Measuring Small Changes Versus Measurement Error

Abstract

To the Editor: The recent prospective study by Szulc et al.1 dealt with essential mechanisms of macroscopic bone biology: the relationship between periosteal apposition and endocortical bone loss. In short, they concluded that the failure of periosteal apposition to compensate for cortical thinning after menopause leads to bone fragility of osteoporosis. Because of obvious reasons, the knowledge on bone dimensional changes over time has been largely based on cross-sectional data from differently aged people (e.g., with DXA, pQCT, and QCT).2-4 Given the cross-sectional design, the strength of this kind of evidence is limited. Nevertheless, such observations are useful as being indicative of expected magnitudes and rates of periosteal and endosteal changes (Table 1). Two prospective studies have assessed changes in bone width and cortical thickness over a long period; the 15-yr follow-up of SPA data from radial shaft by Ahlborg et al.5 and the 21-yr follow-up of standardized X-ray film data from several skeletal sites by Heaney et al.6 In the former study,5 the mean increase in the radial shaft width was 0.07 mm/yr, whereas the cortical thickness seemed to increase 0.01 mm/yr. In the latter study,6 the radial shaft width at the one-third site did not increase (−0.001 mm/yr), whereas the cortical thickness decreased 0.06 mm/yr. In comparison, the 7-yr follow-up of DXA data from radial shaft by Szulc et al.1 suggested that the mean increases in the radial shaft width at the one-third site ranged from no change (−0.001 mm/yr) to 0.03 mm/yr as assessed in different subgroups divided according to menopausal status and hormone replacement therapy (HRT). The mean decreases in the cortical thickness varied between 0.008 and 0.02 mm/yr, respectively. Evidently, the age-related changes in bone dimension changes are slow processes requiring a long time for reliable detection by any noninvasive method. This brings us to the first methodological concern, the attainable resolution of planar DXA image. The pixel width in the study by Szulc et al.1 was apparently 1 mm, >10 times larger than the estimated yearly changes. The pixel width implies that it is possible to measure increases in bone width only in steps of 1 mm. However, averaging 20 width values from adjacent scan lines (provided that the standard 20-mm region of interest was used) improves the resolution. However, the change in the mean bone width is based on data that are made up of coarse ±1-mm changes. Thus, the inherent uncertainty and imprecision in the width is readily ∼1 mm, which is much larger in magnitude than the reported results (∼1 μm = 0.001 mm). The second concern relates to the calculation of the cortical thickness from the DXA-derived bone width and BMC. In line with common practice, it was assumed that the radial shaft is a concentric hollow cylinder with constant cortical density in every individual. However, the cross-section of the radial shaft is not a perfect cylinder, and thus, even a small variation in the bone position during the follow-up measurements can result in an apparent changes in bone width. Moreover, cortical density can vary between individuals and is also affected by HRT and age.7, 8 One can easily observe ∼0.05-g/cm3 differences in the cortical density between individuals or groups, and such a deviation from the assumption would lead to a ∼0.2-mm change in the estimated cortical thickness, which is again much larger in magnitude than the reported results (∼0.1 μm = 0.0001 mm) by Szulc et al.1 Finally, regarding the estimation of yearly changes in bone dimensions, the regression analysis always provides, irrespective of the quality of individual data points, a slope that denotes the rate of change as a function of time. In this context, it would have been illustrative to see the variation in consecutive bone width values among some randomly selected individuals. If the annual changes reported by Szulc et al.1 had been robust, they should have got the similar trends by reanalyzing random subsets of prospective data from each individual. Even so, the above issues caused by assumptions and technical limitations of the DXA measurement in this particular application could not be properly handled by any means. Thus, the uncertainty in the results by Szulc et al.1 remains formidable. The pursuit after description of true biological bone traits is quite understandable.9 Playing on numbers can facilitate the understanding of the phenomena, but one should never belittle the physical constraints of their measurements. When one evaluates subtle changes, substantially smaller in magnitude than the resolution and precision of the measurement, the estimates of the true biological variance include noise attributable to resolution, accuracy, and precision of the measurement per se and the variance arising from assumptions and may not justify the strong, general conclusion about bone biology of Szulc et al.1