Semiparametric confidence sets for cross-sectional and longitudinal neuroimaging.

The majority of neuroimaging inference focuses on hypothesis testing rather than effect estimation. With concerns about replicability, there is growing interest in reporting standardized effect sizes from neuroimaging group-level analyses. Confidence sets for effect sizes were recently developed for neuroimaging, but are restricted to simple univariate contrasts (e.g., one-sample or two-sample test Cohen's d) and cross-sectional data. Thus, existing methods exclude increasingly common longitudinal associations of biological brain measurements with, potentially nonlinear, inter- and intra-individual variations in diagnosis, development, or symptoms. We use modern methods for confidence sets combined with a recently proposed robust effect size index to provide a very general approach and software for effect size confidence set inference in neuroimaging. Our method involves robust estimation of the effect size image and spatial and temporal covariance function based on generalized estimating equations. We use a nonparametric bootstrap to estimate the joint distribution of the robust effect size image across voxels to construct confidence sets. These confidence sets identify regions of the image where the lower or upper simultaneous confidence interval is above or below a given threshold with high probability. We evaluate the coverage and simultaneous confidence interval width of the proposed procedures using realistic simulations and perform longitudinal analyses of aging and diagnostic differences of cortical thickness in Alzheimer's disease and diagnostic differences of resting-state hippocampal activity in psychosis. This comprehensive approach, along with the visualization functions integrated into the pbj R package, offers a robust tool for analyzing repeated neuroimaging measurements.