The Imprecision of Predictive Equations for Energy Needs: Statistical Inference of the Margin of Error for Individuals
Authors: Murphy William J 
Published: November 2023

Purpose

A variety of estimating equations, some recommended by Evidence‐Based Practice Guidelines, are used in clinical nutrition practice to determine patient energy expenditure. These are used by practitioners to determine dietary intake recommendations, formulate nutrition support prescriptions, and set weight loss Caloric targets among other purposes. However, the use of a simple regression equation does not produce an estimate for an individual. The point estimates produced from such equations describe the average energy needs for all individuals with identical sex, height, weight, age, and other factors in the model. When estimating for an individual, a prediction interval (PI) should be used that includes the uncertainty in the estimate. The purpose of this study was to quantify that uncertainty in estimates of energy needs for individual persons and to consider the impact of this uncertainty on clinical applications.

Methods

We assessed the uncertainty of predictions made with the Total Energy Expenditure (TEE) models from the 2005 Dietary Reference Intakes (DRI). The DRI models for adults were separated by sex and weight (normal v. overweight) and modeled Doubly Labeled Water measured energy expenditure with age, height, weight, and physical activity level category. Published model parameters were insufficient for PI calculations, so we recreated the models using the original data and the non‐linear least squares (NLS) regression procedure described in the DRI report.

Since there is no direct method for the calculation of prediction intervals for NLS models, we applied a 2nd‐order Taylor expansion to determine the variance in the mean estimate at the point of each prediction and took the square root of the sum of estimate variance and model residual variance as the standard deviation (SD) for the PI. We used this SD in a 95% t‐confidence interval to calculate PIs. We determined the PI for each individual in the original data set and assessed what proportion of measured energy expenditures fell within the PIs (coverage rate) and descriptive statistics for the PIs.

Results

Of the 783 individuals, 56% were female and 46% were overweight. The mean and SD age was 48±20 years, height was 1.7±.09 m, and weight was 74±18 kg. The coverage rate of the PIs was 96%. Close to the target of 95%, this indicates that the PI calculations were accurate. The width of PIs ranged from 908 to 1,423 Calories (kcal) with a median of 968. Therefore, 95% of individual patients can be expected to have a true TEE within 454 to 712 kcal of the simple estimate. PIs were wider when predicting for heights, weights, and ages distal to the mean values and when the mean estimate was larger.

Conclusion

Individual variation in energy needs is large, and clinicians should consider this when using energy needs equations which provide only an estimate of the mean TEE for similar patients. The difference between an individual's energy needs and the simple estimate from an equation can often be large enough to nullify a 300 kcal per day restriction for weight loss or lead to measurable weight loss within weeks of nutrition support. When more precise methods such as indirect calorimetry are not available, estimated energy needs should be adapted for individual patients through the observation of weight trends and clinical characteristics of malnutrition.