Estimating changes in free-living energy intake and its confidence interval

Abstract

Background: Free-living energy intake in humans is notoriously difficult to measure but is required to properly assess outpatient weight-control interventions.

Objective: Our objective was to develop a simple methodology that uses longitudinal body weight measurements to estimate changes in energy intake and its 95% CI in individual subjects.

Design: We showed how an energy balance equation with 2 parameters can be derived from any mathematical model of human metabolism. We solved the energy balance equation for changes in free-living energy intake as a function of body weight and its rate of change. We tested the predicted changes in energy intake by using weight-loss data from controlled inpatient feeding studies as well as simulated free-living data from a group of "virtual study subjects" that included realistic fluctuations in body water and day-to-day variations in energy intake.

Results: Our method accurately predicted individual energy intake changes with the use of weight-loss data from controlled inpatient feeding experiments. By applying the method to our simulated free-living virtual study subjects, we showed that daily weight measurements over periods >28 d were required to obtain accurate estimates of energy intake change with a 95% CI of <300 kcal/d. These estimates were relatively insensitive to initial body composition or physical activity level.

Conclusions: Frequent measurements of body weight over extended time periods are required to precisely estimate changes in energy intake in free-living individuals. Such measurements are feasible, relatively inexpensive, and can be used to estimate diet adherence during clinical weight-management programs.

Figures

FIGURE 1.

Weight changes and estimated changes in energy intake (ΔEI) during 800-kcal/d inpatient controlled diets. A: Results for a 135-kg, 45-y-old woman. The left panel shows daily body weight measurements (circles), and the right panel depicts the ΔEI measurements (red curve) and their 95% CI (dotted red curves) along with our ΔEI estimate (black dots) and its 95% CI (blue curves) (number of data points = 6, time interval between data points = 1 d). B: Results for a 107-kg, 49-y-old woman. C: Results for a 39-y-old, 199-kg man. BW, body weight.

FIGURE 2.

Comparison of our simple method for estimating change in energy intake (ΔEI) with a recently proposed computational model for determining individual EI. A: Measured body weight (BW) data from a 83.8-kg, 45-y-old woman (circles) along with the moving linear regression estimate (red curve) (number of data points = 3, time interval between data points = 14 d). B: ΔEI estimated with our simple model (black dots) along with its 95% CI (blue curves) and the computational model prediction for ΔEI (open red squares).

FIGURE 3.

Simulated free-living data from a sedentary 90-kg male virtual study subject generated by using a computational model of macronutrient metabolism. A: Simulated body weight (BW) data for an example run of the model incorporating day-to-day fluctuations in energy intake (EI), dietary sodium, and carbohydrate. B: Estimated changes in EI (ΔEI; black dots) along with the 95% CI (blue lines) and moving average actual EI (red line) for the same example subject as depicted in panel A (number of data points = 28, time interval between data points = 1 d). C: Residuals of the estimated EI changes (black dots) for 10 runs using the same subject. Blue lines denote the calculated 95% CI.

FIGURE 4.

Simulated free-living data from a sedentary 120-kg female virtual study subject generated by using a computational model of macronutrient metabolism. A: Simulated body weight (BW) data for an example run of the model incorporating day-to-day fluctuations in energy intake (EI), dietary sodium, and carbohydrate. B: Estimated changes in EI (ΔEI; black dots) along with the 95% CI (blue lines) and moving average actual EI (red line) for the same example subject as depicted in panel A (number of data points = 28, time interval between data points = 1 d). C: Residuals of the estimated EI changes (black dots) for 10 runs using the same subject. Blue lines denote the calculated 95% CI.

FIGURE 5.

Simulated free-living data from an active 70-kg male virtual study subject generated by using a computational model of macronutrient metabolism. A: Simulated body weight (BW) data for an example run of the model incorporating day-to-day fluctuations in energy intake (EI), dietary sodium, and carbohydrate. B: Estimated changes in EI (ΔEI; black dots) along with the 95% CI (blue lines) and moving average actual EI (red line) for the same example subject as depicted in panel A (number of data points = 28, time interval between data points = 1 d). C: Residuals of the estimated EI changes (black dots) for 10 runs using the same subject. Blue lines denote the calculated 95% CI.

FIGURE 6.

Simulated free-living data from a sedentary 90-kg male virtual study subject who added an exercise program in addition to the diet. A: Simulated body weight (BW) data for an example run of the model incorporating day-to-day fluctuations in energy intake (EI), dietary sodium, and carbohydrate. B: Estimated changes in EI (ΔEI; black dots) along with the 95% CI (blue lines) and moving average actual EI (red line) for the same example subject as depicted in panel A (number of data points = 28, time interval between data points = 1 d). C: Residuals of the estimated EI changes (black dots) for 10 runs using the same subject. Blue lines denote the calculated 95% CI.