Analysis of Correlated Image Features Using Scalar‐On‐Matrix Regression

Image features from digital kidney biopsies may serve as novel biomarkers of kidney function in glomerular disease. Every subject's biopsy contains a different number of histologic objects, and for every object, a common set of image features is measured across all subjects. These data can be represented by a matrix for each subject with the row dimension representing the objects and the column dimension representing the image features which are computed per object. However, no existing regression method can select informative features of outcomes when feature matrices are unbalanced across subjects and features are correlated. Therefore, we developed the Random CLUstering Structured lasSO (Random CLUSSO), a bootstrap‐based and L1‐penalized scalar‐on‐matrix approach. We demonstrated through simulations that Random CLUSSO has lower bias and a higher true positive rate for identifying informative image features relative to existing approaches when features are correlated. Finally, we applied Random CLUSSO to predict kidney function using image features from kidney biopsies of subjects with glomerular disease from the Nephrotic Syndrome Study Network (NEPTUNE) and Cure Glomerulonephropathy (CureGN) studies.