Unraveling Heterogeneity of ADNI’s Time-to-Event Data Using Conditional Entropy—Part I: Cross-Sectional Study

Data analysis is a scientific endeavor of bottom-up data-driven engineering nature. This nature requires all employed conceptual criteria and algorithmic computations equipped with scientific interpretability. It must be free from top-down modeling via man-made structures and assumptions. We demonstrate data analysis of such nature on a critical disease in the real world. In the context of the Alzheimer’s Disease Neuroimaging Initiative (ADNI), we analyze time-to-event data transiting from mild cognitive impairment (MCI) to Alzheimer’s disease (AD) diagnosis. We first address issues related to non-informative censoring using conditional-vs-marginal entropies and the Redistribute-to-the-right algorithm. By employing Categorical Exploratory Data Analysis (CEDA) with 16 covariate variables, we identify a set of key factors, including the Mean of Composite Cognitive Score for Memory (V9) and 13-item-AD Assessment Scale-Cognitive Subscale at baseline (V8). For comparison purposes, this heavily censored data set is also analyzed using Cox’s proportional hazard (PH) modeling and partial likelihood-based approach. Due to complicated structural dependency among covariate features on a global scale, important factors, like V8, are missed in PH results. To further compare PH and CEDA results on locality scales, we subdivide the entire collection of 903 subjects respectively with respect to the four categories of V9 and V8 as a measure of handling induced heterogeneity. Through graphic displays featured with conditional entropy expansions, CEDA is seen to uncover and select more multi-scale informative feature-factors than PH results in all 8 sub-collections when accommodating covariate’s structural dependencies and heterogeneity.