Discriminative Ability of Heel Quantitative Ultrasound in Postmenopausal Women with Prevalent Vertebral Fractures: Application of Optimal Threshold Cutoff Values Using Classification and Regression Tree Models

Abstract

Quantitative ultrasound (QUS) of the heel has been proposed as a screening tool to evaluate the bone status and risk of osteoporotic fragility fractures. The aim of this study was to define threshold values that would maximize the predictive ability of QUS to discriminate subjects with vertebral fractures using the classification and regression trees (CART) models. A cross-sectional analysis was made of a cohort of 1,132 postmenopausal women with a mean age of 58 years. A total of 205 women (18.1 %) presented with a history of vertebral fracture. For all patients, a questionnaire of osteoporosis risk factors was given and measurements of the heel QUS and bone mineral density at the lumbar spine and the proximal femur, obtained by dual-energy X-ray absorptiometry (DXA), were made. Spinal radiographs were assessed for vertebral fractures. Sensitivity, specificity, predictive values, likelihood ratios, and receiver operator characteristics (ROC) curve QUS values were calculated using the optimal threshold identified in the CART models. Cutoff values calculated from best CART model (i.e., a QUS index >90.5 %) yielded a sensitivity of 80.3 % (95 % CI 69.2-88.1), a negative predictive value of 94 % (95 % CI 90.1-96.5), and a specificity of 68.8 % (95 % CI 63.3-73.8). This cutoff value would obviate the need to perform DXA in 32.8 % of the women of our population at risk for vertebral fractures. The area under the ROC curve of the best model was 0.8071. QUS was shown to discriminate between women with and without a history of vertebral fracture and constitutes a useful tool for assessing vertebral fracture risk. The application of decision trees (CART analyses) was helpful to define the optimal threshold QUS values.

Using Classification and Regression Trees (CART) to Identify Prescribing Thresholds for Cardiovascular Disease

“…As a result, the precise form of the relationship between a predictor and outcome is not delimited by the inclusion/exclusion of higher order terms. It is this strength that has seen CART used in a variety of prognostic analyses to identify risk thresholds for inhospital mortality [21], vertebral fractures [22] and cirrhosis [23].…”

Factors affecting the formation of membranous substances in the palates of elderly persons requiring nursing care

“…The resulting tree diagram provided a visual representation of the relationship between these input variables and their relative impact on the formation of membranous substances. The decision trees were calculated using the chi‐squared automatic interaction detection (CHAID) method. The entire sample of independent variables (parent nodes) was divided into two child nodes (subgroups) based on the independent variable with the highest chi‐squared value in relation to the dependent variable.…”