Proportional Feedback Control of Energy Intake During Obesity Pharmacotherapy

Abstract

Objective: Obesity pharmacotherapies result in an exponential time course for energy intake whereby large early decreases dissipate over time. This pattern of declining drug efficacy to decrease energy intake results in a weight loss plateau within approximately 1 year. This study aimed to elucidate the physiology underlying the exponential decay of drug effects on energy intake.

Methods: Placebo-subtracted energy intake time courses were examined during long-term obesity pharmacotherapy trials for 14 different drugs or drug combinations within the theoretical framework of a proportional feedback control system regulating human body weight.

Results: Assuming each obesity drug had a relatively constant effect on average energy intake and did not affect other model parameters, our model correctly predicted that long-term placebo-subtracted energy intake was linearly related to early reductions in energy intake according to a prespecified equation with no free parameters. The simple model explained about 70% of the variance between drug studies with respect to the long-term effects on energy intake, although a significant proportional bias was evident.

Conclusions: The exponential decay over time of obesity pharmacotherapies to suppress energy intake can be interpreted as a relatively constant effect of each drug superimposed on a physiological feedback control system regulating body weight.

Figure 1

(A) Mathematical model results assuming a constant effect of obesity pharmacotherapy on placebo-subtracted energy intake in the presence (solid curve) or absence (dashed curve) of proportional feedback control of energy intake. In the context of such a feedback control system regulating body weight, a constant drug effect results in an early intake reduction (-P_early) that exponentially decays to late effect (-P_late) related to P_early according to the pre-specified model parameters. (B) Corresponding placebo-subtracted body weight changes in the presence (solid curve) or absence (dashed curve) of the proportional feedback control system regulating body weight.

Figure 2

(A) A significant linear relationship was observed between the previously published parameters defining the best-fit exponential time courses characterizing early (P_early) and late (P_late) effects of 14 different obesity pharmacotherapies on energy intake. The solid line is the best-fit linear regression line through the origin and the dashed line is the predicted linear relationship assuming that each drug has a constant effect without altering any of the pre-specified model parameters. The outlier data point indicated by the open square is for the drug combination Phentermine/Fenfluramine. (B) Removal of the Phentermine/Fenfluramine outlier results in closer agreement between the best-fit regression line (solid) with the predicted slope (dashed).

Figure 3

(A) Bland-Altman plot comparing the previously measured parameters defining the long-term effects of obesity pharmacotherapies on energy intake (P_late) with the predicted values assuming that each drug or drug combination each has a constant effect without altering any of the pre-specified model parameters. The mean error is indicated by the dashed horizontal line and the 95% CI limits of agreement are defined by the horizontal dotted lines. The solid best-fit linear regression line indicates a proportional bias in the predictions. (B) Removal of the Phentermine/Fenfluramine outlier results in a similar mean error in the predicted values for P_late (dashed horizontal line) and the 95% CI limits of agreement are more narrow (dotted horizontal lines).