properties against the total number of valid studies Ip, using the MKDA (left panel) and SDM (right panel) kernels. Top left (both panels): probability that at least one center is detected. Top right (both panels): probability that all 8 centers are detected. Bottom left (both panels): mean number of centers detected. Bottom right (both panels): mean voxel-wise true positive rate.

Fig 8

Convergence diagnostics for the BHICP analysis of the emotions dataset. Top panel: traceplots for the total number of population centers (left), integrated intensity in the left amygdala (middle), and integrated intensity in the right amygdala (right) obtained with two different chains initialised at overdispersed starting values. Bottom panel: mean voxel-wise posterior activation center intensity ${\sum }_{i=1}^I[{\lambda }_i^0(v)+{\rho }_i(v)]$ at axial slices z = −22 (left), z = −16 (middle) and z = −2 (right), as obtained from the second run of the model.