Permutation Test for Image‐on‐Scalar Regression With an Application to Breast Cancer

Image based screening is now routinely available for early detection of cancer and other diseases. Quantitative analysis for effects of risk factors on digital images is important to extract biological insights for modifiable factors in prevention studies and understand pathways for targets in preventive drugs. However, current approaches are restricted to summary measures within the image with the assumption that all relevant features needed to characterize an image can be identified and appropriately quantified. Motivated by data challenges in breast cancer, we propose a nonparametric statistical framework for risk factor screening that uses the whole mammogram image as outcome. The proposed permutation test allows assessment of whether a set of scalar risk factors is associated with the whole image in the presence of correlated residuals across the spatial domain. We provide extensive simulation studies and illustrate an application to the Joanne Knight Breast Health Cohort using the mammogram imaging data.