Performing Group Difference Testing on Graph Structured Data from GANs: Analysis and Applications in Neuroimaging

Abstract

Given impressive abilities of GANs in generating highly realistic images, they are also being used in novel ways in applications in the life sciences, raising an interesting question in scientific or biomedical studies. Consider the setting where we are restricted to only using the samples from a trained GAN for downstream group difference analysis, will we obtain similar conclusions? In this work, we explore if ?generated? data, i.e., sampled from such GANs can be used for performing statistical group difference tests in cases versus controls studies, common across many scientific disciplines. We provide a detailed analysis describing regimes where this may be feasible. We complement the technical results with an empirical study focused on the analysis of cortical thickness on brain mesh surfaces in an Alzheimer?s disease dataset. To exploit the geometric nature of the data, we use simple ideas from spectral graph theory to show how adjustments to existing GANs can yield improvements. To our knowledge, our work offers the first analysis assessing whether the Null distribution in ?healthy versus diseased subjects? type statistical testing using data generated from the GANs coincides with the one obtained from the same analysis with real cortical thickness data.