Combining information from different types of BMD measurement should improve the evaluation of patients' risk of fracture. This study used a bivariate gaussian model to examine the effect of combining two different BMD measurements. The results show that, in practice, there is little benefit unless the measurements are completely unrelated.
Introduction: Intuitively, the combination of information from two or more different types of bone densitometry investigation should improve our ability to identify patients at high risk of fracture. However, the best way to combine measurements and the resulting gain in fracture discrimination are not known.
Materials and methods: In this study, we used a bivariate gaussian model to investigate the effect of combining two different types of bone densitometry measurements. The measurements had individual relative risk values RR1 and RR2 and a correlation coefficient r between their Z-scores. Different approaches to the combination of the two measurements were compared by calculating the area under the curve (AUC) for the receiver operating characteristic (ROC) curve, which was obtained by plotting the percentage of fracture patients against the percentage of the whole population with a Z-score below some chosen threshold. ROC curves were calculated for three cases: (1) one type of measurement only; (2) two different types of measurements combined using their mean Z-score weighted according to the theoretical optimum weighting factors predicted by the bivariate gaussian model; and (3) two different types of measurements combined using the conventional World Health Organization (WHO) approach, where one or other measurement is below a set threshold. The theoretical model was tested using measurements of speed of sound (SOS) in the radius, phalanx, and metatarsal in patients with vertebral and Colles' fractures.
Results: Results were calculated for RR values of 1.5, 2.0, and 2.5 and r = 0, 0.5, and 0.7. Although a significant improvement in fracture discrimination was obtained when r = 0 and RR1 = RR2, the improvements obtained when r > or = 0.5 or RR1 double dagger RR2 were relatively modest. Slightly better fracture discrimination was obtained using the weighted mean Z-score approach compared with the WHO approach, although the differences were small. The results of the in vivo study in Colles' and vertebral fracture patients showed close agreement with the predictions of the bivariate gaussian model.
Conclusion: In practice, from a theoretical point of view, there is unlikely to be any benefit from combining information from different types of bone densitometry measurements unless they are completely unrelated.