Tests for comparing images based on randomization and permutation methods

Tests comparing image sets can play a critical role in PET research, providing a yes-no answer to the question "Are two image sets different?" The statistical goal is to determine how often observed differences would occur by chance alone. We examined randomization methods to provide several omnibus test for PET images and compared these tests with two currently used methods. In the first series of analyses, normally distributed image data were simulated fulfilling the requirements of standard statistical tests. These analyses generated power estimates and compared the various test statistics under optimal conditions. Varying whether the standard deviations were local or pooled estimates provided an assessment of a distinguishing feature between the SPM and Montreal methods. In a second series of analyses, we more closely simulated current PET acquisition and analysis techniques. Finally, PET images from normal subjects were used as an example of randomization. Randomization proved to be a highly flexible and powerful statistical procedure. Furthermore, the randomization test does not require extensive and unrealistic statistical assumptions made by standard procedures currently in use.