Recovering data from basal metabolic rate and body-mass index

Many clinically significant parameters are estimated from height (h), weight (w) and age (y). Two important examples are body mass index (BMI) and basal metabolic rate (BMR). There are circumstances when it might be desirable to estimate h, w and y for a particular subject from BMI and BMR (or other similar combinations). While there is only one mathematical expression for BMI, there are many competing expressions for BMR which complicates this process. Here we describe methods for solving this problem for three different classes of BMR equation when the coefficients are known. We also provide means of identifying the coefficients of an unidentified BMR equation. We apply these technique to our own data, data published by others and in computer simulations, from which we conclude that in the most challenging case our method yields the correct result in more than 99% of cases and identifies the likelihood of error in about 0.96% of cases, leaving only about 0.03% of cases of unidentified error. Application of these techniques to data obtained using an Omron HBF-362 demonstrate some of the difficulties that can arise.