Quantification of the effect of GLP‐1R agonists on body weight using in vitro efficacy information: An extension of the Hall body composition model

Abstract

Obesity has become a major public health concern worldwide. Pharmacological interventions with the glucagon‐like peptide‐1 receptor agonists (GLP‐1RAs) have shown promising results in facilitating weight loss and improving metabolic outcomes in individuals with obesity. Quantifying drug effects of GLP‐1RAs on energy intake (EI) and body weight (BW) using a QSP modeling approach can further increase the mechanistic understanding of these effects, and support obesity drug development. An extensive literature‐based dataset was created, including data from several diet, liraglutide and semaglutide studies and their effects on BW and related parameters. The Hall body composition model was used to quantify and predict effects on EI. The model was extended with (1) a lifestyle change/placebo effect on EI, (2) a weight loss effect on activity for the studies that included weight management support, and (3) a GLP‐1R agonistic effect using in vitro potency efficacy information. The estimated reduction in EI of clinically relevant dosages of semaglutide (2.4 mg) and liraglutide (3.0 mg) was 34.5% and 13.0%, respectively. The model adequately described the resulting change in BW over time. At 20 weeks the change in BW was estimated to be −17% for 2.4 mg semaglutide and −8% for 3 mg liraglutide, respectively. External validation showed the model was able to predict the effect of semaglutide on BW in the STEP 1 study. The GLP‐1RA body composition model can be used to quantify and predict the effect of novel GLP‐1R agonists on BW and changes in underlying processes using early in vitro efficacy information.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Glucagon‐like peptide‐1 receptor agonists (GLP‐1RAs) and related compounds have shown significant results in weight loss and improving metabolic outcomes in individuals with obesity. The Hall body composition model is a mathematical framework to simulate changes in energy balance and body composition.

• WHAT QUESTION DID THIS STUDY ADDRESS?

Can we quantify and predict the effects of GLP‐1RAs on energy intake and weight loss by extending the existing Hall body composition model for GLP1‐RAs?

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

The Hall body composition model was extended with (1) a lifestyle change/placebo effect, (2) an activity effect for the studies with weight management support, and (3) a GLP‐1R agonistic effect.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

The developed GLP‐1RA body composition model is a quantitative decision‐making tool that can be used to quantify and predict the effect of novel GLP‐1R agonists on body weight (BW) using early in vitro efficacy information. It can improve our mechanistic understanding of the processes underlying BW changes of novel GLP‐1RA candidate drugs.

INTRODUCTION

Obesity has become a major global public health concern, demanding innovative approaches for effective weight management (WM). Pharmacological interventions, as with glucagon‐like peptide‐1 receptor agonists (GLP‐1RAs), have resulted in weight loss and improved metabolic outcomes in individuals with obesity. ¹ , ² However, a comprehensive understanding of the precise mechanisms underlying the weight loss effects of GLP‐1RAs and the long‐term impact on body weight (BW) dynamics is still evolving.

Mathematical modeling offers valuable investigation of complex physiological systems and underlying mechanisms, and prediction of the interventional outcomes. Over the years weight loss models have been developed from simple regression to comprehensive mathematical strategies. ³ A subgroup of the models is based on the energy balance equation that states that the rate of energy stores is the difference between the energy intake (EI, calories consumed) and the energy expenditure (EE, calories burned). The Hall model ⁴ is an example of an energy balance‐based comprehensive mathematical model (Figure 1). The Hall model integrates various physiological factors, including EI, EE, and metabolic rate adjustments (the body's adaptive responses to changes in energy balance), to simulate how changes in diet, physical activity and other factors affect BW over time. Although more descriptive models can be used to predict the effects of drugs on weight loss, ⁵ the Hall model provides a deeper understanding of the physiology of weight change (WTCH) at the mechanistic level. In addition, a more detailed description of biological and pharmacological processes is associated with higher expected predictive power. ⁶ , ⁷ Therefore, this model was deemed a good starting point to increase mechanistic insight into the effects of GLP‐1R agonists, enabling weight loss predictions.

FIGURE 1.

Schematic representation of the main principles of the Hall model, including the model extension with diet/lifestyle change, weight change on activity, and GLP‐1R agonistic effects. Body weight is constructed from fat mass (FM) and fat‐free mass (FFM) (carbohydrates, protein, bone mass, and intra‐ and extra‐cellular fluid). These compartments are linked through the metabolic processes from carbohydrate, fat, and protein intake to carbohydrate, fat, and protein oxidation. Through gluconeogenesis, glucose can be synthesized from amino acids (protein) after proteolysis and fat after lypolysis. After glycogenolysis, glucose can be converted to fat (triglyceride) through de novo lipogenesis. The total energy expenditure TEE can be constructed from all the sub‐components of energy expenditure (RMR, PAE, and TEF) within the model. The change in body weight is based on the energy balance between energy intake (EI) and total energy expenditure (TEE). Diet and GLP‐1R agonistic effects directly affect the amount of energy intake per day.

The present research describes and predicts the effect of GLP‐1RAs on weight loss over time and explores the underlying physiological processes involved using quantitative systems pharmacology modeling techniques. ⁸ By integrating the Hall model with available GLP‐1RAs' weight loss clinical data into a GLP‐1RA body composition model, we aim to gain a deeper quantitative understanding of the drug effects of GLP‐1RAs on weight regulation. This approach will enable us to simulate the time‐dependent changes in BW, underlying building blocks such as fat mass (FM) and fat‐free mass (FFM), and metabolic parameters, thereby predicting the short‐term and long‐term effects of GLP‐1R agonists on weight loss.

METHODS

Data

A literature dataset was created, including body composition and EE data, to validate our implementation of the Hall model in NONMEM and R. Data were extracted from the publications that were described in the Hall model paper ⁴ as well as from additional published diet studies. ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ For the development and validation of the GLP‐1RA body composition model, treatment and placebo data from several liraglutide and semaglutide clinical studies were added to the dataset. ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹ Table 1 shows an overview of the publications included in the analysis. Data were extracted from publications using the DigitizeIt software. ³²

TABLE 1.

Overview of studies included in the analysis.

Study type	Dataset use	Publication	Population	Calorie restriction
Diet studies	Validation of model implementation	Diaz 1992 9	Healthy	50%
		Jebb 1993 10	Healthy	33%, −67%
		Jebb 1996 11	Healthy	33%, −67%
		Schrauwen 1997 12	Healthy	0, 10%
		Das 2017 13	Healthy	0, −10%, −15%, −25%
		Heilbronn 2006 14	Healthy	−10%, −65%
		Guo 2018 15	Healthy	−25%
		Redman 2007 16	Healthy	−25%
		Racette 2011 17	Healthy	−28%
		Weiss 2015 18	Non‐diabetic obese	−20%
		Rumpler 1991 19	Non‐diabetic obese	−40%, −55%
		de Boer 1986 20	Non‐diabetic obese	−50%
Liraglutide studies	Model development	Can 2014 21	Non‐diabetic obese	0
		Pi‐Sunyer 2015, SCALE 22	Non‐diabetic obese, pre‐diabetic	0
		Astrup 2009 23	Non‐diabetic obese	−5%, −17%
		le Roux 2017, SCALE 24	Pre‐diabetic	0
Semaglutide studies	Model development	Blundell 2017 25	Non‐diabetic obese	0
		Hjerpsted 2017 26	Non‐diabetic obese	0
		Sorli 2017, SUSTAIN 1 57	Type 2 diabetic	0
		Wadden 2021, STEP 3 28	Non‐diabetic obese	1000–1200 kcal/d (8 weeks), 1200–1800 kcal/d
		Garvey 2022, STEP 5 29	Non‐diabetic obese	−500 kcal/d
		Rubino 2022, STEP 8 30	Non‐diabetic obese	−500 kcal/d
		Pratley 2018, SUSTAIN 7 31	Type 2 diabetic	0
	External validation	Wilding 2021, STEP 1 27	Non‐diabetic obese	−500 kcal/d

Note: The diet studies used to validate the model implementation, were extracted from the original Hall model publication. For model extension, liraglutide and semaglutide data were extracted from the literature. Next to calorie restriction, exercise was promoted in the semaglutide STEP studies.

Compound potency assay and free fraction

To determine the half maximal effective concentration (EC₅₀) of liraglutide and semaglutide, a GLP‐1R Activation Assay was used based on the elevation of cyclic adenosine monophosphate (cAMP) production in Chinese hamster ovary cells that express the human GLP‐1 receptor. The EC₅₀ values were determined in the absence of serum albumin to reflect the potency of the free compound (Table 2). The results from this assay were assumed to be linearly related to the in vivo potency.

TABLE 2.

Compound EC₅₀ and free fraction information.

Compound	GLP‐1R EC50 (pM) a	Free fraction (%)
Liraglutide	1.2	Estimated
Semaglutide	0.9	0.0025

^a In vitro EC₅₀ in absence of serum protein.

Free fraction of the compounds in plasma were measured in‐house at AstraZeneca. As no accurate free fraction information was available for liraglutide, its free fraction was estimated during model development.

The Hall model

The Hall model code was downloaded from the supplemental material belonging to the 2009 publication. ⁴ The downloaded Berkeley Madonna code was converted to NONMEM code for further development. The Hall model consists of three coupled differential equations representing carbohydrate, fat, and protein energy balance. Each equation describes the metabolic processes of carbohydrate, fat, and protein intake to carbohydrate, fat, and protein oxidation. Glucose is synthesized from amino acids (protein) and fat through gluconeogenesis after proteolysis and lipolysis, respectively. After glycogenolysis, glucose is converted to fat (triglyceride) via de novo lipogenesis. BW is constructed from FM (the fat compartment) and FFM (carbohydrates, protein, bone mass, and intra‐ and extra‐cellular fluid). The total energy expenditure (TEE) can be constructed from all the sub‐components of EE (RMR, PAE, and TEF) within the model. The body composition model has many equations describing the BW and composition based on the balance between EI and EE, including the underlying biological processes. Here, we included only the adjusted and newly added equations. The complete model code can be found in the supplementary materials (S10). The published Hall body composition model code uses input datasets containing time‐varying information on the amount of EI and meal composition to simulate the effect on body composition and underlying processes. No changes were made to the original model equations. However, to allow the model to estimate a GLP‐1R agonistic effect on EI. The BW steady state was derived by calculating the EI needed to keep a constant BW and added to the model code, similar to the web based BW simulator on the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) website. ³³ The initial body fat mass (F_init) was calculated using the published values of height (HGHT), and baseline body weight (BW_init) and the regression equations of Jackson et al. for men ($\mathrm{F}\_{\text{init}}_{\mathrm{m}}$, Equation 1a) and women ($\mathrm{F}\_{\text{init}}_{\mathrm{w}}$, Equation 1b), respectively ³⁴ :

$$\begin{array}{c}{\text{F\_init}}_{\mathrm{m}}=\hfill \\ \frac{\text{BW\_init}}{100}\left[0.14\times \mathrm{age}+37.31\times \ln \left(\frac{\text{BW\_init}}{{\text{HGHT}}^2}\right)-103.94\right]\hfill \end{array}$$ (1a)

$$\begin{array}{c}{\text{F\_init}}_{\text{w}}=\hfill \\ \frac{\text{BW\_init}}{100}\left[0.14\times \mathrm{age}+39.96\times \ln \left(\frac{\text{BW\_init}}{{\text{HGHT}}^2}\right)-102.01\right]\hfill \end{array}$$ (1b)

From F_init (g) and BW_init (g) the FFM (g) at baseline was calculated (FFM0) using Equation 2:

$$\mathrm{FFM}\_\text{init}=\mathrm{BW}\_\text{init}-\mathrm{F}\_\text{init}$$ (2)

Resting metabolic rate at baseline (RMR_init (kcal/d)) was calculated using the equation from Mifflin et al. for men (Equation 3a) and women (Equation 3b), respectively, ³⁵

$$\begin{array}{c}{\text{RMR\_init}}_{\text{m}}=\hfill \\ 10\times {\mathrm{BW}}_{\text{init}}+6.25\times \text{HGHT}*100-5\times \mathrm{AGE}-161\hfill \end{array}$$ (3a)

$$\begin{array}{c}{\text{RMR\_init}}_{\mathrm{w}}=\hfill \\ 10\times {\text{BW}}_{\text{init}}+6.25\times \text{HGHT}*100-5\times \mathrm{AGE}+5\hfill \end{array}$$ (3b)

where HGHT is the height in meters and AGE is the age in years.

Since the current analysis used mean study data, exact gender stratification was not possible. In those cases, the equations for males or females were used depending on the fraction of females in the study, that is, when the fraction of females was ≥0.5 the equation for females was used.

For the model to be in a steady state at baseline, the energy intake (EI_init (kcal/d)) must be equal to the TEE (kcal/d), which is the product of RMR_init and PAL (Equation 4):

$$\mathrm{EI}\_\text{init}=\mathrm{RMR}\_\text{init}*\mathrm{PAL}$$ (4)

The baseline physical activity level (PAL) was taken from Heymsfield et al. ³⁶ and assumed to be low active to active. This corresponds to a PAL of 1.6 at baseline, which is in line with an average physical functioning (PF) score of 50%, as determined in the STEP studies. ³⁷

From Equation 4, the EI at baseline was calculated. The total baseline EI (EI_init) was divided over fat, proteins and carbohydrates assuming that standard meals consisted of 37% fat, 13% proteins and 50% carbohydrate. ⁴ Hence the imputed fraction fat (f_fat), protein (f_prot), and carbohydrates (f_carb) were 0.37, 0.13, and 0.5, respectively. From the EI_init (kcal/day) and the f_fat, f_protein, and f_carb the total amount of energy in grams (g) was calculated according to the equations in the Hall model code. The newly derived model steady state was tested using simulations.

Lifestyle change effect

In the existing Hall model, changes in EI can be used as model input to predict the resulting weight loss. The model was extended with a lifestyle change (LSC) effect to allow for the estimation of the change in EI to describe and predict the weight loss observed in the placebo arms of the GLP‐1RA clinical studies.

The effect of diet, referred to as LSC effect due to study participation, was assumed to result in lowering EI, (i.e., food intake). This LSC effect (LSCeff) was described by an inverse Bateman function (Equation 5).

$$\text{LSCeff}=1-\frac{\left(\text{LSCI}*k_{\mathrm{lsc}}*{\mathrm{e}}^{-k_{\mathrm{lsc}}*\text{TIMEd}}–{\mathrm{e}}^{-k_{\mathrm{red}}*\text{TIMEd}}\right)}{\left(k_{\mathrm{red}}-k_{\mathrm{lsc}}\right)}$$ (5)

In this equation, LSCI is the initial reduction in EI due to LSCs, or the amplitude of the effect, expressed as a fraction. k _lsc (d⁻¹) is the rate constant of the LSC effect, k _red (d⁻¹) is the rate constant of the reduction in LSC effect and TIMEd is the time in days. Placebo data were pooled to estimate the LSC effect rate constants k _lsc and k _red. LSCI parameter was estimated per study if needed.

Activity effect

The Hall model describes the proportional relationship between energy expended during physical activities and its effect one BW of an individual. With weight loss the physical activity energy expenditure (PAE) decreases, due to increase in muscle efficiency. ³⁸ Low‐intensity physical activities (activ) may be subject to the effects of adaptive thermogenesis (T), whereas higher‐intensity exercise (exerc) appears to not be affected. ⁴

An additional increase in activity as a result of the WM and behavioral support in the semaglutide STEP studies was observed, ²⁷ , ²⁸ , ²⁹ , ³⁰ that correlated with the observed weight loss (Figure 2). To account for this increase in activity, an activity effect (ACTeff) on the exercise part of the PAE was estimated (Equations (6a), (6b), (6c)),

$$\mathrm{PAE}=\text{activ}\_\mathrm{b}*\left(1+\mathit{\sigma T}\right)*\mathrm{BW}+\text{exerc}*\mathrm{BW}$$ (6a)

$$\text{exerc}=\text{exerc}\_\mathrm{b}+\text{ACTeff}$$ (6b)

$$\text{ACTeff}=\mathrm{EMA}{\mathrm{X}}_{\mathrm{ACT}}\left(\frac{\text{WTCH}}{\text{WTCH}+{\text{EWTCH}}_{50}}\right)$$ (6c)

with activ_b and exerc describing the low intensity activity and exercise part of the PAE in kcal/d/kg, respectively. In these equations, exerc_b (kcal/d/kg) refers to the baseline exercise, EMAX_ACT is the maximum of the effect (kcal/d/kg), WTCH the change in BW in kilograms, and EWTCH₅₀ is the WTCH at 50% of the maximum in kilograms.

FIGURE 2.

Physical functioning score change from baseline versus body weight change from baseline for the semaglutide STEP 1 ²⁷ and the STEP 3 ²⁸ studies. Gray circles represent the placebo observations, blue circles the semaglutide observations.

GLP‐1R agonist effect

For the analysis of the GLP‐1R agonistic drug effects on BW, data from the liraglutide and semaglutide clinical studies were used (Table 1). Plasma liraglutide and semaglutide concentrations (pmol/L) were predicted using published PK models. ³⁹ , ⁴⁰ The GLP‐1R agonistic effect on EI was described with an EMAX relation, driven by the in vitro EC₅₀ normalized free drug concentration (Equation 7a). The in vivo EC₅₀ of the GLP‐1 effect (TVGLP₅₀) on EI was estimated as a factor of the in vitro EC₅₀ assuming a linear relationship between the in vitro and in vivo EC₅₀. A time‐dependent increase in the EC₅₀ was estimated to describe the tolerance of the effect (Equation 7b).

$$\mathrm{GL}{\mathrm{P}}_{\text{effect}}=1-\text{EMAX}\times \frac{\frac{C_{\text{drug},\text{free}}}{\mathrm{E}{\mathrm{C}}_{50,\text{drug},\text{in vitro}}}}{\mathrm{GLP}50+\frac{C_{\text{drug},\text{free}}}{\mathrm{E}{\mathrm{C}}_{50,\text{drug},\text{in vitro}}}}$$ (7a)

$$\mathrm{GL}{\mathrm{P}}_{50}=\text{TVGL}{\mathrm{P}}_{50}+\frac{\mathrm{SSE}{\mathrm{C}}_{50}\times \text{TAFD}}{T_{50}+\text{TAFD}}$$ (7b)

In these equations, C _drug,free represent the free drug concentration and EC_{50,drug,in vitro} the in vitro drug EC₅₀ for the GLP‐1R in absence of serum protein (Table 2). SSEC₅₀ is the estimated steady state EC₅₀, and T ₅₀ the time of half the maximum in vivo EC₅₀.

A schematic overview of the GLP‐1RA body composition model including the lifestyle‐ and drug effects is represented in Figure 1.

Model evaluation

The goodness‐of‐fit (GOF) of the model to the fitted data was informed by the objective function value (OFV), defined as minus twice the log‐likelihood in NONMEM version 7.5. ⁴¹ When comparing nested models, a likelihood ratio test was performed, where it was assumed that the difference in OFV was chi‐squared distributed. In the case of adding one parameter to the model, a decrease of more than 6.63 points in the OFV (theoretically corresponding with a p‐value of 0.01) was considered significant. The GOF was also investigated by visual inspection of diagnostic plots of the observations and weight residuals versus prediction and time. In addition, the root mean square percent error (RMSPE) was calculated using the following equation:

$$\text{RMSPE}=100*\sqrt{\frac{1}{n}\sum _{\mathrm{i}=1}^n{\left(\frac{y_i-{\widehat{y}}_i}{y_i}\right)}^2}$$

where n denotes the number of observations, y _i denotes the observation, and ŷ _i denotes the corresponding prediction.

The model was externally validated by predicting the effect of semaglutide in the STEP 1 study, ²⁷ assuming the same LSC effect as estimated for the semaglutide STEP 5 and 8 studies. The NONMEM model code was implemented in R using mrgsolve ⁴² to perform these simulations. To account for parameter uncertainty, 1000 profiles per treatment arm were simulated, sampled from the covariance matrix generated by NONMEM. The 90% confidence interval was obtained by calculating the 5 and 95 percentiles of the simulated dependent variables. Visual agreement between simulated and observed profiles was used to assess validity of model predictiveness.

RESULTS

The Hall model and lifestyle change effect

As a first step, it was assessed whether the adjusted Hall model could describe BW changes from the diet studies (Table 1) using the model extension of the LSC effect on the EI (Equation 5). Some of these studies were also included in the Hall publication [3] to validate their model.

The percentage calorie reduction or increment was extracted from the publications and added to the dataset as a fraction. The effect of the change in calorie intake on BW was modeled as a LSC effect described with an inverse Bateman function on the EI (Equation 5). The parameter describing the initial change in calorie intake, the LSCI, was initially fixed to the calorie change fraction from the input dataset. The rate constant for the on‐set of the effect, k _lsc, was fixed to a high number (e.g., 10 d⁻¹) to reflect a rapid on‐set of calorie reduction on BW changes. Exploratory runs showed that estimating the k _lsc did not significantly change the model fit. k _red was estimated as a single parameter for all studies, describing the reduction of the effect over time (Model A). For comparison, the calorie restriction was also estimated per study (Model B). This significantly improved the model fit (Figure 3, blue lines), with a drop in OFV of 231 points and an improved RMSPE of 1.1% for model B compared to 2.4% for model A (Table 3). The estimated calorie restrictions were well in line with the published values (R ²  = 0.84) (Table 3).

FIGURE 3.

Model fit of body weight in the diet studies, ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ , ²¹ facetted by study and per cent calorie restriction. Gray circles represent the mean observations. Orange lines represent the model fit using the calorie restriction from the publication and blue lines represent the model fit when estimating the calorie reduction per study.

TABLE 3.

Model RMPSE, dOFV, and final parameter estimates.

Parameter	Description	Diet studies		Drug studies
		Model A	Model B	Model C	Model D
RMSPE	Root mean square percent error between predicted and observed	2.4%	1.1%	8.1%	6.8%
dOFV	Difference in OFV	–	−231 compared to model A	–	−39 compared to model C

Model parameter			Value (%RSE)	Value (%RSE)	Value (%RSE)	Value (%RSE)
LSCI	Amplitude of lifestyle change effect	Diaz 1992 9	−0.5 (FIX)	−0.466 (−0.712)
		Jebb 1993 10	−0.33 (FIX)	−0.426 (−0.190)
		Jebb 1996 11	0.67 (FIX)	0.433 (0.187)
		Das 2017 13	0.1 (FIX)	0.282 (15.5)
			0.15 (FIX)	0.354 (15.5)
			0.25 (FIX)	0.315 (15.3)
		Heilbronn 2006 14	0.65 (FIX)	0.446 (2.71)
		Guo 2018 15	0.25 (FIX)	0.270 (11.6)
		Redman 2007 16	0.25 (FIX)	0.281 (2.59)
		Racette 2011 17	0.28 (FIX)	0.300 (3.64)
		Weiss 2015 18	0.2 (FIX)	0.262 (4.44)
		Rumpler 1991 19	0.4 (FIX)	0.556 (0.701)
			0.55 (FIX)	0.528 (0.716)
		de Boer 1986 20	0.5 (FIX)	0.701 (1.70)
		Can 2014 21			0 (FIX)	0 (FIX)
		Pi‐Sunyer 2015, SCALE 22			0.119 (5.92)	0.112 (3.38)
		Astrup 2009 23			0.230 (4.34)	0.224 (3.99)
		Astrup 2015 TIME > 100 d			0.126 (6.25)	0.117 (5.41)
		le Roux 2017, SCALE 24			0.106 (5.32)	0.0993 (3.11)
		Blundell 2017 25			−0.0313 (−30.7)	−0.0288 (−37.8)
		Hjerpsted 2017 26
		Sorli 2017, SUSTAIN 1, 57 Pratley 2018, SUSTAIN 7 31			0 (FIX)	0 (FIX)
		Wadden 2021, STEP 3 28			0.490 (4.42)	0.548 (5.57)
		Garvey 2022, STEP 5, 29 Rubino 2022, STEP 8 30			0.142 (9.47)	0.150 (8.80)
k lsc	Rate constant of lifestyle change effect (d‐1)		10.0 (FIX)	10.0 (FIX)	10.0 (FIX)	10.0 (FIX)
k red	Rate constant of the reduction in lifestyle change effect (w‐1)		0.000659 (27.5)	0.00144 (23.2)	0.0161 (11.9)	0.01365 (5.05)
k red		STEP 5, 8			0.0227 (11.1)	0.0379 (9.31)
k red		STEP 3			0.0483 (8.07)	0.0647 (9.44)
TVGLP50	GLP‐1 EC50 potency normalized effects (fold x in‐vitro EC50)				46.0 (26.1)	48.1 (25.2)
T 50	Half time point for change in EC50 (days)				767 (31.2)	1439 (40.3)
SSEC50	Steady state EC50 for food intake reduction				2036 (21.9)	3798 (32.2)
fulira	Free fraction liraglutide				0.00222 (3.56)	0.00243 (4.19)
EMAX_ACT	Maximum inhibition of weight change exercise (kcal/day/kg)					48.1 (25.2)
EWC50_ACT	Weight change at 50% of the effect (kg)					1439 (40.3)
σ 2 body weight (kg)			2.95 (31.0)	0.676 (59.3)	0.125 (22.2)	0.105 (19.7)
σ 2 body weight (%) change from baseline					0.233 (16.1)	0.209 (16.1)

Note: Models A and B: model extended with diet/lifestyle change effect based on diet studies Model A: using published calorie restriction information and Model B estimating the calorie restriction. Models C and D: model extended with lifestyle change and drug effect based on liraglutide and semaglutide clinical studies. Model D, is the final model including activity effect.

Estimated lifestyle change effect, drug effect, and activity effect parameters for models A, B, and D. The relative standard error RSE (%) is calculated as the standard error SE/Estimate*100.

To investigate whether the model was able to predict the underlying building blocks of BW and the energy terms, simulations were performed and overlayed with available data from the publications. The model was able to predict the changes in FM (Figure S1), FFM (Figure S2), EI (Figure S3), TEE (Figure S4), RMR and PAE (Figure S5), and the respiratory quotient (RQ) (Figure S6).

GLP‐1R agonist and activity effect

After the model adjustments were validated on the diet studies, a GLP‐1R agonistic drug effect was added to the model, assuming an inhibition of the amount of EI. For this part of the analysis, the liraglutide and semaglutide clinical studies were used (Table 1). The semaglutide STEP 1 study ²⁷ was excluded from the analysis and used for external validation. For the LSC effect (or placebo effect), k _lsc was kept fixed at 10 (d⁻¹), k _red was estimated, and LSCI was estimated per study. All drug effect parameters were estimated (Equations 6a and Equation 6b). The estimated model parameters are presented in Table 3. The model was able to adequately describe the BW (%) change from baseline for all studies assuming only a LSC effect and a drug effect on EI (Model C, RMSPE 8.1%). However, in the semaglutide STEP studies, WM and intensive behavioral treatment (IBT) were also provided to the subjects. ²⁷ , ²⁸ , ³⁰ For instance, in the STEP 3 study, ²⁸ participants received weekly intensive behavioral support in which they discussed progress, reviewed their food diary/Web application, and addressed any adherence issues. During the STEP 1 and 3 study, ²⁷ , ²⁸ physical function was assessed using the SF‐36 questionnaire. ⁴³ The PF score was derived from vigorous activity as well as more moderate, daily activities. Plotting the PF score versus the WTCH revealed a clear correlation between the increase in weight loss and increase in activity (Figure 2). Based on this, in addition to the LSCeff, an activity effect (ACTeff) was added to the exercise part of the PAE equation describing an increase in activity with increasing weight loss (Equations (6a), (6b), (6c) ‘Section 2’). The addition of the activity effect (Model D) resulted in a significant decrease in OFV of 39 points and lower residual error estimates (Table 3). In addition, the RMSPE improved from 8.1% (Model C) to 6.8% (Model D). Model D was selected as the final GLP‐1RA body composition model. Parameter estimates of the model with and without the ACTeff included are presented in Table 3. For the final drug model, model D, the reduction rate of the LSC effect, k _red was estimated to be higher for the STEP studies, compared to the other drug studies (0.0379 w⁻¹ for STEP 5 and 8 and 0.0647 w⁻¹ for STEP 3 vs. 0.00195 w⁻¹ for the other studies). The estimated LSCI in the semaglutide STEP 5 and 8 studies was 0.15 and 0.55 for the STEP 3 study, suggesting a calorie reduction of 15% and 55%, respectively.

Drug effect parameters could be estimated with good precision (Table 3). Liraglutide free fraction was estimated to be 0.00243, which corresponds with 98% plasma protein binding, which is well in line with 98–99% protein binding determined for clinically relevant in vivo concentrations of liraglutide. ⁴⁴ The TVGLP₅₀ was estimated to be 48.1 indicating a 48.1‐fold lower in vivo potency (higher EC₅₀) as compared to the measured in vitro efficacy. The tolerance of the GLPeff was estimated to be slower (higher T ₅₀) but stronger (higher SSEC₅₀) when including the activity effect.

Calculated from the compound's average steady‐state concentration, the estimated GLP‐1R agonistic drug effect resulted in a 34.5% decrease in EI for 2.4 mg semaglutide at week 20 compared to a 13% decrease for 3 mg liraglutide.

The EMAX of the ACTeff was estimated to be 0.00193 (kcal/d/kg), and the estimated weight loss at which half of the maximum effect was reached (EWC₅₀_ACT) was −22.9 kg. The model was able to predict the underlying body composition building blocks, such as FM and FFM (Figure S7), as well as the TEE and underlying oxidative processes (Figure S8). The resulting increase in EE per day through exercise was predicted to be up to 75 kcal/day (Figure S9).

The final model adequately described the change in BW over time (Figure 4). At 20 weeks BW changes of −17% and −8% were predicted for semaglutide (2.4 mg, average over STEP 3, 5 and 8 studies) and liraglutide (3 mg, STEP 8 study), respectively, which is well in line with published outcomes of these studies. ²⁸ , ²⁹ , ³⁰

FIGURE 4.

Model fit of body weight (%) change from baseline in the drug studies, ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁸ , ²⁹ , ³⁰ , ³¹ facetted by study and dose. Gray circles represent the mean observations. Gray lines are the model fit of the placebo groups, orange lines the model fit of liraglutide groups and blue lines the model fit of the semaglutide groups.

External validation showed, based on visual agreement, that the model was able to predict the 2.4 mg semaglutide‐induced WTCH in the STEP 1 study ²⁷ (RMPSE 2.4%), assuming the same LSCeff and ACTeff as compared to the STEP 5 and 8 studies ²⁹ , ³⁰ (Figure 5). Overall the observations fall within the 90% confidence interval of the simulated parameter uncertainty, individual variability was not taken into account.

FIGURE 5.

External validation: prediction of the body weight (%) change from baseline in the STEP 1 study, ²⁷ facetted by study and dose. Gray circles represent the mean observations. The gray line is the model prediction, and the shaded area represents the 90% confidence interval obtained by performing model simulations, simulating 1000 profiles per treatment arm taking into account parameter uncertainty.

DISCUSSION

The Hall model and lifestyle change effect

The Hall body composition model ⁴ was used as a starting point to analyze and quantify the effects GLP‐1Ras on BW. The model was successfully re‐coded to be able to describe the effects of changes in EI on BW, BW building blocks and underlying processes based on a set of diet studies. ⁹ , ¹⁰ , ¹¹ , ¹² , ¹³ , ¹⁴ , ¹⁵ , ¹⁶ , ¹⁷ , ¹⁸ , ¹⁹ , ²⁰ The re‐coded model was able to describe and predict the changes in BW using calorie restriction information extracted from the study procedures (Model A) reasonably well, judging from visual inspection of model and goodness of fit. However, estimating the calorie restriction in combination with the reduction rate of such a LSC effect significantly improved the model fit, resulting in a decrease in RMPSE (from 2.4 to 1.1%, respectively) and a drop in OFV of 231 points.

The estimated mean calorie intake reduction was in general well in line with the prescribed reduction in calorie intake according to protocol, which shows that the model can be used to estimate changes in calorie intake in diet studies based on changes in BW (Figure 3). Besides describing the changes in BW, also changes in underlying building blocks such as FM and FFM (Figures S1, S2), energy terms EI, TEE and RMR (Figures S3–S5) and RQ could be predicted over time. Overall, the validation showed that the model could be used as a starting point to investigate drug effects on BW and underlying processes.

GLP‐1R agonist and activity effect

To study the effect of GLP‐1RAs on BW mean data from a selection of short‐ and long‐term semaglutide and liraglutide clinical studies were used. ²¹ , ²² , ²³ , ²⁴ , ²⁵ , ²⁶ , ²⁷ , ²⁸ , ²⁹ , ³⁰ , ³¹

The WTCH in the placebo arms of the included clinical studies was modeled using the same LSCeff on EI as was done for the diet studies. Although the weight loss due to study participation is probably driven mainly by changes in food intake (i.e., EI), it may also be partly driven by changes in activity and exercise (i.e., TEE). Since the mean data extracted from the publication did not contain sufficient information to distinguish between an effect on EI and TEE and simulations with the Hall model showed that there is only a slight difference in WTCH due to a lowering of EI compared to an increase in TEE, ³³ assuming an effect on EI only appears justified.

The effects of GLP‐1RA on delayed gastric emptying and increased satiety are known to result in weight loss. ⁴⁵ To quantify these effects on BW, a GLP‐1R agonistic drug effect on EI was added to the model, assuming a decrease in EI due to drug administration. The drug effect was driven by the free drug concentration normalized by the in vitro EC₅₀ for the GLP‐1R. As a result, the model can be used to predict in vivo WTCHs based on early in vitro EC₅₀ and free fraction information The assumption of linear scaling appears plausible based on the operational model of agonism, ⁴⁶ and it has been demonstrated in many cases with experimental data. ⁴⁷ , ⁴⁸ , ⁴⁹ The estimated GLP‐1R agonistic drug effect resulted in a 34.5% decrease in EI for 2.4 mg semaglutide compared to a 13.0% decrease for 3 mg liraglutide. These estimations align with the experimental results of a 35% reduction for semaglutide and a 16% reduction for liraglutide in EI. ²¹ , ⁵⁰

Including tolerance of the effect on EI by estimating a time‐dependent increase in the (in vivo) EC₅₀ over time significantly improved the description of the long‐term BW effects of liraglutide and semaglutide. This is in line with expectations, as tolerance is a well‐known phenomenon for GLP‐1R agonistic effects on the gastric system. ⁵¹ , ⁵²

The model with the combined LSC and drug effects (Model C) adequately described the data (RMSPE 8.1%). However, the amount of physical activity increased in the semaglutide STEP studies with increasing weight loss due to drug administration combined with intensive WM and IBT (Figure 2). Indeed, adding the ACTeff on PAE significantly improved the model (Model D, RMSPE 6.8%), resulting in a drop in OFV of 39 points for two additional parameters, corresponding with a p‐value of 0.026E‐9, suggesting that the subjects in the studies that included WM and IBT were motivated to increase their activities with increasing weight loss. The increase in EE due to increase in activity was predicted to be up to 75 kcal/day in the STEP 3 study (Figure S9). The PAE is proportional to the BW and thus decreases with weight loss because physical activity cost less energy at a lower BW. However, the increase in activity/exercise in the STEP studies partly compensates for this decrease in total PEA (Figure S9). The estimation of the activity effect mainly affected the estimated tolerance of the drug effect. Suggesting an overprediction of the drug effect when not considering an increase in the activity due to weight loss. In addition, the k _red was affected, resulting in a faster return to the baseline of the LSC effect. This indicates that increased weight loss and activity might result in a decrease in the LSC/diet effect.

This analysis shows that the underlying relative contributions of study participation, drug administration and WM support can be quantified using the proposed model‐based approach. Additional analysis based on rich individual data, as well as a comparison with real world data, is needed to further quantify the relative contributions of the effects on weight loss in these types of clinical trials.

In addition to adequately describing the WTCHs, the model was able to predict the effect of semaglutide and liraglutide on the underlying building blocks such as FM and FFM (Figure S7), and underlying processes such as TEE, protein oxidation, fat oxidation, and carbohydrate oxidation (Figure S8), making the model useful for gaining mechanistic insight in the effects of GLP‐1RAs and related compounds on the system.

Effect of diabetes

The dataset used for this analysis mainly included data from clinical studies in non‐diabetic obese subjects. However, the Pi‐Sunyer 2015 and le Roux 2017 studies ²² , ²⁴ also included pre‐diabetic subjects, and the Pratley 2018 study included obese subjects with diabetes. ³¹ It has been shown that type 2 diabetes in obesity is related to a less effective response to GLP‐1RA on weight loss. ² Despite this, the GLP‐1RA body composition model was also able to describe the weight loss in Type 2 Diabetic (T2DM) patients in the Pratley 2018 study, ³¹ without any additional parameters to distinguishing between the two populations. In a comparative analysis of liraglutide and semaglutide clinical data in persons with and without diabetes, it was suggested that one of the limitations on the inter‐trial comparison is that the studies with and without diabetes were unbalanced regarding race and sex, and that difference in body composition may result in differences in drug exposure. ² In addition, the obesity studies included WM and IBT, which may not always be representative of typical patient adherence in the general population. Although the Hall model takes into account that differences in meal macronutrient composition may result in different preferential partitioning of energy storage towards for instance body fat or body protein, the effect of differences in hormone levels and responses (e.g., insulin, glucagon, GLP‐1, and GIP), which are known to differ between different patient populations (healthy, pre‐diabetic, obese non‐diabetic, and T2DM), and their potential effect on adipose tissue storage and adaptive brain response to hunger or satiety, as described by the Carbohydrate–Insulin model, ⁵³ , ⁵⁴ are not incorporated. Therefore, further investigation of the differences in weight loss and the underlying processes in (pre‐)diabetic obese versus healthy obese patients after treatment with GLP‐1 agonists is needed, for instance by integrating the existing glucose, glucagon, GLP‐1, GIP, insulin model (4GI) with the Hall model, combining the energy balance with appropriate hormone‐related responses. ⁵⁵

In conclusion, the developed extended GLP‐1RA body composition model can be used to predict the effect of GLP‐1RAs on BW and underlying building blocks and processes, based on compound's early in vitro efficacy information. Future work involves the integration of the Hall body composition model with the 4GI glucose homeostasis model ⁵⁶ to explore the effects of glucose homeostasis on weight loss and weight loss on insulin sensitivity. ⁵⁷ Furthermore, a similar modeling approach can be applied to investigate and compare effects of GLP‐1RAs, GLP‐1R/glucose dependent insulinotropic polypeptide receptor (GIPR) and GLP‐1R/ glucagon receptor (GCGR) dual agonist, such as tirzapetide and cotadutide and GLP‐1R/GIPR/GCGR triple agonists such as retatrutide on weight loss and related parameters using the GLP‐1RA body composition model as a starting point.

AUTHOR CONTRIBUTIONS

All authors wrote the manuscript. R.B. and N.S. designed the research; R.B. performed the research and analyzed the data.

FUNDING INFORMATION

No funding was received for this work.

CONFLICT OF INTEREST STATEMENT

Rolien Bosch and Nelleke Snelder are consultants at LAP&P. Rolien is a PhD student at the Erasmus Medical Centre. Eric Sijbrands has no potential conflicts of interest.

Supporting information

Data S1:

Bosch R, Sijbrands EJG, Snelder N. Quantification of the effect of GLP‐1R agonists on body weight using in vitro efficacy information: An extension of the Hall body composition model. CPT Pharmacometrics Syst Pharmacol. 2024;13:1488‐1502. doi: 10.1002/psp4.13183