# SDM-PSI reference manual

## Introduction

Seed-based *d* Mapping (formerly *Signed Differential Mapping*) with Permutation of Subject Images,
or SDM-PSI, is a statistical technique for meta-analyzing
studies of differences in brain activity or structure that used neuroimaging techniques
such as fMRI, VBM, DTI or PET. It may also refer to a specific piece of software created by
the SDM Project to carry out such meta-analyses.

### Overview of the method

SDM adopted and combined various positive features from previous methods, such as ALE or MKDA, and introduced a series of improvements and novel features. One of the new features, introduced to avoid positive and negative findings in the same voxel as seen in previous methods, was the representation of both positive differences and negative differences in the same map, thus obtaining a signed differential map ('SDM'). Another relevant feature, introduced in version 2.11, was the use of effect sizes (leading to effect-size SDM or 'ES-SDM'), which allows combination of reported peak coordinates with statistical parametric maps, thus allowing more exhaustive and accurate meta-analyses. Yet another improvement, introduced in version 4.11, was the use of anisotropic kernels during the recreation of effect size maps in order to account for the anisotropy in the spatial covariance.

In version 6.11 the new generation of the method (SDM with Permutation of Subject Images, SDM-PSI) was implemented. Some of the new features of SDM-PSI were:

- (nearly) Unbiased estimation of effect sizes based on MetaNSUE algorithms .
- Familywise correction for multiple comparisons using common permutation tests, i.e., permuting subject images (PSI). Note that previous methods used instead tests for spatial convergence, which rely on spatial assumptions that may not be met and have a lower power in the presence of multiple effects .
- Freedman-Lane-based permutation, for its optimal statistical properties .
- Threshold-free cluster enhancement (TFCE) statistics, which was neither too conservative nor too liberal in the simulation work (whereas voxel-based statistics were too strict and cluster-based statistics too liberal) .

The method has five steps. First, coordinates of cluster peaks (e.g. the voxels where the differences between patients and healthy controls were highest), and statistical maps if available, are selected according to SDM inclusion criteria. Second, for studies with peak coordinates, the lower and upper bounds of possible effect size images are estimated. Third, MetaNSUE is used to estimate the most likely effect size and its standard error and to create several imputations based on adding noise to these estimations within the bounds. Fourth, each imputed dataset is meta-analyzed and then Rubin's rules are used to combine these imputed meta-analyzed datasets. Finally, subject images are recreated in order to run a standard permutation test, in which the process is repeated with each set of permuted images and the maximum statistic of the final image is saved; the distribution of these maxima is used to family-wise error-correct for multiple comparisons.

### Inclusion criteria for peak coordinates

It is not strange in neuroimaging studies that some regions (e.g., a priori regions of interest) are more liberally thresholded than the rest of the brain. However, a meta-analysis of studies with such intra-study regional differences in thresholds would be biased towards these regions, as they are more likely to be reported just because authors apply more liberal thresholds in them. In order to overcome this issue SDM introduced a criterion in the selection of the coordinates, which can be summarized as:

"While different studies may employ different thresholds, you should
ensure that the ** same threshold throughout the whole brain** was
used

*within*each included study."

### Pre-processing of studies

Pre-processing of statistical parametric maps is straightforward, they are simply registered to the SDM template and the t-values are converted to effect-sizes. For studies with only peak coordinates, the maps of the lower and upper bounds of possible effect sizes are created for each study within a specific mask (e.g., for gray matter volume, cortical thickness, white matter, TBSS, cerebrospinal fluid and etcetera). This is conducted by means of an anisotropic un-normalized Gaussian Kernel, so that voxels more correlated with the peak coordinate have effect-sizes similar to those of the peak, according to specific gray matter, white matter, fractional anisotropy or cerebrospinal fluid correlation templates. Within a study, values obtained by close anisotropic kernels are combined by square-distance-weighted averaging.

### Statistical comparisons

SDM provides several different statistical analyses in order to complement the main outcome with sensitivity and heterogeneity analyses.

- The main statistical analysis is the mean analysis, which consists in calculating the mean of the voxel values in the different studies. This mean is weighted by the inverse of the variance and accounts for inter-study heterogeneity.

- Subgroup analyses are mean analyses applied to groups of studies to allow the study of heterogeneity.

- Linear model analyses (e.g., meta-regression) are a generalization of the mean analysis to allow comparisons between groups and the study of possible confounds.

The statistical significance of the analyses is assess either using uncorrected p-values or FWER-corrected p-values. Values in an atomical label or coordinate can also be extracted for further processing or graphical presentation.

### SDM software

SDM is software written by the SDM project to aid the meta-analysis of voxel-based neuroimaging data. It is distributed as freeware including both a command-line and a graphical interface.