FDA Sodium Reduction Targets and the Food Industry: Are There Incentives to Reformulate? Microsimulation Cost‐Effectiveness Analysis

Policy Points The World Health Organization has recommended sodium reduction as a “best buy” to prevent cardiovascular disease (CVD). Despite this, Congress has temporarily blocked the US Food and Drug Administration (FDA) from implementing voluntary industry targets for sodium reduction in processed foods, the implementation of which could cost the industry around $16 billion over 10 years. We modeled the health and economic impact of meeting the two‐year and ten‐year FDA targets, from the perspective of people working in the food system itself, over 20 years, from 2017 to 2036. Benefits of implementing the FDA voluntary sodium targets extend to food companies and food system workers, and the value of CVD‐related health gains and cost savings are together greater than the government and industry costs of reformulation. Context The US Food and Drug Administration (FDA) set draft voluntary targets to reduce sodium levels in processed foods. We aimed to determine cost effectiveness of meeting these draft sodium targets, from the perspective of US food system workers. Methods We employed a microsimulation cost‐effectiveness analysis using the US IMPACT Food Policy model with two scenarios: (1) short term, achieving two‐year FDA reformulation targets only, and (2) long term, achieving 10‐year FDA reformulation targets. We modeled four close‐to‐reality populations: food system “ever” workers; food system “current” workers in 2017; and subsets of processed food “ever” and “current” workers. Outcomes included cardiovascular disease cases prevented and postponed as well as incremental cost‐effectiveness ratio per quality‐adjusted life year (QALY) gained from 2017 to 2036. Findings Among food system ever workers, achieving long‐term sodium reduction targets could produce 20‐year health gains of approximately 180,000 QALYs (95% uncertainty interval [UI]: 150,000 to 209,000) and health cost savings of approximately $5.2 billion (95% UI: $3.5 billion to $8.3 billion), with an incremental cost‐effectiveness ratio (ICER) of $62,000 (95% UI: $1,000 to $171,000) per QALY gained. For the subset of processed food industry workers, health gains would be approximately 32,000 QALYs (95% UI: 27,000 to 37,000); cost savings, $1.0 billion (95% UI: $0.7bn to $1.6bn); and ICER, $486,000 (95% UI: $148,000 to $1,094,000) per QALY gained. Because many health benefits may occur in individuals older than 65 or the uninsured, these health savings would be shared among individuals, industry, and government. Conclusions The benefits of implementing the FDA voluntary sodium targets extend to food companies and food system workers, with the value of health gains and health care cost savings outweighing the costs of reformulation, although not for the processed food industry.


SUMMARY OF EVIDENCE ABOUT THE RISKS OF EXCESS SODIUM CONSUMPTION
Excess dietary sodium consumption has been linked to an increased risk of cardiovascular disease (CVD). 1 For CVD, the excess risk appears to be mainly mediated through the deleterious effect of excess sodium consumption on blood pressure. 2,3 Our methods for evaluating the causality of effects of sodium reduction on BP and BP reduction on CVD have been previously described. 3 Text S1-S3 The World Health Organization (WHO) and the United States (US) national guidelines recommend a daily sodium intake of less than 2,000 mg/d and 2,300 mg/d, respectively, after assessing the totality of evidence. 4,5 There is some controversy regarding the optimal level of sodium consumption. 6 Some researchers claim that sodium consumption lower than 3,000 mg/d can increase the risk of CVD and overall mortality. 7,8 However, it appears that this argument is based on biased measurement methodology. 9,10 A recent discussion on the subject can be found in Mozaffarian et al. who concluded that the optimal level of sodium consumption below which no health gains have been observed is somewhere in the range of 614 mg/d to 2391 mg/d. 3 text S4 In our study we have incorporated the uncertainty around the ideal sodium consumption in our probabilistic sensitivity analysis.
Evidence that directly links sodium risk reversibility to CVD mortality or morbidity outcomes is lacking.
A meta-analysis of several randomized control trials that tested low sodium diets was underpowered and therefore inconclusive. 11 In comparison, a plethora of evidence exists supporting the effect of low sodium diet on blood pressure which appears to happen within weeks. 2,3,12 Finally, the cardiovascular risk reversibility of blood pressure has been evident in several randomized control trials and appears to occur within a 5-year period. 13

HIGH-LEVEL DESCRIPTION OF THE US SODIUM POLICY MODEL
The US Sodium Policy model * is a discrete time dynamic stochastic microsimulation model. 14,15 Within the US Sodium Policy model each unit is a synthetic individual and is represented by a record containing a unique identifier and a set of associated attributes.
For this study, we considered age, sex, race/ethnicity † , education ‡ , income § , sodium consumption, and systolic blood pressure (SBP). This was matched to the age, sex, race/ethnicity ** , education † † , income ‡ ‡ distribution of individuals working in the food system from the American Community Survey 2010-2014 in the IPUMS-USE database. 16 A set of stochastic rules is then applied to these individuals, such as the probability of developing coronary heart disease (CHD) or dying, as the simulation advances in discrete annual steps. The output is an estimate of the burden of CHD and stroke, in the synthetic population including both total aggregate change and, more importantly, the distributional nature of the change.
The US Sodium Policy model is a complex model that simulates the life course of synthetic individuals and consists of four modules: The 'population' module, the 'disease' module, the 'health economics' module, and the 'policy' module. We will fully describe the US Sodium Policy model by describing the processes in each of the modules in the following chapters. The description is from an epidemiological rather than technical perspective. Figure Table S 1 and Table S 2 summarize the sources of the input parameters and the main assumptions and limitations, respectively.

Technical information
The US Sodium Policy model is being developed in R v3. 4.0 17 and is currently deployed in a 40-core workstation with 192Gb of RAM running Ubuntu v16.4 server edition. The US Sodium Policy model is built around the R package 'data.table' 18 , which imports a new heavily optimized data structure in R.
Most functions that operate on a data table have been coded in C to improve performance. Each iteration for each scenario is running independently in one of the CPU cores, and the R package 'foreach' 19 is responsible for the distribution of the jobs and collection of the results. To ensure statistical independence of the pseudo-random number generators running in parallel, the R package 'doRNG' 20 was used to produce independent random streams of numbers, generated by L'Ecuyer's combined multiple-recursive generator. 21 Reduction in stroke incidence Reduction in coronary heart disease mortality

Reduction in sodium consumption
Reduction in allcause mortality Reduction in systolic blood pressure Processed food sodium reformulation Reduction in coronary heart disease incidence Reduction in stroke mortality Figure S 1 Model logic. The arrow between reduction in systolic blood pressure and reduction in all-cause mortality does not imply a causal effect of systolic blood pressure on every mortality cause.

POPULATION MODULE
Synthetic individuals enter the simulation in the initial year (2014 for this study). The number of synthetic individuals that enter the simulation is user-defined and for this study was set to 100,000.
The algorithm ensures that the age, sex, race/ethnicity, income, and education distribution of the sample is the same as the worker groups identified in the American Community Survey 2010-2014. 16 The exposures to sodium and SBP are being calculated annually (in simulation time) for each synthetic individual until the simulation horizon is reached, or death occurs.

Estimating exposure to risk factors
The US Sodium Policy model estimates the exposure of the synthetic individual to the modeled risk factors. It is essential the risk profile of each synthetic individual to be similar to the risk profiles that can be observed in the real US population. For this, we first built a 'close to reality' synthetic population of US from which we sampled the synthetic individuals. Then, we used generalized linear models (GLM) for sodium consumption and SBP, to simulate individualized risk factor trajectories for all synthetic individuals.
Generating the 'close to reality' synthetic population for the US Sodium Policy model The 'close to reality' synthetic population ensures that the sample of synthetic individuals for the simulation is drawn from a synthetic population similar to the real one regarding age, sex, race/ethnicity, and risk factors conditional distributions. In our implementation, we used the same statistical framework originally developed by Alfons et al., 22 and we adapted it to make it compatible with epidemiological principles and frameworks. 23 In general, this method uses a nationally representative survey of the real population to generate a 'close to reality' synthetic population. Therefore, the method expands the, often small, sample of the survey into a significantly larger synthetic population, while preserving the statistical properties and important correlations of the original survey.
The main advantages over other approaches are: 1) it accounts for the hierarchical structure of the

Implementation of individualized risk factor trajectories
The US Sodium Policy model only applies the previous process for the initial year of the simulation (2014 for this study). As the simulation evolves, sodium consumption and SBP are recalculated to take into account age and period effects. This feature justifies the classification of the US Sodium Policy model as a dynamic microsimulation. It uses the continuous NHANES series to capture the time trends by age, sex, and race/ethnicity and project them into the future.

Demographic and socioeconomic variables
As the simulation progress in annual circles, the age of the synthetic individuals in the model increase by one year in each loop. Their sex and socioeconomic variables remain stable. Therefore, social mobility is not simulated in the current version of the US Sodium Policy model. * For this study, we assumed that the 24h recall food questionnaire of NHANES is representative of sodium consumption in the US population. An independent validation study with 24h urine collections supports this assumption. 27

Continuous variables
In the US Sodium Policy model, the value of each continuous risk factor (sodium, SBP) is calculated in a two-step process for each synthetic individual and each projected year. The first step simulates aging effects, while the second step simulates period effects. We follow this approach mainly for two reasons. Firstly, to simulate physiological mechanisms of aging. For example, the increase of SBP due to age-related stiffening of the arteries. Secondly, because the variance of the risk factor distributions increases with age, and we wanted to model this. Below we describe the steps: Step year old non-Hispanic black man in 2014 with the same percentile rank of 0.52. Figure S 3 illustrates the previous example. Although individuals retain their percentile for the respective risk factor throughout the simulation (vertical position in Figure S 3), this step remains stochastic because each time this step is implemented a different sample from the synthetic population is drawn. Finally, the distance from the mean for each risk factor is calculated stratified by 5-year age group, sex, and race/ethnicity. For instance, if a synthetic individual has SBP of 140 mmHg and the mean SBP in the respective group of same age group, sex and race/ethnicity is 130 mmHg, the distance from the mean is 140 -130 = 10 mmHg.
Step 2: We fitted regression models to the continuous NHANES data. For sodium, we used NHANES0914 † , and we fitted a GLM with sodium as the dependent variable and year, age, sex, and race/ethnicity as independent variables (including significant quadratic effects and first order interactions based on Akaike's information criterion (AIC)). For SBP we followed a similar approach, * For the percentile rank the formula = ( − 1) ( − 1) ⁄ is used, where is the percentile rank and = ( 1 , … , ) is the rank vector constructed from a random observation vector ( 1 , … , ). In this model specifically, vector is constructed from the subset of the respective continuous risk factor values, by 5year age group, sex and race/ethnicity, for each year of the simulation. † We used only the recent years of NHANES for two reasons: 1) there was a change in the estimation of sodium intake in NHANES since 2009 which renders older NHANES sodium estimates not immediately compatible with most recent ones; 2) Most importantly, while mean sodium intake was almost constant between years 1999 and 2008 a slow declining trend was obvious in more recent years. but we used the full range of continuous NHANES9914. For both models, we used a logarithmic link function; therefore, we assumed logarithmic declining time trends for both sodium and SBP. These models are used to predict the mean of the relevant group. These predicted means are added then, to the distances calculated in the previous step. The result is the final value of the relevant risk factor that will be used for risk estimation.

Lag times
All the functions that have been described above for risk factor trajectories include time and age (in years) as one of the independent variables. Therefore, lag times can be potentially calculated on a per risk factor basis. When the 'disease' module of the US Sodium Policy model, uses the exposure to SBP to estimate the risk of a synthetic individual to develop CVD in a specific simulated year, the lag-timed exposure is used. In this study, we assumed that the mean lag time between exposure to high SBP and CVD is five years. 13,28,29 Mean lag times were roughly informed from risk reversibility trials and the median observation times of the cohort studies we used to inform the risk magnitude for SBP. We assumed no lag time between a change in sodium intake and impact on SBP, as this happens within few weeks. 2 Figure S 3 Plot of the percentile rank against the systolic blood pressure of non-Hispanic black male synthetic individuals for age groups 30-34 and 60-64.

60-64
Closed and open cohort approaches The American Community Survey 2010-2014 provided a snapshot of the joint age, sex, race/ethnicity, income, and education distribution of the food system (and processed food industry) workforce. This distribution remained relatively stable during the 5-year observation period of the survey. In addition, we couldn't find any estimates regarding workforce retention in the sector. Therefore, we did not have much information to simulate individuals leaving and joining the workforce in detail. To overcome this limitation we ran the simulation twice. the first time, simulating a closed cohort of 'current' workers at the start of the model assuming that these workers will remain in the food system (or processed food industry) workforce over the 20-year simulation period.
The second time, simulating an open cohort and easing the assumption that workers will stay in the food system or processed food industry. In this approach, individuals were allowed to leave or join the workforce, under the constraint that the joint age, sex, race/ethnicity, income, and education distribution we observed in the American Community Survey 2010-2014 should remain stable throughout the simulation period. To avoid massive unrealistic movements in and out of the workforce, * we added a second constraint to the algorithm to ensure that the minimum necessary number of individuals should move in and out of the workforce. * For example, having all the workforce of a specific age, sex, race/ethnicity, income, and education replaced by new individuals the next simulation year.

DISEASE MODULE
The risk (probability) for each synthetic individual aged 30-84, to develop each of the modeled diseases is estimated conditional on previous exposure to SBP, age, sex, and race/ethnicity. For every simulated year, the model selects synthetic individuals to develop CHD and stroke based on their risk.
Finally, the risk of dying from one of the modeled diseases or any other cause is estimated and applied.

Estimating the annual individualized disease risk and incidence
To estimate the individualized annual probability of a synthetic individual to develop a specific disease conditional on his/her relevant risk exposures we follow a 3-step approach. Below we describe the general approach that is used for simulations with more than one risk factors. For this study, only one risk factor was included (high SBP). The implementation of the above method is described in more detail using CHD as an example. The same process is used for both CHD and stroke.

Step 1
The population attributable risk (PAF) is an epidemiological measure that estimates the proportion of the disease attributable to an associated risk factor. 30 It depends on the relative risk associated with the risk factor and the prevalence of the risk factor in the population. In a microsimulation context where exposure to risk factors are known to the individual level and assuming multiplicative risk factors PAF can be calculated with the formula: where is the number of synthetic individuals in the population, and 1… is the relative risks of the risk factors associated with CHD. We calculated PAF based on the formula above stratified by age, sex, and race/ethnicity only in the initial year of the simulation. Consistent with findings from the respective meta-analyses that were used for the US Sodium Policy model (Table S 1), SBP below 110 mmHg, was considered to have a relative risk of 1. All the relative risks were taken from published meta-analyses (Table S 1).
Step 2 The formula below can estimate the incidence of CHD not attributable to the modeled risk factors: Where is the CHD incidence and is from Step 1. represents CHD incidence if all the modelled risk factors were at optimal levels. The not attributable incidence is calculated by year, age, sex, and race/ethnicity.
To account for future time trend in CHD incidence that is not attributable to the modeled risk factors (in this study SBP), the model updates every simulated year. For this we assume that half of the forecasted annual change in CHD mortality is attributed to changes in CHD incidence and the other half to changes in CHD case fatality. We based this assumption on observational evidence from England, and modelling studies in the England and the US. [31][32][33][34] Furthermore, we included this assumption in our probabilistic sensitivity analysis (page 23).
Step 3 Assuming that is the baseline annual probability of a synthetic individual to develop CHD for a given age, sex, and race/ethnicity due to risk factors not included in the model, the individualized annual probability to develop CHD, ℙ(CHD | age, sex, race/ethnicity, exposures), given his/her risk factors were estimated by the formula: , race/ethnicity, ) = * 1 * 2 * 3 * … * Where 1 … the relative risks that are related to the specific risk exposures of the synthetic individual, same as in step 1.

Estimating disease incidence at initial simulation year
It is evident that for the method above, disease incidence ( ) in the population, need to be known, at least for the initial year of the simulation. However, the true incidence of CHD (and stroke) in the US, is largely unknown. Several estimates exist nonetheless all have limitations, and the same applies to incidence trends. 35,36 Therefore, for the estimation of CHD and stroke incidence by age, sex, and race/ethnicity we opted for a modelling solution to synthesize all the available nationally representative sources of information and to minimize bias. Specifically, we used CHD mortality (ICD10 I20-I25) for US in 2014, 37 self-reported prevalence of CHD from NHANES1314, 24  information about at least three of these variables is available. A similar approach has been followed by the Global Burden of Disease team and others. 40,41 We considered CHD an incurable chronic disease (i.e. remission rate was set to 0); therefore, the derived DisMod II incidence refers to the first ever episode of CHD excluding any recurrent episodes. For the DisMod II calculations, we assumed that incidence and case-fatality rates had been declining by 2% (relative), over the last 20 years. We used the derived CHD incidence rates by age, sex, and race/ethnicity to inform the US Sodium Policy model.
We used the same approach for stroke. 42,43 Estimating disease prevalence at initial simulation year For the initial year of the simulation, some synthetic individuals need to be allocated as prevalent cases for each of the modeled diseases. We used DisMod II model estimates for prevalence of CHD and stroke by age, sex, and race/ethnicity. At the beginning of each simulation, the estimated number of prevalent cases are sampled independently from the synthetic individuals in the population with weights proportional to their SBP exposures.

Simulating mortality
All synthetic individuals are exposed to the risk of dying from any of their acquired modeled diseases or any other non-modeled cause in a competing risk framework. The US Sodium Policy model is calibrated to observed CHD, stroke, and any-other-cause mortality for years 2014-2015 37 and mortality forecasts for years 2016-2036. For years after 2015, coherent functional demographic models by sex and race/ethnicity were fitted to the reported CHD, stroke, and any-other-cause mortality rates from years 1999 to 2015, 37 and then were projected to the simulation horizon using the R package 'demography'. 44 Functional demographic models are generalizations of the Lee-Carter demographic model, influenced by ideas from functional data analysis and non-parametric smoothing. 45 The coherent approach ensures that subgroup forecasts do not diverge over time. 46 Finally, we used the observed and forecasted mortality rates to create life tables for each simulated year, by age, sex, race/ethnicity, and disease (CHD, stroke, any-other-cause). We applied the anyother-cause life tables to all synthetic individuals, and the CHD and stroke life tables to prevalent cases of CHD and stroke only, respectively. For the synthetic individual that died of more than one causes in a specific year, a cause was randomly selected to minimize bias.
In reality, hypertensive individuals have a higher risk to die not only of CHD and stroke but from a spectrum of other diseases also. year from any-other-cause is equal to the defined one in the life table. The algorithm is based on PAF approach, and the relative risk was derived from an individual level meta-analysis by Stringhini et al. 47 In this meta-analysis the relative risk of all-cause mortality for hypertensives was 1.31 (1.24-1.38), and the relative risk of non-CVD-non-cancer mortality was 1.29 (1.21-1.38). Hence, we used a relative risk of 1.3 in the US Sodium Policy model.

HEALTH ECONOMICS MODULE
In the previous two modules, the US Sodium Policy model creates synthetic individuals with traits similar to those observed in the US population and tracks their future exposures to sodium and SBP, and important events (first manifestation of CHD and stroke, death from CHD, stroke, or any other cause).

Health state utilities
We  48 We further modeled the number of coexisting chronic conditions to increase with age.

Disease costs
The US Sodium Policy model applies CHD, stroke, and hypertension costs to cases of these diseases, during the simulation. These costs are mean estimates by age, sex, and race/ethnicity.
Disease costs per person-year were derived from a report of projections of CVD costs, prepared for the American Heart Association (AHA) by Research Triangle Institute (RTI) International which was based on MEPS data. 49 The AHA report assumed that price increases and new technologies would produce a 2.45% increase in medical costs, above the impact of inflation, demographic change, and disease severity. We assumed an equal annual increase in medical costs. Medical costs per person- year for CHD, stroke, and hypertension were calculated by dividing total medical costs by the number of people with each condition in 2015 and disaggregated by the ratio of the point of service (physician, hospital, prescription, home health, nursing home, and other). The AHA paper included the ratio of medical costs at the point of service for each disease group; the point of service was grouped into physician, hospital, prescription, home health, nursing home, and other.
Productivity costs of morbidity and mortality for CHD and stroke, and hypertension (including workplace productivity and leisure time) were from the same analysis by RTI International and were converted to costs per person-year. For CHD and stroke, we applied morbidity costs to prevalent cases of CHD and stroke, respectively; we applied mortality costs only to deaths from CHD and stroke. For hypertension, we used the productivity costs not decomposing them into mortality and morbidity costs, because the US Sodium Policy model does not track deaths attributed to hypertension. We assumed that productivity costs would increase by 1.29%, annually.
Informal care costs for stroke were from a study by Joo et al. 50 , while informal care costs for CHD were based on the ratio of healthcare to informal care costs in Europe from a study by Leal et al. 51 We assumed no informal care costs for hypertension alone as we assumed that most would be mediated through CHD and stroke.

Policy costs
The policy costs included: Government costs to administer and monitor the policy. For administrative costs, because there has been no previous initiative that is both national in scope and precisely about sodium reduction, we used data from two existing sources. First, we acquired cost data from the National Sodium Reduction Initiative (NSRI), led by New York City's Health Department. 52 * Second, we acquired cost data from a different FDA policy, new restaurant menu and vending machine labeling regulation, including the cost of outreach, education, review of regulatory issues, developing training for inspectors, and related functions. 53 We used the second data source in the analysis because it generated more conservative (higher-cost) estimates. Monitoring and evaluation cost was obtained through UK FSA's impact assessment and converted to equivalent US dollars 54 . Administrative costs were assumed to occur every year, and monitoring and evaluation costs were assumed to occur every year after full policy implemented in year 3.
Industry costs to reformulate products. Industry costs were calculated using a reformulation cost model developed by the Research Triangle Institute under contract with the FDA. 55 The model accounted for variations in product formula complexity, company size, reformulation type, compliance period and other factors, which produces a more accurate cost estimate compared to a standard per-product cost approach. We calculated the cost of two rounds of reformulation, which corresponded to the FDA's short-term and long-term sodium reduction goals. We assumed the industry cost was equal in the two rounds of reformulation, and divided the costs over the policy implementation years (intervention years 1-3 for the first round, and intervention years 4-10 for the * Sonia Angell, personal communication, Feb 6, 2017 second round). We assumed no policy costs after intervention year 10. All costs were inflated to 2017 dollars and discounted at a 3% rate.

POLICY MODULE
So far, the description of the US Sodium Policy model was for the baseline scenario. The policy module translates the policy scenarios to be modeled by the US Sodium Policy model. Figure  Separately, FDA also published instruction to link the food categories in the proposal, with the food codes that were used in the 24h recall questionnaires for NHANES0710. 57(p082516) Unfortunately the linkage was incompatible with more recent NHANES data that we used to prime the synthetic population. Therefore, to model the effect of the proposed policy to the modeled population we developed the algorithm below: Step 1 We use NHANES0910, and for every participant, we access the 24h recall food questionnaire. The questionnaire contains the amount, food type, and sodium concentration that the participant recalls * We apply this equation only to synthetic individuals with sodium consumption above the optimal level of sodium consumption. Hence, the sodium consumption projection of the baseline scenario is not directly used during this calculation. Only the change in sodium consumption is important and is translated in SBP and health outcomes change.
having consumed the previous day. The FNDDS v5 database was used for the coding of foods. 58 We link these foods with the food categories from the proposed FDA policy. Therefore, we can select which foods in the questionnaires are eligible for reformulation (i.e., their sodium concentration is higher than the proposed FDA targets). *

Step 2
Based on the specific scenario assumptions we randomly select eligible foods to be reformulated from the NHANES food questionnaires. We calculate the expected reduction of sodium intake for each NHANES0910 participant, in absolute and relative terms. For this study, we assumed a gradual linear diffusion of the reformulation effect to the population. Once the maximum policy effect was reached, we assumed it would sustain for the rest of the simulation period.
Step 3 We stochastically match each synthetic individual of the US Sodium Policy model with an NHANES0910 participant based on their age (10-year age group), sex, race/ethnicity, and sodium consumption † .
Then we use the same method described on is transformed to SBP changes as it was described above. The underlying assumption in this step is that the food composition of US diet has been and will be similar to the one in 2010.
This approach bypasses the incompatibility of the linkage between the FDA proposed policy and more recent NHANES data. It also allows the incorporation of sodium consumption time trends in the calculations and provides enough granularity of the policy effect (by age, sex, race/ethnicity, and sodium consumption) without being too computationally intensive. However, it does not address potential behavioral changes of the population as a result of the reformulation and ignores foods prepared in food outlets and restaurant.
Finally, the linkage between the FDA proposed policy and the FNDDS v5 database was not perfect. Of the 4998 different foods that were linked to 155 food categories in the proposed FDA policy, 132 * We assume that the sales-weights are similar to the consumption-weights. † For NHANES participants we used the observed sodium consumption without the expected effect of reformulation.
(2.6%) were not a perfect match, and we manually assigned them to one of the 155 food categories.  Based on the evidence presented above we decided to allow a slowly declining trend in future sodium consumption projections. If the emerging sodium time trend does not continue in the future, will render our results conservative.

UNCERTAINTY AND SENSITIVITY ANALYSIS
The US Sodium Policy model implements a 2 nd order Monte Carlo approach to estimate uncertainty intervals (UI) for each scenario. 60 The framework allows stochastic uncertainty, parameter uncertainty, and individual heterogeneity to be reflected in the reported UI. The following example illustrates the different types of uncertainty that were considered in the US Sodium Policy model. Let us assume that the annual risk of CHD is 5%.
If we apply this risk to all individuals and randomly draw from a Bernoulli distribution with = 5% to select those who will manifest CHD, we only consider stochastic uncertainty. If we allow the annual risk for CHD to be conditional on individual characteristics (i.e. age, sex, exposure to risk factors), then individual heterogeneity is considered. Finally, when the uncertainty of the relative risks due to sampling errors is considered in the estimation of the annual risk for CHD, the parameter uncertainty is considered. From these three types of uncertainty, only the parameter uncertainty can be reduced from better studies in the future.
The structure of the model is grounded on fundamental epidemiological ideas and well-established causal pathways; therefore, we considered this type of uncertainty relatively small and did not study it. However, the discrete-time nature of the model can potentially introduce bias in cases where the synthetic individual dies more than once within a year, and the model cannot identify which event happened first. As we describe on page 15, to minimize this type of bias we randomly select one of * We assumed log-normal distributions for relative risks and hazard ratios, normal distributions for coefficients of regression equations, generalized beta of the second kind for costs, and PERT distributions for other parameters. The cost sources, except industry reformulation costs, did not include any measures of uncertainty like standard error so an estimate of +/-20% was used for uncertainty analyses, fitted to a generalized beta of the second kind distribution, which can account for the skewness of healthcare costs. 62 † For this study life course actually starts at the age of 30, because it is unlikely that CVD cases and deaths in younger ages can be prevented by sodium intake reduction.
the events to be considered as it happened before all others, whenever these cases arise during the simulation.

Input uncertainty
The sources of uncertainty we considered were: 1. The sampling error of the baseline sodium intake. When the model calculates individualized sodium consumptions, it takes into account the sampling error of the regression models that were fitted in the NHANES (see page 10).
2. The sampling error of the baseline SBP. Same as above.
3. The sampling error of the relative risks of SBP on CHD, stroke, and any-other-cause mortality.
We used the reported relative risks and their confidence intervals to construct log-normal (uniform for any-other-cause mortality) distributions. 8. The uncertainty around the true incidence and prevalence rates of CHD and stroke. We described on page 14 how we used DisMod II to estimate the incidence rate of CHD and stroke. We fitted beta distributions by age, sex, and race/ethnicity assuming the 0.025 percentile to be half of the central estimate, the median the central estimate, and the 0.975 percentile double the central estimate.
9. The uncertainty of mortality forecasts. We incorporated the predictive uncertainty of the mortality forecasts to the US Sodium Policy model estimates. 10. The uncertainty around the assumption that half of the forecasted annual change in CHD and stroke mortality is attributed to changes in CHD and stroke incidence, respectively. We allowed this assumption to vary, independently for each disease, between 0% and 100% following a uniform distribution.

Outputs
We summarize the output distributions of the US Sodium Policy by reporting the medians and 95% uncertainty intervals (UI).

CALIBRATION AND VALIDATION
The US Sodium Policy model is calibrated to forecasts of CHD, stroke, and any-other-cause mortality for the whole US population (previously described on page 15). Figure