Controlling for confounds in UK Biobank brain imaging data with small subsets of subjects

The UK Biobank (UKB) Brain Imaging cohort contains data from almost 100,000 subjects and has yielded invaluable understanding of the links between the brain and health outcomes and lifestyles. Much of the understanding of these links has come from exploring the association between Imaging Derived Phenotypes (IDPs) and other variables that are unrelated to brain imaging, so called non-Imaging Derived Phenotypes (nIDPs). When performing analysis of this kind, it is very important to control for well known confounding factors such as age, sex and socio-economic status, as well as confounds which are related to the imaging protocol itself. In previous work, we created a pipeline for constructing imaging confounds for use in statistical inference via a standard multivariate linear regression approach (Alfaro-Almagro et. al. 2021). However, this approach is problematic when the number of confounds exceeds the number of subjects, and is severely underpowered when the number of number of subjects is not much larger than the number of confounds. In this work, we perform a simulation study to evaluate 13 modelling approaches to account for confounds when their number is similar to or exceeds the number of subjects. Based on the simulation results, we recommend a ridge regression based permutation test for low sample sizes (n [&le;] 50), a version of de-sparsified LASSO for intermediate sample sizes (50 < n [&le;] 500), and multivariate linear regression aided by Principal Component Analysis (PCA) for larger sample sizes (n > 500). We also demonstrate the use of our recommended methodology on a real data example of finding associations between Alzheimers Disease (AD) and IDPs.