The ‘body adiposity index’ (BAI) proposed by Bergman et al. ⁽Reference Bergman, Stefanovsky and Buchanan¹⁾ estimates percentage body fat from hip circumference (HC) and body height as ((HC (cm))/(height (m))^1·5–18). A recent study published in The British Journal of Nutrition by Freedman et al. ⁽Reference Freedman, Blanck and Dietz²⁾ found the BAI to be less strongly associated with skinfold thicknesses and cardiovascular risk factors than were either waist circumference or BMI. In other studies, the BAI has been found to correlate with percentage fat about as well as does the BMI, but more often less well⁽Reference Marques-Vidal, Waeber and Vollenweider^3–Reference López, Cespedes and Vicente⁷⁾. In these studies, men and women were treated separately. The original finding was that percentage fat correlated much more strongly with BAI than with BMI⁽Reference Bergman, Stefanovsky and Buchanan¹⁾, but that was for a mixed sample of men and women, and the sexes differ markedly in the relationship between adiposity and BMI⁽Reference Bergman, Stefanovsky and Buchanan^1, Reference Barreira, Harrington and Staiano⁴⁾.

Fundamental to the derivation of the BAI is the negative correlation between percentage fat and height when both sexes are considered together, but this is due only to the tendencies for men to be taller and to contain relatively less fat⁽Reference Freedman, Blanck and Dietz^2, Reference Schultze, Thorand and Fritsche⁵⁾. Bergman et al. ⁽Reference Bergman, Stefanovsky and Buchanan¹⁾ acknowledged that the relationship between BAI and percentage fat is not exactly linear and their Fig. 3 also shows that there is a different curvilinear relationship for each sex. Indeed, for values of BAI near 40–50, percentage fat is predominantly higher in women than in men. It is therefore certain that HC and height can be combined in a better index of adiposity, if only by treating the sexes separately and by allowing for the curvilinear relationships between adiposity and the ratio HC/(height)^1·5. But is 1·5 the optimum height exponent? That it could be nearer to zero is suggested by findings that HC correlates about as well with percentage fat as does the BAI, or slightly more strongly⁽Reference Schultze, Thorand and Fritsche^5, Reference López, Cespedes and Vicente⁷⁾. One approach to estimate the best height exponent is to find, for a given population, the value of x that optimises the index HC/height^x as a predictor of percentage fat. Another approach, not needing data on adiposity, is to determine the value of x that minimises the correlation between HC/height^x and height, thus producing an index that is independent of height. That index could prove to be equally valid for adiposity and for some cardiovascular risk factors. In regard to the second approach, regression of log(HC) on log(height) has given estimates of x to be 0·72 (r 0·33) for men and 0·39 (r 0·14) for women⁽Reference Heymsfield, Heo and Pietrobelli⁸⁾. Future estimates will probably differ slightly amongst datasets, and may then be expected to correlate positively with the corresponding values of r ⁽Reference Burton⁹⁾. Nevertheless, a round-number value of 0·5 (i.e. between 0·72 and 0·39) could well prove to be appropriate – as seems to be true for the equivalent index based on height and waist circumference⁽Reference Burton⁹⁾. The relationships between the index and percentage fat would need to be defined for men and women separately. Many researchers already have the data to explore this and, if a useful index is then identified, it can be tested as a predictor of cardiovascular risk factors.