Primary objective: The purpose of the present review is to critically examine the various models used to describe health-related performance indices (e.g. grip-strength, lung function, arterial blood pressure, anaerobic and aerobic power, etc.).
Main outcomes and results: The majority of health-related performance indices are known to increase proportionally with body size and decline with age, although some, for example arterial blood pressure and cholesterol, increase with both age and excessive body weight. Historically, the confounding effects of body size and age have been controlled using multiple linear or polynomial regression models assuming a constant additive error variance. Based on maximum likelihood goodness-of-fit criterion, an alternative class of allometric models with a multiplicative error term arc shown to describe such proportional relationships more adequately in both cross-sectional and longitudinal studies.
Conclusions: When modelling health-related performance indices, multiplicative, allometric models incorporate the concept of a proportional association as an integral part of its model form. Such models guarantee realistic values of health-related response variables both within and beyond the range of observations, ensuring biologically sound estimates of the response variables for subjects of all ages. After a logarithmic transformation, the models can be fitted using ordinary linear regression that will naturally help to overcome the heteroscedasticity observed in such data. However, if the logarithmic transformation fails to provide a constant error variance, an alternative approach is to model the error variance itself using log-linear regression. For longitudinal data, the use of multilevel modelling provides an alternative method of modelling error variation observed in health-related performance indices.