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

Dual-energy X-ray absorptiometry (DEXA) is the diagnostic standard for osteoporosis, yet its serial data remains 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 proof-of-concept study describes a deterministic mathematical framework for predicting time to osteoporosis (TTO) and time to exit osteoporosis (TEO), defined as the age at which a patient’s T-score trajectory reaches or exits the threshold of − 2.5. We developed two deterministic algorithms converting serial hip DEXA T-scores into age-based predictions: a two-point slope algorithm (TTOc) and a multipoint least-squares regression (TTOt). The algorithms were evaluated on 200 patients drawn from an institutional DEXA database using a pre-specified stratified random-sampling rule (50 patients each with 2, 3, 4, and ≥ 5 scans; seed 42). Three validation analyses were performed: (i) onset-age prediction against observed age of first osteoporotic reading using mean absolute error (MAE) and Bland-Altman analysis; (ii) prospective T-score prediction using scans 1 to N − 1 to predict scan N; and (iii) stability analysis examining how prediction intervals narrowed with increasing scan count. 95% prediction intervals were computed for TTOt by inverse prediction. Of 200 patients, 19 experienced observable crossing into osteoporosis and 4 experienced recovery during follow-up. For the 8 patients with sufficient pre-crossing data, TTOc predicted observed onset age with MAE 5.67 years (mean bias + 1.42; 95% limits of agreement − 16.0 to + 18.8). TTOt gave MAE 7.33 years (bias + 4.73; LoA − 14.2 to + 23.7). For prospective T-score prediction across 300 prediction points in 150 patients, TTOt produced lower MAE than TTOc on prospective T-score prediction (0.385 vs. 0.533 T-score units). Stability analysis demonstrated marked narrowing of TTOt prediction intervals with increasing scan count (mean PI width: 654 years at 3 scans, 202 years at 4 scans, 69.5 years at 5 scans). The two algorithms showed complementary behaviour: TTOc produced lower onset-age error in the validation subset (n = 8), while TTOt produced lower error for next-scan T-score extrapolation. The framework translates static DEXA outputs into patient-specific age-based predictions using mathematics that any reader can inspect on one page. TTOc and TTOt showed distinctly complementary behaviour. The two-point method produced lower onset-age error, while regression produced lower error for next-scan T-score prediction. The stability analysis further establishes a minimum data requirement for reliable interval estimation, with prediction intervals narrowing sharply between three and five scans. External validation, confounder adjustment, and evaluation against clinical endpoints are the necessary next steps before the framework could inform deployed decision support tools. Serial DEXA T-scores can be converted into interpretable, age-based threshold predictions using simple deterministic algorithms, with regression-based prediction error within an order of magnitude of the intrinsic measurement noise of DEXA itself. The framework is transparent by construction, providing a concrete methodological foundation on which future clinical decision support tools for bone health can be built and benchmarked. • Serial DEXA measurements are difficult to interpret in clinical practice. • Existing prediction tools rely on complex or opaque modelling approaches with limited explainability. • The relationship between bone mineral density trajectories and future osteoporosis risk lacks intuitive, patient-facing metrics. • Introduces a transparent, deterministic algorithm (TTO/TEO) that converts serial DEXA data into age-based threshold predictions. • Demonstrates quantitative validation in 200 patients drawn from a single-centre DEXA database using stratified random sampling: onset-age MAE of 5.67 years for the two-point model and T-score trajectory MAE of 0.385 for the regression model, within an order of magnitude of the intrinsic scan-to-scan measurement noise of DEXA. • Identifies distinctly different strengths of two-point and regression approaches and establishes a quantitative minimum-scan requirement for reliable interval estimation. • Provides a transparent mathematical baseline on which future clinical decision support tools in bone health can be built, benchmarked, and challenged. The proposed framework shows how raw DEXA outputs can be translated into age-based trajectory predictions using transparent and inspectable mathematics, to support individualized decision-making. Every prediction in this study can be derived by hand from a patient’s scan record. Pending external validation and confounder adjustment, this foundation could support the development of clinical decision support tools that help clinicians identify patients on concerning trajectories earlier, communicate risk in age-based terms that align with patient intuition, and reason about the timing of interventions. The transparency of the approach may be relevant in regulatory environments that are moving towards stricter requirements for algorithmic accountability in clinical AI.