Projects:LocalStatisticalAnalysisViaPermutationTests

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Statistics

In our statistical framework, group differences between groups of surfaces are computed locally for every surface point using the standard robust Hotelling T^2 two sample metric. Statistical p-values, both raw and corrected for multiple comparisons, result in significance maps. Additional visualization of the group tests are provided via mean difference magnitude and vector maps, as well as maps of the group covariance information.

The local shape analysis involves testing from a few to many thousands of hypothesis (one per surface ele- ment) for statistically significant effects. It is thus important to control for the multiple testing problem, and the most common measure of multiple false positives is the familywise error rate (FWER). The multiple testing problem has been an active area of research in the functional neuroimaging community. One of the widely used methods in the analysis of neuroimaging data makes inferences based on the maximum distribution. In our work, we are employing non-parametric permutation tests to estimate uniformly sensitive extrema distributions. The correction method is based on computing first the local p-values using permutation tests. The minimum of these p-values across the surface is then computed for every permutation. The appropriate corrected p-value at level α can then be obtained by the computing the value at the α-quantile in the histogram of these minimum values. Using the minimum statistic of the p-values, this method correctly controls for the FWER, or the false positives, but no control of the false negatives is provided. The resulting corrected local significance values can thus be regarded as pessimistic estimates akin to a simple Bonferroni correctection.

Additionally to the non-parametric permutation correction, we have also implemented and applied a False Discovery Rate Estimation (FDR) method. The innovation of this procedure is that it controls the expected proportion of false positives only among those tests for which a local significance has been detected. The FDR method thus allows an expected proportion (usually 5%) of the FDR corrected significance values to be falsely positive. The correction using FDR provides an interpretable and adaptive criterion with higher power than the non-parametric permutation tests. FDR thus results in a less conservative estimate of the false-negatives.

Current development is extending the framework to include subject variables, such as gender, age and clinical scores into the current pure group difference computation.