A mathematical and computational framework to predict the time to and recovery from osteoporosis via serial DEXA scans: a proof-of-concept model for digital decision support

Background Dual energy X ray absorptiometry (DEXA) is the diagnostic standard for osteoporosis, yet its serial data remain underutilised in predictive analytics. To our knowledge, no published model provides explicit age based predictions of osteoporosis onset or recovery using serial DEXA T score trajectories. This study describes a mathematical framework for predicting time to osteoporosis (TTO), defined as the age at which a patient’s T score trajectory reaches negative 2 point five. Methods We developed a mathematical framework that converts serial DEXA T-scores into time-to-osteoporosis (TTO) and time-to-exit osteoporosis (TEO) predictions. Using hip DEXA results from 50 consecutive patients with ≥2 scans, T-scores were plotted against age, and we applied two models: (a) a two-point slope algorithm (TTOc) and (b) a multipoint least-squares regression (TTOt). Both were designed to estimate the age at which the T-score trajectory would cross the diagnostic threshold of negative 2 point five. Results Both algorithms successfully predict the age of entry into, or recovery from, osteoporosis. TTOc produced scan-pair–specific short-term projections, whereas TTOt provided smoothed cumulative trajectories. Worked examples demonstrated agreement between models in patients with monotonic decline and highlighted the stabilising effect of regression in fluctuating cases. Discussion This framework transforms static DEXA outputs into patient specific, age-based predictions, enhancing clinical interpretability. In addition to their immediate clinical use, deterministic equations can serve as the foundation for a hybrid machine-learning model that uses slope and intercept values as interpretable features within ensemble or deep learning architectures to improve temporal prediction accuracy across larger datasets. Conclusions This proof-of-concept demonstrates the feasibility of trajectory-based modelling for osteoporosis risk prediction. It represents a step toward AI-assisted DEXA interpretation systems that are transparent, explainable, and directly usable at the point of care. It also reframes DEXA outputs into an age-based measure that patients easily understand, offering clinicians a simplified parameter for monitoring therapy. The incorporation of these findings into DEXA reporting could strengthen patient engagement and adherence.