Power and sample size calculation for neuroimaging studies by non-central random field theory

Determining power and sample size in neuroimaging studies is a challenging task because of the massive multiple comparisons among tens of thousands of correlated voxels. To facilitate this task, we propose a power analysis method based on random field theory (RFT) by modeling signal areas within images as non-central random field. With this framework, power can be calculated for specific areas of anticipated signals within the brain while accounting for the 3D nature of signals. This framework can also be extended to visualize local variability in sensitivity as a power map and a sample size map. We validated our non-central RFT framework based on Monte-Carlo simulations. Moreover, we applied our method to a blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) data set with a small sample size in order to demonstrate its use in study planning. From the simulations, we found that our method was able to estimate power quite accurately. In the fMRI data analysis, despite the small sample size, we were able to determine power and the number of subjects required to detect signals.