Expected changes in obesity after reformulation to reduce added sugars in beverages: A modeling study

Background Several strategies have been proposed to reduce the intake of added sugars in the population. In Mexico, a 10% sugar-sweetened beverages (SSBs) tax was implemented in 2014, and the implementation of other nutritional policies, such as product reformulation to reduce added sugars, is under discussion. WHO recommends that all individuals consume less than 10% of their total energy intake (TEI) from added sugars. We propose gradually reducing added sugars in SSBs to achieve an average 10% consumption of added sugars in the Mexican population over 10 years and to estimate the expected impact of reformulation in adult body weight and obesity. Methods and findings Baseline consumption for added sugars and SSBs, sex, age, socioeconomic status (SES), height, and weight for Mexican adults were obtained from the 2012 Mexico National Health and Nutrition Survey (ENSANUT). On average, 12.6% of the TEI was contributed by added sugars; we defined a 50% reduction in added sugars in SSBs over 10 years as a reformulation target. Using a dynamic weight change model, sugar reductions were translated into individual expected changes in body weight assuming a 43% caloric compensation and a 2-year lag for the full effect of reformulation to occur. Results were stratified by sex, age, and SES. Twelve years after reformulation, the TEI from added sugars is expected to decrease to 10%, assuming no compensation from added sugars; 44% of the population would still be above WHO recommendations, requiring further sugar reductions to food. Body weight could be reduced by 1.3 kg (95% CI −1.4 to −1.2) in the adult population, and obesity could decrease 3.9 percentage points (pp; −12.5% relative to baseline). Our sensitivity analyses suggest that the impact of the intervention could vary from 0.12 kg after 6 months to 1.52 kg in the long term. Conclusions Reformulation to reduce added sugars in SSBs could produce large reductions in sugar consumption and obesity in the Mexican adult population. This study is limited by the use of a single dietary recall and by data collected in all seasons except summer; still, these limitations should lead to conservative estimates of the reformulation effect. Reformulation success could depend on government enforcement and industry and consumer response, for which further research and evidence are needed.

• TEI, total energy intake. See T EI init for total energy intake at baseline.
• ENSANUT, National Health and Nutrition Survey.
• INSP, National Institute of Public Health.
• WHO, World Health Organization.
• T EI init , total energy intake at baseline.
• SSB max , maximum consumption of kcals from SSB such that 10% added sugar is achieved.
• ∆c, theoretical consumption change to achieve κ p × 100% consumption of added sugar.
• i (superscript), ith individual in the sample. T EI (i) init corresponds to total energy intake at baseline for individual i.
• prop, estimated average proportional change for SSBs consumers such that κ p × 100% added sugar is achieved.
• Reduction(y k ), reduction of sugar % at year k.
• λ, proportion of added sugar reduction that one desires to achieve by year .
• , year at which a λ × 100% added sugar reduction is achieved.
• t, variable for day.
• BW , body weight function (kg) as a function of time (BW ≡ BW (t)).
• EE, energy expenditure as function of time (EE ≡ EE(t)).
• AT , adaptative thermogenesis as a function of time (AT ≡ AT (t)).
• RM R init , resting metabolic rate at baseline.
• F init , fat mass at baseline.
• H init , height at baseline.
• ∆T EI, change in energy intake as a function of time (∆T EI ≡ ∆T EI(t)).
• K, constant for the initial energy balance condition (equilibrium).
• p, proportion of lean mass attributable to energy intake/expenditure difference.
• P AL, physical activity level.
• T EF , thermal effect of feeding. Categories of "normal" (1), "overweight" (2) and "obesity" (3) at baseline. ses Socioeconomic level, divided in tertiles, using the weighted sample. sugar ssb Added sugar consumption at baseline from SSB (kcal). kcaltot Daily total caloric intake at baseline (kcal). finalweight Weight after intervention (kg). changekcal Change in energy after intervention (kcal). changeweight Change in weight after 12 years (kg). bmifinal Body mass index after 12 years (kg/m 2 ). changebmi Change in body mass index after 12 years (kg/m 2 ). final bmiprevalences Categories of "normal" (1), "overweight" (2) and "obesity" (3) after intervention. sugar tot Added sugar consumption from all sources before intervention (kcal).  Table B shows the beverages included not included in the sugar regulation. The beverages classification is the same as in Sanchéz-Pimienta, et al which states: [3] "Regular soda" includes all brands of carbonated sodas with caloric sweeteners; "Fruit, flavored, sports, and energy drinks" include noncarbonated flavored water, industrialized juice, and energy and sport drinks; "sweetened coffee and tea" include coffee and tea with caloric sweeteners; "aguas frescas and homemade SSBs" include aguas frescas frescas, a traditional flavored water-based preparation, and fruit shakes without sugar or other caloric sweeteners, atoles without milk, and pozol (fermented corn beverage); and "sweetened milk and milk beverages" include milk, milk shakes, smoothies, coffee or tea made with milk (more than one-third of the preparation), and atoles with milk. [3] 1.2 Survey design ENSANUT is a cross-sectional, multi-stage, probabilistic survey representative of the Mexican population survey whose methodology has been explained elsewhere [4]. To account for this design, we used the R [5] package survey [6] with the following design:

Sugar Regulation Beverages group
Description Included

Industrialized carbonated beverages
Regular soda.

Industrialized non-carbonated beverages
Fruit, flavored, sports, and energy drinks.

Not Included
Homemade sweetened beverages Sweetened coffee and tea, aguas frescas and homemade SSBs.

Dairy beverages
Sweetened milk and milk beverages 2 Estimation of the sugar reduction target for regulation

Formula derivation
To estimate the target for added sugar regulation in SSBs, we estimated the maximum added sugar intake from SSBs such that overall consumption of added sugar was under the WHO guidelines. These guidelines establish that at most, 10% of the total energy intake (T EI init ) should come from added sugars. To find the target, we considered only those individuals that reported a consumption > 0 and we calculated the amount of added sugar from SSBs and from other sources as well as the Total Energy Intake in kcals (T T EI init ).
To estimate the individual level of maximum consumption of kcals from SSBs (SSB max ), such that a 10% added sugar is achieved, we set κ p = 0.1 (10% of total energy intake coming from added sugar). This was specified in the following equation: where Others is the consumption of other added sugars (kcal), T EI init is the current total energy intake (kcal), and SSB init is the current added sugar consumption from SSBs (kcal). The maximum sugar consumption from SSBs (SSB max ) hence equals: Using the SSB max , we obtained the theoretical consumption change, ∆ C : Intuitively, if current sugar consumption from SSBs (SSB init ) was lower than the maximum consumption from SSBs (SSB max ), we kept consumption at the current level (∆ C = 0). If sugar from additional sources was above the 10% threshold, we reduced all sugar from SSBs (∆ C = −SSB init ). Finally, if by reducing SSBs to the SSB max achieves the goal of 10% added sugars in overall energy intake, we reduced sugar consumption from SSBs to ∆ C = SSB max − SSB init .

Individual estimation to obtain added-sugar percent reduction
For each individual, i, in the sample, we estimated their maximum amount of sugar from SSBs (SSB (i) max ), such that the amount of added sugar in their total energy intake,T EI (i) init , is, at most, 10% for each individual. For that purpose, we used equation (2) and considered as inputs the individual's current total energy intake (T EI (i) init ), their SSBs caloric intake (SSB (i) init ), and their caloric intake from other added sugars (Others (i) ). The latter stand for kcaltot, sugar ssb, and sugar tot variables in our database.
Using each individual's SSB (i) init , and SSB (i) max we obtained their theoretical consumption change ∆ (i) C . The individual proportional change of sugar consumption from SSB was then calculated as init . We then estimated the average proportional change for consumers: 1 prop = 0.522, which is equivalent to a reduction of 52.2% of sugar in SSB, which we rounded to 50%.

Regulation scenarios
After obtaining the λ% change of added sugar we then established different scenarios of regulation that would achieve said change. The decreasing scenario (section 2.3.1) was used for all analysis in the article (with k = 50) whilst the increasing (section 2.3.2) and constant (section 2.3.3) scenarios were used for the sensitivity analysis. As was shown in the sensitivity analysis; all scenarios converge after 12 years.

Decreasing scenario
Let y 1 , y 2 , . . . , y 10 denote year 1, year 2 upto year 10 (respectively). The decreasing scenario assumes a yearly SSB-added-sugar reduction in which the yearly difference in added sugar% decreases in time. This scenario was implemented in [8] and is given by: for k = 1, 2, . . . , 10. The previous equation is equivalent to: To achieve a λ × 100% reduction by year y one would plug in the λ in Reduction(y ) (4) to obtain the first year reduction associated to λ: and then substitute in (5) to obtain an expression for the reduction in year k: In the specific case of a a reduction of λ = 0.5 (50%) after 10 years, the k-th year formula is: The proportion reduced yearly from the original amount of sugar for a reduction of λ = 0.5 after 10 years is shown in Table C.
Year y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y 10 Reduction 6.7% 12 Table C: Yearly proportion of sugar reduced from original amount of sugar for a reduction of λ = 0.5 after 10 years and difference in reduction % with previous year (Difference(y k ) = Reduction(y k ) − Reduction(y k−1 )).

Increasing scenario
This implementation scenario was done for sensitivity analysis. Instead of implementing a decrease in reduction of added sugar; we created a scenario in which the yearly difference in % reduction increases over time. In this case, the equation for the k-th year is given by: where λ × 100% is the desired reduction by year . In the case of a 50% (λ = 0.5) SSB-added-sugar reduction by year 10 the specific equation for the k-th year is given by: which yields the values in Table D.
These reduction values are the ones implemented in the paper's sensitivity analysis (see section 4 below).

Constant scenario
This implementation scenario was done for sensitivity analysis (see section 4). In this scenario we implemented a constant % reduction such that if a λ% reduction is implemented over years then each year a λ%/ is reduced such that by year , λ% is achieved. For the specific case of λ = 0.5 (50% reduction) for = 10 years the percent reduction is presented in Table E. The general formula for the k-th year in this case Year y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8 y 9 y 10 Reduction 5% 10% 15% 20% 25% 30% 35% 40% 45% 50.0% Difference 5% 5% 5% 5% 5% 5% 5% 5% 5% 5% Table E: Yearly proportion of sugar reduced using the constant 50 10 % reduction and difference in reduction % with previous year (Difference(y k ) = Reduction(y k ) − Reduction(y k−1 )). is given by: where λ denotes the expected reduction at year . In the particular case of a 50% reduction in 10 years (the one implemented in the paper's sensitivity analysis) the formula is:

Individual modelling of energy intake for reduction scenarios
The caloric reduction scenarios were designed globally. However, the reductions were conducted individually. Thus for each individual i we modelled their energy intake change at day t with a function ∆T EI (i) given by: with · the ceiling function where x stands for the smallest integer larger or equal to x. In the previous equation, T EI

Weight change model
The weight change model [9] defines individual weight (kg) as the sum of fat F and lean mass L, extracellular fluid ECF and glycogen G: Extracellular fluid ECF ≡ ECF (t) is the solution to the ordinary differential equation system: where N a = 3.22 mg/ml, ξ N a = 3000 mg/L/d, and ξ CI = 4000 mg/d, are phisiological constants [9]. ∆N a diet represents the change in sodium (mg/d) for the individual (3). CI b is the carbohydrate intake at baseline (assumed to be 1/2 of energy intake estimated in (3)) and CI ≡ CI(t) is the carbohydrate intake after the consumption reduction (assumed to be half the energy intake after reduction, CI ≡ ∆T EI(t)/2). Glycogen mass G ≡ G(t) is described by the ordinary differential equation: where ρ G = 4206.501kcals/kg (17.6M J/kg), and k G = CI b /G 2 init is a constant with G init = 0.5 kg the initial glycogen mass.
Fat and lean mass, F ≡ F (t) and L ≡ L(t), represent the solutions to the following system of nonlinear ordinary differential equations: with ρ F = 9440.727 kcals/kg (39.5 MJ/kg), ρ L = 1816.444 kcals/kg (7.6 MJ/kg) are constants, and p ≡ C/(C + F ) a function of fat mass with C = 10.4 · ρ L ρ −1 F . Total energy expenditure EE is given by: with RM R init the initial resting metabolic rate (as estimated by (21)), P AL the physical activity level (assumed P AL = 1.5), L init , F init , BW init the initial lean, fat and body weight masses. The constant δ is determined defined as δ = RM R init (1 − β T EF ) · P AL − 1 /BW init with β T EF = 0.1. Furthermore, the thermal effect of feeding is defined as T EF ≡ β T EF ∆T EI(t) with ∆T EI(t) as specified in (13). Finally, adaptative thermogenesis is given by the solution to the ODE system: We remark that for each individual, the initial resting metabolic rate RM R init is described by the equations [10]: with H init , AGE init initial height and age respectively. Initial fat mass was obtained via the function: (1/100) · BW init · 0.14 · AGE init + 37.31 × ln(BW init /H 2 init ) − 103.94 if Sex = Male, (1/100) · BW init · 0.14 · AGE init + 39.96 · ln(BW init /H 2 init ) − 102.01 if Sex = Female.
Additional information on the model can be found in [9,11,12,13]

Individual implementation
For each individual i in the ENSANUT sample we estimated their energy intake change (13) as a function of time from their individual SSB consumption, SSB init (sugar ssb in database) and their reported total energy intake T EI (i) init (kcaltot). We used this quantity to obtain their carbohydrate intake change CI (i) (t) = ∆T EI (i) (t)/2 and their carbohydrate intake at baseline CI Finally each individual's energy balance constant was estimated as init . For all individuals we set a physical activity level of 1.5 (P AL (i) = 1.5) which corresponds to "sedentarism" in accordance to [9].
For each individual, we estimated lean and fat masses, glycogen and extracellular fluid from the system of equations given by (15)(16)(17)(18)(19)(20) using the parameters described above and setting ∆N A (i) diet = 0. 2 To solve this system of differential equations, we used a 4th order Runge-Kutta algorithm (RK4) [14] with a stepsize ∆t = 1. RK4 was programmed in C++ for speed and connected to R via the Rcpp package. [15,16].
The RK4 algorithm throws numerical estimates for each time t of each individual's extracellular fluid ECF (i) (t), glycogen G (i) (t), fat and lean masses F (i) (t), L (i) (t). We estimated body weight for each individual adult in the ENSANUT sample as: where t stands for the number of days since the intervention. Each individual's BMI was estimated as: The previous model is completely programmed in the bw package in R [17]. Finally, we used the survey package [18,19] to create summary statistics of BW (i) (t) and BM I (i) (t) (both in the overall adult population and in specific subpopulations by sex, SES, and age). For these estimates we accounted for the survey design as established in section 1.2.
This model has been written in pseudocode and is presented in Algorithm 1. The different scenarios described in section 2.3 were implemented following the same algorithm by changing the formula for the reduction by year k in (13) and thus obtaining a different ∆T EI(t). for i in 1 to n do ∆T 16: init , Sex (i) using (21).

Model under compensation assumptions
As different combinations of compensation and regulations result in different values of energy reduction (λ × 100%, following the notation of section 2.3) at year 10, we created a consumption-percent change matrix Λ whose entries correspond to the overall reduction associated to both, the % compensation and the % added sugar reduction ( Table F). The rows of the matrix stand for % added sugar reduction whilst the columns for % compensation (both in multiples of 10). Hence for a reduction of 10% (1 × 10%) and compensation of 30% (3 × 10%) the entry Λ 1+1,3+1 of the matrix equals 1 × 10 − 3 % = 7%. In general, each entry of the matrix corresponds to a λ × 100% reduction es given by Λ i+1,j+1 = i × 10 − j %. Table  F shows the reductions Λ i+1,j+1 × 100% modelled for the sensitivity analysis.  Table F: Matrix Λ with percent reductions. For i × 10% added sugar reduction and j × 10% compensation the entry Λi+1,j+1 ((i + 1)-th row, (j + 1)-th column) denotes the corresponding % added sugar diminishment.
Each entry λ ≡ Λ i,j of the matrix was applied to the main scenario (7) to obtain the k-th year reduction. The reductions resulting from (7) were then plugged into (13) and the weight change model (section 3) was applied. There results were associated to a weight reduction matrix W whose entries W i+1,j+1 correspond to weight (kg) reduced after added sugar reduction to i × 10% accounting for j × 10% compensation. We represented the matrix graphically with the ggplot2 package [20] using cell-shading as seen in figure 1 in the main article.