Relation of ratio indices of anthropometric measures to obesity in a stunted population

The ratios of anthropometric measures are used to estimate obesity while controlling for allometric scaling. A good index should be uncorrelated with its denominator; this often requires exponentiation of the denominator. The stability of the derived exponents across populations is not known. We obtained subscapular (SUBS) and triceps (TRI) skinfolds, weight (WT), height (HT), waist circumference (WC), fat mass (FM), and fat-free mass (FFM) in a population of Guatemalan adults [height 1.63 +/- 0.06 m (868 males); 1.51 +/- 0.06 m (1047 females)]. We derived exponents for the indices WT/HTP, SUBS/TRIP, TRI/SUBSP, WC/HTP, FM/WTP and FM/FFMP such that the ratios were free from association with their denominators. The derived exponents were (Men: SUBS/TRI0.88, FM/WT2.69, FM/FFM2.86, WC/HT0.68, and WT/HT2.17; Women: SUBS/TRI0.93, FM/WT2.01, FM/FFM3.37, WC/HT0.47, WT/HT2.03). For all examined indices the derived exponents differed (P < 0.05) from 1 and differed (P < 0.05) between men and women. The exponents for the men also differed from those previously published for Brazilian men (JCK Wells and CG Victora [2005]: Int J Obes 29:483-489). The derived indices were not more strongly correlated with adiposity than were simple unexponentiated ratios. Although exponentiation of the denominator eliminates the association of index with its denominator, the resulting exponents lack generalizability across populations, especially those where stunting remains prevalent.