A statistical method to minimize magnification errors in serial vertebral radiographs

Incident vertebral deformities are commonly defined by observed changes in height between measurements on two consecutive radiographs. However, conventional radiographs are subject to magnification, and this magnification may differ between films, leading to artifactual changes in height. In order to minimize this effect, it is common practice to record the spine-film and film-focus distances, and from this to calculate a magnification factor for each film. We present a simple statistical method for correcting for differences in magnification between two films if the spine-film and film-focus distances are unknown. This method is shown to reduce the variance of the magnification differences in vertebral heights by 14%, considerably more than is possible using the spine-film distance. Using the statistical method, the number of vertebrae that showed not only a reduction in one or more height of 15%, but were also judged clinically to be free from any incident deformity by an expert radiologist, was reduced from 100 to 46. The number showing a reduction of 20% that were judged fracture-free was reduced from 15 to 9. In the subset of subjects for whom the spine-film distance was known, the reduction in false positives was similar, whichever method was used to correct for magnification. There was no difference in the number of confirmed incident fractures detected when magnification correction by either method was employed. It is concluded that correcting for magnification differences using the statistical method outlined here reduces the number of false positive deformities very substantially and by a similar extent as correcting the magnification using reliable, measured spine-film and film-focus distances. A further advantage of this method is that it can be used retrospectively.