Fracture prediction by bone density measurements at sites other than the fracture site: the contribution of BMD correlation.
It is widely believed that the most reliable BMD measurement for predicting fracture risk at any given skeletal site is one made at the fracture site itself. This study examines the hypothesis that the ability of BMD measurements at other distant sites in the skeleton remote from the fracture site to predict fracture risk is due to their correlation with the BMD measurements at the fracture site. We refer to this assumption as the correlation hypothesis. We show that the correlation hypothesis predicts the relationship betadist = rbetafrac, where beta is the gradient of the exponential relationship between fracture risk and Z-score, betafrac is the beta-value for the fracture site, betadist the beta-value for the distant BMD site, and r is the correlation coefficient between the Z-scores at the two sites. In practice it is important to consider the effect of BMD measurement errors on the (r, beta) relationship. We show that the effect of errors at the distant site is to reduce betadist and r in a way that preserves their original relationship. When errors at the fracture site are taken into account the effect on the (r, beta) plot is for the point representing the fracture site to fall below the extrapolation of the straight-line relationship predicted for the points representing the distant BMD sites. We tested the correlation hypothesis by using data from the Study of Osteoporotic Fractures to examine the (r, beta) plots for hip, spine and forearm fractures. For the hip the data are consistent with a straight-line relationship and suggest that measurements made at other sites provide no additional information about fracture risk over and above that provided by hip BMD itself. For spine and forearm fractures the data show that distant sites do provide additional information about fracture risk in a way that is quantitatively consistent with the BMD measurement errors reported in cadaver studies. It is clear that random BMD errors at the fracture site cause loss of information about fracture risk and that some of this lost information is recoverable from measurements made at other sites in the skeleton. Overall, this study points to BMD correlation as an important factor in explaining the ability of measurements made at distant sites to predict fracture risk.
Blake
Glen M
GM
Guy's, King's and St Thomas' School of Medicine, Guy's Campus, St Thomas Street, SE1 9RT, London, UK. glen.blake@kcl.ac.uk
Fogelman
Ignac
I
D015502:Absorptiometry, Photon; D015519:Bone Density; D001842:Bone and Bones / Q000000981:diagnostic imaging / Q000293:injuries* / Q000378:metabolism; D004198:Disease Susceptibility; D005598:Fractures, Spontaneous / Q000175:diagnosis* / Q000378:metabolism; D006801:Humans; D015233:Models, Statistical; D010024:Osteoporosis / Q000175:diagnosis / Q000378:metabolism; D011237:Predictive Value of Tests; D012307:Risk Factors