Modeling physiological and anthropometric variables known to vary with body size and other confounding variables

This review explores the most appropriate methods of identifying population differences in physiological and anthropometric variables known to differ with body size and other confounding variables. We shall provide an overview of such problems from a historical point of view. We shall then give some guidelines as to the choice of body-size covariates as well as other confounding variables, and show how these might be incorporated into the model, depending on the physiological dependent variable and the nature of the population being studied. We shall also recommend appropriate goodness-of-fit statistics that will enable researchers to confirm the most appropriate choice of model, including, for example, how to compare proportional allometric models with the equivalent linear or additive polynomial models. We shall also discuss alternative body-size scaling variables (height, fat-free mass, body surface area, and projected area of skeletal bone), and whether empirical vs. theoretical scaling methodologies should be reported. We shall offer some cautionary advice (limitations) when interpreting the parameters obtained when fitting proportional power function or allometric models, due to the fact that human physiques are not geometrically similar to each other. In conclusion, a variety of different models will be identified to describe physiological and anthropometric variables known to vary with body size and other confounding variables. These include simple ratio standards (e.g., per body mass ratios), linear and additive polynomial models, and proportional allometric or power function models. Proportional allometric models are shown to be superior to either simple ratio standards or linear and additive polynomial models for a variety of different reasons. These include: 1) providing biologically interpretable models that yield sensible estimates within and beyond the range of data; and 2) providing a superior fit based on the Akaike information criterion (AIC), Bayes information criterion (BIC), or maximum log-likelihood criteria (resulting in a smaller error variance). As such, these models will also: 3) naturally lead to a more powerful analysis-of-covariance test of significance, which will 4) subsequently lead to more correct conclusions when investigating population (epidemiological) or experimental differences in physiological and anthropometric variables known to vary with body size.