Scanner three-dimensional images are composed of thousands of tiny cubes (or rectangular cuboids) called voxels, in the same way that digital photographs are composed of thousands of tiny squares called pixels. Voxel-based methods consist of conducting the meta-analytic calculations separately in each voxel of the brain, thus freeing the meta-analysis from aprioristic anatomical definitions. There are different types of voxel-based meta-analyses, including image-based, coordinate-based and mixed image- and coordinate-based meta-analyses.
An image-based meta-analysis should be understood as a voxel-based version of the standard meta-analysis, that is, it consists of thousands of standard meta-analyses, each of them applied to a different voxel [
2,
19]. The data of each study is retrieved from its statistical parametric maps (the three-dimensional images resulting from the comparison between patients and controls), and thus include the whole brain. This technique shares some limitations with any voxel-based analysis, mainly relating to the massive number of statistical tests (that is, one test for each voxel). The correction of multiple comparisons is an unsolved issue, with current methods being either too liberal or too conservative [
19]. For this reason, thresholds based on uncorrected
P-values and cluster-size are usually preferred [
1,
19,
20]. Also, such massive-scale testing prevents a careful visual inspection of the analyses (for example, to describe relevant non-significant trends).
However, the biggest drawback of image-based meta-analyses is that the statistical parametric maps of the original studies are seldom available, therefore seriously limiting the inclusion of studies.
Given the poor availability of statistical parametric maps, early meta-analyses of voxel-based studies consisted of label-based (rather than image-based) reviews, as discussed earlier. These methods quickly evolved to coordinate-based meta-analyses, which in their simplest form consisted of counting, for each voxel, how many activation peaks had been reported within its surroundings [
21]. In the fictitious example, the dots of the label-based review (Figure
3A) would be replaced with spheres (Figure
3B, C), and the brain would not be divided into conventional regions but rather the number of spheres surrounding each voxel would be counted, thus obtaining a count for each voxel. It must be noted that calculations in activation likelihood estimation (ALE) [
22] are not exactly based on counting the number of spheres but on computing the probability of a union, though in practice, the latter behaves like the former.
The use of voxels rather than conventional divisions of the brain improved the anatomical localization of the findings. However, the first available methods, namely ALE and kernel density analysis (KDA) [
21], had some additional issues which enlarged the list of drawbacks of label-based reviews. Specifically, they only counted the total number of peaks, independently of whether they came from the same or different studies, and thus the analysis could not be weighted by sample size and a single study reporting many peaks in close proximity could drive the findings of the whole analysis.
These drawbacks led to the creation of a second generation of coordinate-based meta-analytic methods, mainly evolved versions of KDA, such as multilevel KDA [
23] and parametric voxel-based meta-analysis [
24]; evolved versions of ALE [
25,
26]; and signed differential mapping (SDM) [
3,
27‐
30] (Figure
3D, E), which overcame these limitations by separating the peaks of each study. Moreover, some of these new methods weighted the studies by their sample size and included a series of complementary analyses to assess the reliability and robustness of the findings. One of the methods, SDM, also addressed between-study heterogeneity by reconstructing positive and negative maps in the same image, thus counteracting the effects of studies reporting findings in opposite directions [
31] and incorporating meta-regression methods. Finally, SDM included templates for white matter [
32], allowing multimodal meta-analyses which were not possible with previous methods [
33]. However, these methods still did not employ the standard statistical methods of the ROI-based meta-analyses, for example, they did not weight by the precision of each study.
Several of these methods have recently been applied to mood and anxiety disorders. One such was a meta-analysis of studies investigating bipolar disorder [
34] using SDM, which found patients to have gray matter reductions in the left medial frontal and/or anterior cingulate cortex (MF/ACC) and bilateral anterior insula, with complementary analyses showing findings in the left ACC and right insula to be robust, and left MF/ACC volume to be higher in samples where patients were being treated with lithium. An SDM meta-analysis of studies investigating major depressive disorder also found patients to have gray matter reductions in the MF/ACC [
35], and complementary analyses showed this finding to be robust and more severe in multiple-episode samples. Recent SDM meta-analyses of studies investigating anxiety disorders have also found patients to have gray matter reduction in the MF/ACC [
13], along with abnormalities in the basal ganglia. Specifically, patients with OCD were found to have increased gray matter volume in the bilateral putamen and caudate nuclei [
3], with complementary analyses showing findings in the MF/ACC and left basal ganglia to be robust, and bilateral increases of basal ganglia volume to be higher in samples including patients with higher symptom severity. Conversely, patients with anxiety disorders other than OCD were found to have decreased gray matter volume in the left putamen nucleus [
13].
An example of the use of these methods in functional neuroimaging is the recent study by Delvecchio
et al. [
36], which meta-analyzed the functional brain response to emotional faces using ALE. They found that both patients with bipolar disorder and patients with unipolar depression displayed limbic hyperactivations. However, only patients with bipolar disorder showed a set of hypoactivations in the prefrontal cortex and hyperactivations in the thalamus and basal ganglia. Conversely, only patients with major depressive disorder showed hypoactivations in the sensorimotor cortices. Another example from the anxiety disorders literature is a multilevel KDA meta-analysis, which found that patients showed hyperactivations in the amygdala and insula [
37]. Interestingly, these hyperactivations were more observed in phobias, whilst patients with post-traumatic stress disorder displayed a hypoactivation of the MF/ACC. Finally, an ALE meta-analysis of functional differences in patients with OCD detected that symptom provocation was possibly associated with activation of the orbitofrontal cortex, prefrontal cortex, anterior cingulate cortex, precuneus, premotor cortex, superior temporal gyrus, basal ganglia, hippocampus and uncus [
38].
These methods may also be applied to functional connectivity studies [
39,
40]. Laird
et al., for instance, studied the default mode network by first creating ALE maps, and then deriving meta-analytic co-activation maps [
40]. With this approach, they could identify an affective sub-network component. This approach is promising, given the increasing interest in functional connectivity studies in various mood and anxiety disorders.
Mixed image- and coordinate-based meta-analyses
Recently, effect size SDM (ES-SDM) was designed to allow the combination of studies from which images (statistical parametric maps) are available with studies from which only peak coordinates are reported, thus allowing a more exhaustive inclusion of studies, as well as more accurate estimations [
19].
This is achieved by first using peak coordinates and their statistical values to recreate the statistical parametric maps, and then conducting an image-based meta-analysis. Thus, this method has some statistical advantages as compared to previous coordinate-based methods, namely the use of standard statistical methods (for example, weighting the calculations by both sample size and study precision, use of effect sizes, inclusion and assessment of residual heterogeneity, and so on).
In a meta-analysis of the BOLD response to emotional facial stimuli [
19], the sensitivity to detect real activations (that is, the number of actually activated voxels appearing as significant in the meta-analysis, divided by the total number of actually activated voxels) was similar between ES-SDM (55%) and SDM (51%) when only using peak coordinates. However, the inclusion of the statistical parametric maps led to a gradual and substantial increase of the sensitivity of ES-SDM (73% when the statistical parametric map of one study was included, 87% when the statistical parametric maps of two studies were included, 93% when the statistical parametric maps of three studies were included, and so on). Therefore, given the potential of this new method, we would encourage authors to make their statistical parametric maps widely available to the community on their laboratory websites or via other means.