A Multimodal Mathematical and Computational Framework for Personalized Medication-Adherence and Cognitive-Risk Modeling in Alzheimer's Disease

A Working Paper Presenting a Research Protocol and Proposed Evaluation Framework

Abstract

Digital medication-management tools for Alzheimer's disease (AD) typically record only whether a dose was taken, leaving the temporal and behavioral structure of adherence largely unused as a predictive signal. This working paper proposes a seven-layer mathematical and computational research framework that (i) formalizes multimodal behavioral data — medication-taking events, response latency, activity, and cognitive-task performance — as a time-indexed state vector; (ii) applies probabilistic and statistical inference to identify features associated with adherence difficulty; (iii) compares logistic, ensemble, neural, and temporal machine-learning model families under a common, pre-registered evaluation protocol; and (iv) tests whether personalized, participant-conditioned models outperform population-level baselines. No real patient data have been collected or analyzed. Instead, we validate the complete pipeline end-to-end on a synthetic, computer-generated cohort (150 synthetic participants, 9,000 participant-days) with a known data-generating process, and report the genuine simulation outputs: population-level models achieved AUROC 0.62–0.66, a temporal/personalized model achieved AUROC 0.83 and correctly recovered a personalization effect deliberately embedded in the synthetic data (bootstrap 95% CI on the AUROC gain excluded zero: [0.002, 0.084]), and permutation feature importance recovered the two dominant synthetic drivers (cognitive-score drift, response latency). These synthetic results validate the analysis pipeline only and make no claims about real AD patients. We situate the framework within the wearable- and sensor-based dementia-monitoring literature, specify testable hypotheses and evaluation metrics aligned with TRIPOD/PROBAST reporting standards, and describe how findings would extend an existing IoT-based medication-reminder system toward personalized, explainable adherence-risk prediction.