A simple model predicting individual weight change in humans

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Abstract
Excessive weight in adults is a national concern with over 2/3 of the US population deemed overweight. Because being overweight has been correlated to numerous diseases such as heart disease and type 2 diabetes, there is a need to understand mechanisms and predict outcomes of weight change and weight maintenance. A simple mathematical model that accurately predicts individual weight change offers opportunities to understand how individuals lose and gain weight and can be used to foster patient adherence to diets in clinical settings. For this purpose, we developed a one-dimensional differential equation model of weight change based on the energy balance equation paired to an algebraic relationship between fat-free mass and fat mass derived from a large nationally representative sample of recently released data collected by the Centers for Disease Control. We validate the model's ability to predict individual participants’ weight change by comparing model estimates of final weight data from two recent underfeeding studies and one overfeeding study. Mean absolute error and standard deviation between model predictions and observed measurements of final weights are less than 1.8±1.3 kg for the underfeeding studies and 2.5±1.6 kg for the overfeeding study. Comparison of the model predictions to other one-dimensional models of weight change shows improvement in mean absolute error, standard deviation of mean absolute error, and group mean predictions. The maximum absolute individual error decreased by approximately 60% substantiating reliability in individual weight-change predictions. The model provides a viable method for estimating individual weight change as a result of changes in intake and determining individual dietary adherence during weight-change studies.