Composite index of skeletal mass: principal components analysis of regional bone mineral densities

Principal components analysis is a statistical method that is used to reduce and explore data to facilitate further analyses. This method was applied to bone mineral densities measured at seven sites in 109 black and 44 white women, ages 22-80, at an internal medicine clinic in urban Detroit. We excluded subjects with a history of diseases or drugs known to affect bone metabolism. Principal components analysis was used to summarize the interrelationship of the densities and yielded two major results. First, the seven site measurements were reduced to a single, composite index (PC1) of skeletal mass that accounted for 73% of the variation in density among subjects. PC1 had roughly equal weights among the sites. A second combination of the seven sites indicated that the contrast between axial and appendicular regional densities accounted for another 10% of the variation among subjects. In investigating the relationship of density to age, body mass index, and ethnic group, we found that the principal components composite index had a stronger correlation with age (r = -0.58) and with body mass index (r = 0.34) than almost all of the regional densities. Black-white differences were larger for the composite index than for any single site density. A multiple regression of the composite index on ethnicity, body mass index, and age yielded a larger R2 (0.46) than any of the individual site densities. The second principal component, although of theoretical interest, showed a minimal ability to discriminate among subjects using the three independent variables of this study.