MD3F: Multivariate Distance Drift Diffusion Framework for High-Dimensional Datasets

\High-dimensional biomedical datasets have become easier to collect in the last two decades with the advent of multi-omic and single-cell experiments. These can generate over 1000 measurements per sample or per cell. More recently, focus has been drawn toward the need for longitudinal datasets, with the appreciation that important dynamic changes occur along transitions between health and disease. Analysis of longitudinal omics data comes with many challenges, including type I error inflation and corresponding loss in power when thousands of hypothesis tests are needed. Multivariate analysis can yield approaches with higher statistical power; however, multivariate methods for longitudinal data are currently limited. We propose a multivariate distance-based drift-diffusion framework (MD3F) to tackle the need for a multivariate approach to longitudinal, high-throughput datasets. We show that MD3F can result in surprisingly simple yet valid and powerful hypothesis testing and estimation approaches using generalized linear models. Through simulation and application studies, we show that MD3F is robust and can offer a broadly applicable method for assessing multivariate dynamics in omics data