Reverse engineering the FRAX algorithm: Clinical insights and systematic analysis of fracture risk

Abstract

The Fracture Risk Assessment Tool (FRAX) is a computational tool developed to predict the 10-year probability of hip fracture and major osteoporotic fracture based on inputs of patient characteristics, bone mineral density (BMD), and a set of seven clinical risk factors. While the FRAX tool is widely available and clinically validated, its underlying algorithm is not public. The relative contribution and necessity of each input parameter to the final FRAX score is unknown. We systematically collected hip fracture risk scores from the online FRAX calculator for osteopenic Caucasian women across 473,088 unique inputs. This dataset was used to dissect the FRAX algorithm and construct a reverse-engineered fracture risk model to assess the relative contribution of each input variable. Within the reverse-engineered model, age and T-Score were the strongest contributors to hip fracture risk, while BMI had marginal contribution. Of the clinical risk factors, parent history of fracture and ongoing glucocorticoid treatment had the largest additive effect on risk score. A generalized linear model largely recapitulated the FRAX tool with an R² of 0.91. Observed effect sizes were then compared to a true patient population by creating a logistic regression model of the Study of Osteoporotic Fractures (SOF) cohort, which closely paralleled the effect sizes seen in the reverse-engineered fracture risk model. Analysis identified several clinically relevant observations of interest to FRAX users. The role of major osteoporotic fracture risk prediction in contributing to an indication of treatment need is very narrow, as the hip fracture risk prediction accounted for 98% of treatment indications for the SOF cohort. Removing any risk factor from the model substantially decreased its accuracy and confirmed that more parsimonious models are not ideal for fracture prediction. For women 65 years and older with a previous fracture, 98% of FRAX combinations exceeded the treatment threshold, regardless of T-score or other factors. For women age 70+ with a parent history of fracture, 99% of FRAX combinations exceed the treatment threshold. Based on these analyses, we re-affirm the efficacy of the FRAX as the best tool for fracture risk assessment and provide deep insight into the interplay between risk factors.

Keywords: Bone mineral density; FRAX; Generalized linear model; Hip fracture risk; Osteoporosis.