Juliana De Oliveira Mota

Géraldine Boué

Sandrine Guillou

Fabrice H F Pierre

Jeanne Marie Membre
email: membre@oniris-nantes.fr

Jeanne Marie Membré

Estimation of the burden of disease attributable to red meat consumption in France: Influence on colorectal cancer and cardiovascular diseases

Keywords: CRC, colorectal cancer, CVD, cardiovascular disease, DALY, disability adjusted life years, RR, relative risk, GBD, Global Burden

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Quantifying the impact of dietary habits on human health is essential for decision-making in preventive medicine [START_REF] Karp | Bridging the etiologic and prognostic outlooks in individualized assessment of absolute risk of an illness: application in lung cancer[END_REF]. Diet is a key determinant of health status: it has been considered as one of the major factors in reducing the burden of disease (GBD 2017Risk Factor Collaborators, 2018;[START_REF] Wolk | Potential health hazards of eating red meat[END_REF]. For instance, in Europe, a diet high in saturated fat was responsible for 1.1% of the overall burden of disease. In the USA, 35% of the total deaths resulting from cancer was estimated to be attributable to diet (food and drink), excepting alcohol [START_REF] Pomerleau | The burden of disease attributable to nutrition in Europe[END_REF].

Since 1990, the Global Burden of Disease (GBD) study, supported by the World Health Organization, has estimated the health effects of major diseases, injury and risk factors with the Disability Adjusted Life Years (DALY) metric, which takes into account mortality and morbidity. This metric expresses the number of years of life lost (YLL) from premature death and the number of years lived with disability (YLD) (WHO, no date). In addition, by quantifying the impact of disease, the burden of disease helps in formulating risk-mitigating strategies: several consumption patterns could be evaluated and compared by a scenario analysis.

The estimation of the burden of disease is also used in risk-benefit assessments of food to quantitatively compare different health impacts associated with food consumption in a targeted population. This has been done in several studies [START_REF] Berjia | Burden of diseases estimates associated to different red meat cooking practices[END_REF][START_REF] Cardoso | Portuguese preschool children: Benefit (EPA+DHA and Se) and risk (MeHg) assessment through the consumption of selected fish species[END_REF][START_REF] Farchi | Meat consumption reduction in Italian regions: health co-benefits and decreases in GHG emissions[END_REF]Hoekstra et al., 2013b;[START_REF] Thomsen | A probabilistic approach for risk-benefit assessment of food substitutions: A case study on substituting meat by fish[END_REF][START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF][START_REF] Wikoff | Benefitrisk analysis for foods (BRAFO): Evaluation of exposure to dietary nitrates[END_REF]. This emerging discipline aims to balance the probability of an adverse health effect, in terms of incidence and severity, against the probability of beneficial effects attributable to an exposure to a specific dietary component [START_REF] Efsa | Guidance on human health risk-benefit assessment of foods[END_REF]. So far, it has been mainly applied to the consumption of fish [START_REF] Anses | Avis de l'Agence nationale de sécurité sanitaire de l'alimentation, de l'environnement et du travail relatif aux recommandations sur les bénéfices et les risques liés à la consommation de produits de la pêche dans le cadre de l'actualisation des repères nutritionnels du PNNS[END_REF][START_REF] Becker | Risks and benefits of fish consumption[END_REF][START_REF] Domingo | Benefits and risks of fish consumption: Part I. A quantitative analysis of the intake of omega-3 fatty acids and chemical contaminants[END_REF][START_REF] Efsa | Statement on the benefits of fish/seafood consumption compared to the risks of methylmercury in fish/seafood[END_REF]Hoekstra et al., 2013b;[START_REF] Ponce | Use of quality-adjusted life year weights with doseresponse models for public health decisions: a case study of the risks and benefits of fish consumption[END_REF].

To evaluate the effect of food on human health, results from epidemiological cohort studies can be used. These studies aim to identify the risk factors associated with specific diseases (National Research Council, 2012) by following a group of populations over a limited time. A statistical treatment takes into account the confounding factors and calculates the excess risk attributable to a risk factor. The relation is primarily expressed in terms of relative risk (RR), defined by the National Cancer Institute as "a measure of the risk of a certain event happening in one group compared to the risk of the same event happening in another group". Moreover, "a relative risk of greater than one or of less than one usually means that being exposed to a certain substance or factor either increases (relative risk greater than one) or decreases (relative risk less than one) the risk of cancer" (NCI, no date).

Risk assessment studies often limit themselves to the RR, but it is possible to go further, and estimate the number of cases and DALYs, as done by the GBD study. Following the same strategy, in the present study, the burden of disease associated with red meat consumption by the French population was estimated in terms of DALYs. Indeed, in recent years, red meat has become a public health concern in France as well as in other western countries [START_REF] Casalonga | Quelles viandes manger?, 60 millions de consommateurs[END_REF]. In addition, red meat has been much consumed in France. In 2013, the average consumption of unprocessed red meat was 52.5 grams per day per adult, compared to 34.9 g/day for unprocessed white meat [START_REF] Duchène | La consommation de viande en France[END_REF].

We decided to focus our study on colorectal cancer (CRC) and cardiovascular disease (CVD).

This was done because, first, CRC is the cancer with the strongest evidence linking it to red meat (WCRF/AICR, 2017a). Second, CVD, because even if the strength of the evidence has not been clearly determined, it is the second most important cause of mortality in France, after tumors (INSEE, 2018). The World Cancer Research Fund International/Imperial College London and the World Health Organization have classified red meat consumption as "probably carcinogenic to humans". This classification was based on the positive association between the risk of CRC and the consumption of red meat, with a risk increase of 12% per increase of 100 g in red meat consumed [START_REF] Bouvard | Carcinogenicity of consumption of red and processed meat[END_REF]WCRF/AICR, 2017a), which led to the recommendation to limit red meat consumption to 500 g per week (ANSES, 2016).

Likewise, an increase by 15% in the CVD mortality risk with an increase by 100 g in the amount of red meat consumed was found [START_REF] Abete | Association between total, processed, red and white meat consumption and all-cause, CVD and IHD mortality: a meta-analysis of cohort studies[END_REF]. The consumption of red meat might also be associated with breast cancer [START_REF] Wolk | Potential health hazards of eating red meat[END_REF], prostate cancer (WCRF/AICR, 2018; [START_REF] Wolk | Potential health hazards of eating red meat[END_REF], nasopharyngeal cancer and lung cancer (WCRF/AICR, 2018). However, conclusions on the effect of consumption of unprocessed red meat by the WCRF remain limited, so we decided not to include them in this study. Therefore, a model quantifying both the risk and burden of disease of CRC and CVD due to red meat consumption in France was built.

Studies have already evaluated the impact of the consumption of red meat on CRC and/or CVD [START_REF] Berjia | Burden of diseases estimates associated to different red meat cooking practices[END_REF][START_REF] Farchi | Meat consumption reduction in Italian regions: health co-benefits and decreases in GHG emissions[END_REF][START_REF] Thomsen | A probabilistic approach for risk-benefit assessment of food substitutions: A case study on substituting meat by fish[END_REF][START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF].

However, the uncertainty and variability propagated by the model inputs is not often taken into account, and it is considered important to not ignore it [START_REF] Nauta | Meeting the challenges in the development of risk-benefit assessment of foods[END_REF]. Uncertainty corresponds to the lack of data and knowledge, and variability to the heterogeneity within a population [START_REF] Cummins | Fundamental principles of risk assessment[END_REF][START_REF] Thompson | Variability and uncertainty meet risk management and risk communication[END_REF][START_REF] Vose | Risk analysis: a quantitative guide[END_REF]. Separating the uncertainty and variability of the inputs enables identifying which of them are driving the output of the risk model and identifying what data will be needed to increase the precision and the confidence of the estimated output [START_REF] Cummins | Quantifying Microbial Propagation[END_REF]. Despite the recommendations by international organizations (FAO/ WHO, 2006), the separation of uncertainty and variability is not systematically done in risk assessment.

To summarize, the objective of this study was to estimate the burden of disease in France of CRC and CVD attributable to the consumption red meat. Based upon epidemiological studies, probabilistic models were set up for both gender and for specific age classes to quantify the risk of each outcome and the consequent burden of disease. A second order Monte Carlo simulation procedure was implemented to include uncertainty and variability, separately, in the analysis. Several consumption scenarios were analysed to help decision makers in refining their recommendations.

Model development

Model framework for colorectal cancer and cardiovascular risk assessment attributable to the consumption of red meat

The model was developed for males and females more than three years old. The age classes were 3-24, 25-44, 45-64, 65-84 and ≥ 85 years old. These age classes were defined in accordance with the age classes of the incidence data.

The flowchart of the risk assessment model is presented in Fig. 1. From red meat consumption in France, epidemiological studies, and French data on incidence of the outcome, the baseline probability of the outcome without red meat consumption was estimated. From this, the distribution of red meat intake in France, and the proportion of red meat consumers, the probability of the outcome with and without red meat consumption was calculated. Then the probability of the outcome specifically due to the consumption of red meat was estimated.

Therefore, the number of cases and the corresponding burden of disease (DALY) per year, gender and age class were determined. Two outcomes were taken into account in the study: CRC occurrence and CVD mortality. The latter included diseases due to ischemic heart disease, acute coronary syndrome, myocardial infarction, cerebrovascular diseases, heart failure and venous thromboembolism. The relation between the consumption of red meat and the occurrence of disease, including both disease with full recovery and disease leading to fatalities, was established for CRC (WCRF/AICR, 2017b). However, in the case of CVD, this relation has been either found to be not significant [START_REF] Kaluza | Processed and unprocessed red meat consumption and risk of heart failure: prospective study of men[END_REF][START_REF] Kaluza | Long-term processed and unprocessed red meat consumption and risk of heart failure: A prospective cohort study of women[END_REF][START_REF] Micha | Red and processed meat consumption and risk of incident coronary heart disease, stroke, and diabetes mellitus: a systematic review and meta-analysis[END_REF], or, mortality and occurrence were mixed up in the estimation of RR [START_REF] Bechthold | Food groups and risk of coronary heart disease, stroke and heart failure: a systematic review and dose-response meta-analysis of prospective studies[END_REF][START_REF] Kaluza | Red meat consumption and risk of stroke: a metaanalysis of prospective studies[END_REF][START_REF] Micha | Red and processed meat consumption and risk of incident coronary heart disease, stroke, and diabetes mellitus: a systematic review and meta-analysis[END_REF][START_REF] Yang | Red meat consumption and the risk of stroke: a dose-response meta-analysis of prospective cohort studies[END_REF].

Nevertheless, significant CVD mortality attributable to the consumption of red meat was established in [START_REF] Abete | Association between total, processed, red and white meat consumption and all-cause, CVD and IHD mortality: a meta-analysis of cohort studies[END_REF]. For this reason, in the case of CVD, the model only estimated the number of deaths due to the consumption of red meat.

The inputs used in the model are summarized in Table 1 andTable 2.

Red meat consumption in France

Red meat consumption in metropolitan France was evaluated between 2005 and 2007 for males and females from 3 to 79 years old by the dietary survey INCA 2 (ANSES, 2014). A more recent dietary survey (INCA 3) was available (ANSES, 2017), but, unfortunately, the raw data were not accessible. Nevertheless, French food habits did not change over time regarding meat consumption. Indeed, for adults, for example, we observe only a slight decrease of the mean (49.7 g/d versus 47.3 g/d) [START_REF] Anses | Données de consommations et habitudes alimentaires de l'étude INCA 2[END_REF]2017). From the original data (ANSES, 2014), we exclusively selected the individuals who responded to the 7-day survey, which corresponds to 96% of the survey participants. Information about red meat consumption for individuals less than 3 years old and over 79 years old was not available. We then assumed that the consumption distribution of people in the age classes 65-84 and ≥ 85 years was the same as for people from 65 to 79 years old. The consumption of red meat took into account the consumption of unprocessed beef, pork, lamb and veal. More information about the individuals included in the study and the mean quantity of red meat consumed is available in Tables 1 and2.

From these consumption data, two variables were calculated: the mean consumption for each age class and gender and the probability density of consumption for red meat eaters. To estimate this latter, the function fitdist of the package fitdistrplus in the R software package (version 3.4.0) was used. Based upon the Akaike Information Criterion (AIC), the Gamma distribution provided the best fit, among the Weibull, Normal, Lognormal and Gamma distributions.

Health impact of the consumption of red meat

The health impact of the consumption of red meat is mostly evaluated by epidemiological studies with the effect then being expressed in terms of the RR. The inputs for both considered outcomes, i.e. CRC occurrence and CVD mortality, were determined from a metaanalysis. The values for an increase by 100 g in the consumption of red meat were 1.12 [95% CI: 1.00-1.25] (WCRF/AICR, 2017a) and 1.15 [95% CI: 1.05-1.26] [START_REF] Abete | Association between total, processed, red and white meat consumption and all-cause, CVD and IHD mortality: a meta-analysis of cohort studies[END_REF], respectively. The epidemiological studies of the meta-analysis identified and took into account the major confounders for the Relative Risk, in order to only take into account the effect of consuming red meat on health, as much as possible. The main confounders were age, sex, smoking status, and body mass index, as well as the intake of fruits, vegetables, energy, and alcohol. To estimate RR, the World Cancer Research Fund International used a log-linear dose-response model (WCRF/AICR, 2017b) in which the confidence interval follows a normal distribution [START_REF] Hamling | Facilitating meta-analyses by deriving relative effect and precision estimates for alternative comparisons from a set of estimates presented by exposure level or disease category[END_REF][START_REF] Woodward | Epidemiology: study design and data analysis[END_REF]. This was used to determine the uncertainty around the RR parameters. We also hypothesized an effect of the consumption of red meat on CRC and CVD as soon as the individual consumed more than zero grams.

Therefore, the dose-response per outcome was modelled by age class and gender considering the amount of red meat consumed in grams per day, as presented in Equation 1. Descriptions of and sources of information for the inputs are available in Tables 1 and2.

Male

# %&(,.L+ 1M(,,N.EE×+, OP * # %&(,.L+ 1M(,,N.EE×+, OP * # %&(,.RS 1M(,,+.TU×+, OP * # %&(,.RR 1M(,,+.+L×+, OP * # %&(,.V 1M(,,+.VV×+, OP * Percentage U Female # %&(,.LE 1M(,,E.UT×+, OP * # %&(,.LE 1M(,,E.UT×+, OP * # %&(,.LE 1M(,,+.LU×+, OP * # %&(,.RR 1M(,,+.+V×+, OP * # %&(,.V+ 1M(,,+. U: uncertainty; V: variability; D: deterministic; * Following R parametrization

Estimation of the probability of the occurrence of colorectal cancer and cardiovascular disease mortality attributable to the consumption of red meat

To estimate the probability of the outcome attributable to the consumption of red meat, the incidence rate of the outcome, defined as the number of new cases of the outcome during a year divided by the population size (CDC, no date), and RR were taken into account.

Combining these two inputs, the baseline probability of the outcome, which corresponds to the probability not associated to the consumption of red meat, was adapted from Hoekstra et al. ( 2013) (Hoekstra et al., 2013b), as follows:

(2)

X Y8Z[ (8,9 ! = \]4 (5,6 34 (^̅ ( , ! × 100,000

where X Y8Z[ (8,9 ! is the baseline probability of the outcome, \]4 (8,9 ! is the incidence rate for the outcome for 100,000 people per years, (^̅ ( , ! is the RR of the mean consumption of red meat for the outcome, and `̅ (8,9 is the mean consumption of red meat.

The incidence rate of the occurrence of CRC was collected from a report of the French Institute for Public Health Surveillance, which estimated the number of cancer cases in France in 2012 per 100,000 person-years [START_REF] Binder-Foucard | Estimation nationale de l'incidence et de la mortalité par cancer en France entre 1980 et 2012. Partie 1 -Tumeurs solides[END_REF]. Incidence rate data corresponding to CVD mortality per 100,000 deaths per year were available in the 2017 report of the statistical data from the French Ministry of Solidarity and Health (DREES, 2017). We assumed that children under 3 years of age did not develop CRC or CVD. Incidence data are provided in Table 2.

The total probability of having the outcome, whether consuming red meat or not, was calculated assuming that people either ate or did not eat red meat, knowing the proportion of red meat consumers in the French population (Equations 3 and 4):

(3)

X [aa (7 (8,9 ! = X [aa (7 > 0 (8,9 ! × Xc#d #5e#cf (5,6 + X Y8Z[ (8,9 ! × h1 -Xc#d #5e#cf (5,6 j with (4) X [aa (7 > 0 (8,9 ! = ( ( , ! × X Y8Z[ (8,9 !
Where X [aa (7 (8,9 ! is the total probability of the outcome (with and without red meat consumption), taking into account the probability distribution of the quantity of red meat consumed (7 . Here,7 (8,9 is the quantity of red meat consumed by red meat eaters in grams per day , X [aa (7 > 0 (8,9 ! is the probability of the outcome when eating red meat (7 > 0 , taking into account the probability distribution of the quantity of red meat consumed, Xc#d [8k[lZ (8,9 is the proportion of consumers of red meat in the French population estimated by a beta distribution using INCA 2 survey data, X Y8Z[ (8,9 ! is the baseline probability for the outcome (Equation 2), and ( ( , ! is the RR of the quantity of red meat consumed.

The probability of the outcome (either CRC occurrence or CVD mortality) attributable to the consumption of red meat, X lm(8,9 ! (7 , was then calculated by subtracting the baseline probability from the total probability:

(5)

X lm (7 (8,9 ! = X [aa(8,9 ! (7 -X Y8Z[ (8,9 !

Estimation of the burden of disease in Disability Adjusted Life Years

The burden of disease of the outcome attributable to the consumption of red meat was estimated using the DALY indicator. This metric estimates the equivalent number of years in good health lost due to the outcome, and is commonly used in risk and benefit assessments [START_REF] Hoekstra | BRAFO tiered approach for benefit-risk assessment of foods[END_REF][START_REF] Nauta | Meeting the challenges in the development of risk-benefit assessment of foods[END_REF][START_REF] Tijhuis | State of the art in benefit-risk analysis: Food and nutrition[END_REF].

The estimation of DALY for CRC was adapted from previous studies [START_REF] Soerjomataram | Estimating and validating disability-adjusted life years at the global level: a methodological framework for cancer[END_REF]. As represented in Fig. 2, the stages of the illness for people who survived were the diagnosis and therapy stages followed by the remission stage. For people who died, the stages were the diagnosis and therapy stages followed by the latency stage, pre-terminal stage and terminal stage. The calculation took into account the disability, from 0 (perfect health state)

and 1 (death), and the duration of the sequelae for each stage of progression of the illness.

Finally, it was assumed that stoma was the only sequelae of colorectal cancer, and this sequelae was considered as permanent. The number of cases who survived (with or without sequelae) and the number of cases who died were calculated (Equations 6 to 9).

(6)

W n.[.lm(8,9 = :X lm (` (8,9 ! oooooooooooooooo × W (8,9 ; × (1 -Xfpcd (8,9 The duration of each stage and the proportion of stoma in the survivors were obtained from [START_REF] Soerjomataram | Estimating and validating disability-adjusted life years at the global level: a methodological framework for cancer[END_REF].

The CRC expressed in DALY was calculated as follows.

( The output was considered significant when the lower bound of the 95% confidence interval was higher than zero.

Model implementation

Identification of sources of uncertainty and variability and implementation

To estimate the outputs, the model needs to be given inputs. Inputs are variables defined by either one value or a range of different values with their probability of occurrence reflecting the variability and/or the uncertainty associated with the data [START_REF] Boué | Public health riskbenefit assessment associated with food consumption-a review[END_REF][START_REF] Membré | Quantitative microbiological risk assessment in food industry: theory and practical application[END_REF].

Four types of inputs were defined:

-Deterministic input is a fixed number for a given age class and gender. Life -Input with variability and uncertainty not separated. The RR error term, Ԑ ! , of the outcome represents the uncertainty due to the compilation of the meta-analyses and implementation of the model (choice between linear or non-linear dose-response) [START_REF] Hamling | Facilitating meta-analyses by deriving relative effect and precision estimates for alternative comparisons from a set of estimates presented by exposure level or disease category[END_REF][START_REF] Woodward | Epidemiology: study design and data analysis[END_REF] but also the variability due to biological differences between individuals. A discrimination between these is not feasible, as RR is not a datum but the result of meta-analyses. Disability weights are uncertain due to the adjustments of data but also variable due to biological differences, the stage of the outcome and the age and gender of the individuals. For this kind of input, we chose to quantify the variability and the uncertainty as only uncertainty.

The type of implementation of each input is given in Table 2.

Monte Carlo 2D simulation

Inputs were implemented using probability distributions and simulated with Monte Carlo simulation in two dimensions (MC2D). In our models, 10,000 iterations were run to capture the uncertainty and 10,000 iterations for the variability, using the mcstoc function in R (mc2d package). To verify the stability of the outputs, three simulations were carried out for each age class and gender. Variations less than 5% were achieved.

Sensitivity analysis

First of all, a sensitivity analysis was performed to identify the major sources of uncertainty in the output. The current distribution of red meat intake in France for males in the age class 65-84 was used as the benchmark for the comparison (no uncertainty, only variability). For CVD, the simulation was run, sequentially with uncertainty due to the fitted distribution of red meat consumption, uncertainty from the proportion of eaters of red meat, and uncertainty due to RR. In addition to the previously mentioned uncertainties, for CRC, the influence of the uncertainty from the 5-year net survival rate and uncertainty due to the disability weight was evaluated. Each confidence interval of the DALY from the simulations was compared with the confidence interval of the simulation taking into account all uncertainties of the model.

Then, the influence of the consumption of red meat, corresponding to the main source of variability in the model, was tested by running various scenarios of red meat consumption.

We established consumption scenarios for both genders for the 45-64 and 65--84 age classes.

There were considered 100,000 people in each gender and age class to evaluate the effect of a specific quantity of red meat consumed, independently of the original number of people in this gender and age class. The following levels of consumption of red meat were tested: 25 g/d, 50 g/d, 75 g/d, 100 g/d and 125 g/d.

Non-quantifiable sources of uncertainty

When building the model, several assumptions were made; they were considered as extra sources of uncertainty. Although non-quantifiable, their influence on the output was qualitatively appraised. We adopted the same method as suggested in "BRAFO tiered approach for benefit-risk assessment of foods" [START_REF] Hoekstra | BRAFO tiered approach for benefit-risk assessment of foods[END_REF]. The effect of each hypothesis on the output of the model was estimated, using information from the literature, as follows: no change or little effect on the output, likely overestimation, likely underestimation, overestimation with certainty, underestimation with certainty, or, no possible conclusion.

Results

Burden of disease associated with consumption of red meat

The mean probability of CRC cases and CVD deaths associated with the consumption of red meat are represented with 95% confidence intervals by age class and gender in Fig. 3. For both outcomes, males were more at risk than females, and the risk increased with age. The risk rose drastically beyond the 45-64 age class for both genders for CRC occurrence, with a risk 13 times and 9 times higher than the previous age class for males and females, respectively. For CVD, the risk increased beyond the 65-84 age class for females, with a risk over 9 times higher than for the 45--64 age class. Before this age, the risk was close to zero.

Furthermore, for both outcomes, the more advanced the age was, the higher the gap between the probabilities of the outcome for males and females.

Males ≥ 85 years old were the most likely to be affected, for both outcomes. Moreover, the mortality from both outcomes seemed to be similar for the same age class and gender, except for those over 85 years old (Fig. 4).

For males, being 45-64 and being 65--84 were the major contributors to the burden of disease (expressed in DALY, Fig. 5) due to CRC attributable to the consumption of red meat, with 5

[95% CI = 0.4-14] and 5 [95% CI = 0.2-13] DALY per 100,000 people per year, respectively. The same holds for females, with 3 [95% CI = 0-9] and 3 [95% CI = 0-10] DALY per 100,000 people per year, respectively.

The two major contributor population groups for this CVD were the male population in the 45-64 and 64-85 age classes with 5 [95% CI = 1-11] and 5 [95% CI = 1-12] DALY per 100,000 people per year, respectively.

Analysis of different scenarios of red meat consumption and effect on burden of disease

In the developed model, the different levels of red meat consumption were the only sources of variability. To estimate the effect of red meat intake on the output, independently of the number of people in the age class, a consumption scenario for 100,000 people for males and females 45-64 and 65-84 years old was run. The results are presented in Table 3. occurrence, the number of DALY was significantly higher than zero only for a consumption equal to or higher than 100 g/day, for both genders for both age classes. In contrast, for cardiovascular death, the number of DALY was significant for red meat intake equal to or higher than 75 g/day, for both genders and age classes.

Influence of uncertainty and assumptions on model outputs

A sensitivity analysis enabled identifying the main source of uncertainty from the inputs taken into account for the calculation of the DALYs. Of all the variables taken into account in the model, RR was the largest source of uncertainty (Fig. 6).

Indeed, the uncertainty interval for RR was more than 40 times larger than that for disabilityweight in the CRC estimation of DALY, and 25 times larger than that for the proportion of eaters of red meat in the CVD estimation. The uncertainty from levels of consumption, proportion of eaters of red meat, and 5-year net survival rate did not really affect the results for colorectal cancer as much as the uncertainty only due to consumption when estimating the burden of disease for CVD mortality.

Beside this quantitative uncertainty analysis, a qualitative analysis of the influence of the assumptions made to build the model on the outputs is provided in Table 4. The hypotheses "stoma was the only sequelae taken into account in the quantification of the disability of colorectal cancer" and "Red meat consumption only enhanced mortality due to cardiovascular disease" underestimated with certainty the estimated output. The assumption that "the sequelae after colorectal cancer was permanent" overestimated the output with certainty.

Other assumptions had little effect on the output. Most of the time, the data in the model were from 2012. However, the data available for cardiovascular disease mortality were from 2013 and 2014.

+/-

Children under 3 years of age did not suffer from colorectal cancer or cardiovascular disease death

The first class of incidence for colorectal cancer included an age group ranging from 0 to 14 years. For cardiovascular disease mortality, the first class evaluated included all cases under 25 years old. The consumption for children under 3 years of age was not available. It was then assumed that all the people suffering from colorectal cancer and cardiovascular disease were more than 3 years old. However the occurrence of the outcomes has not been clearly demonstrated.

+/-**

The consumption habits of seniors over 80 years were identical to those for individuals 65 to 79 years old

The consumption for people over 80 years old was not available. The hypothesis was based on the fact that consumption did not vary much for adults over 45 years old and elderly people.

+/-

The consumption of red meat had a linear effect, as suggested in metaanalysis studies

In some studies, the dose-responses of the consumption of red meat and of the consumption of processed meat were not linear [START_REF] Bechthold | Food groups and risk of coronary heart disease, stroke and heart failure: a systematic review and dose-response meta-analysis of prospective studies[END_REF][START_REF] Chan | Red and processed meat and colorectal cancer incidence: meta-analysis of prospective studies[END_REF]WCRF/AICR, 2017b).

+/-

The effect of consuming red meat was effective from a consumption greater than zero grams It was assumed that even a small quantity of red meat could increase the risk. However, in some studies, the risk of colorectal cancer was considered as increasing only from 70 g/d of consumed red meat [START_REF] Alexander | Red meat and colorectal cancer: A quantitative update on the state of the epidemiologic science[END_REF][START_REF] Aykan | Red Meat and Colorectal Cancer[END_REF].

+

The time of each stage of the colorectal processes was a deterministic value

Although there was an effect of age, gender and the stage of diagnosis on the duration of each stage of the colorectal processes, the literature only gave deterministic values, in general expressed by the mean value [START_REF] Soerjomataram | Estimating and validating disability-adjusted life years at the global level: a methodological framework for cancer[END_REF].

=

Life expectancy was the same for all individuals with the same gender in the same age class

The mortality tables did not give the uncertainty of the life expectancy. The data were expressed in deterministic form for the mean age of the class.

=

Proportion of sequelae due to colorectal cancer was a fixed value

In the absence of information, the proportion of sequelae after colorectal cancer was hence in deterministic form.

=

Stoma was the only sequelae taken into account in the quantification of the disability of colorectal cancer

Stoma was the sequelae for which reliable data were the most available in the literature. However colorectal cancer may have other sequelae, such as incontinence, bowel function problems, urination problems, gastrointestinal problems and sexual problems [START_REF] Gatta | Late outcomes of colorectal cancer treatment: a FECS-EUROCARE study[END_REF].

--

The sequelae after colorectal cancer was permanent

The duration of life with sequelae was not available in the literature.

+ +

Red meat consumption only enhanced mortality due to cardiovascular disease

Although epidemiological studies did not find a significant quantitative link between the consumption of red meat and the occurrence of cardiovascular disease, a period of disease may occur before death.

--

Relative risk, disability weight and length of the stages of illness were identical for females and males for all age classes

Data was given with no distinction by gender or age class. +/-

Discussion

The probabilistic risk assessment model built in this study enabled estimating the risk, the number of deaths, and DALYs for both CRC and CVD attributable to the consumption of red meat.

Males were more at risk than women for both outcomes, especially those older than 45 (Fig.

3

), as also found in a study carried out in Alberta, Canada [START_REF] Grundy | Cancer incidence attributable to red and processed meat consumption in Alberta in 2012[END_REF]. This difference is partially explained by the lower consumption of red meat by women, with a mean intake of 35 g/day compared with 50 g/day for men. Heme iron is suspected to be the main component in the mechanism leading to the outcome [START_REF] Wolk | Potential health hazards of eating red meat[END_REF] and in the developed countries, red meat is the richest source of this nutrient [START_REF] Czerwonka | Iron in red meat-friend or foe[END_REF]. This nutrient and its mechanism of carcinogenicity has been associated with CRC [START_REF] Bastide | Heme iron from meat and risk of colorectal cancer: a meta-analysis and a review of the mechanisms involved[END_REF][START_REF] Pierre | Beef meat and blood sausage promote the formation of azoxymethane-induced mucin-depleted foci and aberrant crypt foci in rat colons[END_REF] and CVD [START_REF] Ascherio | Dietary iron intake and risk of coronary disease among men[END_REF][START_REF] Qi | Heme iron from diet as a risk factor for coronary heart disease in women with type 2 diabetes[END_REF][START_REF] Sullivan | Iron and the sex difference in heart disease risk[END_REF].

Organic components from cooking, such N-nitroso-compounds, polycyclic aromatic compounds, and heterocyclic aromatic amines, have also been suspected of carcinogenicity [START_REF] Bouvard | Carcinogenicity of consumption of red and processed meat[END_REF][START_REF] Cross | A large prospective study of meat consumption and colorectal cancer risk: an investigation of potential mechanisms underlying this association[END_REF][START_REF] Sinha | Role of well-done, grilled red meat, heterocyclic amines (HCAs) in the etiology of human cancer[END_REF]. Recent studies have evaluated the role of several chemical components in the carcinogenicity of the consumption of red meat, concluding that their roles were not well defined [START_REF] Domingo | Concentrations of environmental organic contaminants in meat and meat products and human dietary exposure: A review[END_REF]Nadal, 2016, 2017), and that the consumption of meat was not the main factor responsible for the dietary exposure to these components [START_REF] Domingo | Concentrations of environmental organic contaminants in meat and meat products and human dietary exposure: A review[END_REF]. The difference between genders might also be explained by the compositions of the diets of women and men. According to the dietary survey INCA 2, women consumed more fresh dairy products, fish and fruit than men, who, in contrast, consumed a higher proportion of meat, cured meat, potatoes and dried fruit (AFSSA, 2009;ANSES, 2016b). Studies of the carcinogenic mechanism of CRC have shown that the consumption of the dietary calcium salts from dairy products and chlorophyll from vegetables reduces heme iron trapping [START_REF] Balder | Heme and chlorophyll intake and risk of colorectal cancer in the Netherlands cohort study[END_REF][START_REF] Bastide | Heme iron intake, dietary antioxidant capacity, and risk of colorectal adenomas in a large cohort study of french women[END_REF][START_REF] Pierre | Meat and cancer: haemoglobin and haemin in a low-calcium diet promote colorectal carcinogenesis at the aberrant crypt stage in rats[END_REF], and consequently its harmful effect. In addition, polyphenols, such as those contained in fruits and red wine, decrease the oxidative effect of heme iron, by inhibiting lipid peroxidation and DNA damage [START_REF] Bastide | Heme iron intake, dietary antioxidant capacity, and risk of colorectal adenomas in a large cohort study of french women[END_REF][START_REF] Bastide | Heme iron from meat and risk of colorectal cancer: a meta-analysis and a review of the mechanisms involved[END_REF][START_REF] Lampe | Health effects of vegetables and fruit: assessing mechanisms of action in human experimental studies[END_REF]. In Denmark, replacing 14 g of red meat by 25 g of fish would lead to an average decrease of 13 DALY per 100,000 adults [START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF]. Furthermore, in World Cancer Research Fund International conclusions, the consumption of milk and calcium probably reduce the risk of CRC, whereas that of processed meat and alcoholic drinks increases this risk (WCRF/AICR, 2017b).

The estimated number of deaths was 3.1 [95% CI = 1.9-4.5] per 100,000 people per year (Fig. 4) with 3.4 [95% CI = 1.5-6.0] cases per 100,000 people per year for CRC. These latter correspond to 1950 [95% CI = 1200-2800] and 2170 [95% CI = 950-3830] respectively for the French population per year. The major contributor was being a male in the 65-84 age class.

The attributable fraction, calculated as the ratio between the number of cases due to the consumption of red meat (W lm(8,9 ! ) and the total incidence of the outcome (\]4 ! ) in France estimates that for the French population, 5% of CRC cases were attributable to the consumption of red meat. To have an order of magnitude and to check the realism of the results, these estimates were compared with those for other countries whose dietary habits are not too far from French food habits. Our results were in line with recent estimates from the International Agency for Research on Cancer (IARC, 2018). This proportion was also similar to those calculated for the United States, the United Kingdom (WCRF/AICR, no date), and New Zealand [START_REF] Richardson | Modifiable lifestyle factors that could reduce the incidence of colorectal cancer in New Zealand[END_REF] with 5% of the population attributable fraction, as well as those for Northern and Central Europe (7.8% of CRC in men, and 5.8% in women) [START_REF] Norat | Meat consumption and colorectal cancer risk: dose-response meta-analysis of epidemiological studies[END_REF]. This value is also close to that of a study of the Italian population which concluded that if people changed their beef consumption habits to an intake of 150 g/week, 3.7% of the deaths due to CRC would be avoided [START_REF] Farchi | Meat consumption reduction in Italian regions: health co-benefits and decreases in GHG emissions[END_REF]. In contrast, in Australia the attributable risk of CRC in 2010 was estimated to be higher (18%), but there was no distinction between processed meat and red meat [START_REF] Nagle | Cancers in Australia in 2010 attributable to the consumption of red and processed meat[END_REF].

In our study, CVD deaths in France attributable to the consumption of red meat were estimated as 1%. An Italian study also quantified the effect of the consumption of beef on CVD mortality. They estimated 3.3% of the deaths from CVD would be avoided if people ate only 150 g/week of beef [START_REF] Farchi | Meat consumption reduction in Italian regions: health co-benefits and decreases in GHG emissions[END_REF]. In Brazil, a study of the attributable fraction to consuming red meat concluded there was a negligible effect in comparison to the attributable fraction due to consuming processed meat (7.7%) [START_REF] Rezende | Coronary heart disease mortality, cardiovascular disease mortality and all-cause mortality attributable to dietary intake over 20 years in Brazil[END_REF]. This could be explained by the mean consumption of the Brazilian population, which was found to be under 70 g/d.

Our study went further than the attributable fraction since it estimated the burden of disease of both CRC occurrence and CVD mortality attributable to consuming red meat, by expressing them in DALYs. This composite metric is the most used one in risk and benefit assessments [START_REF] Hoekstra | BRAFO tiered approach for benefit-risk assessment of foods[END_REF][START_REF] Nauta | Meeting the challenges in the development of risk-benefit assessment of foods[END_REF]. It has the advantage of making a comparison between different health effects, taking into account morbidity and mortality [START_REF] Murray | Quantifying the burden of disease: the technical basis for disabilityadjusted life years[END_REF][START_REF] Pires | Risk Benefit Assessment of foods: Key findings from an international workshop[END_REF], whereas a comparison based upon the number of cases or fatalities would have been incomplete. In this study, if the estimation had stopped with the number of deaths, it would have been concluded that males from 65 to 84 years old were the population most affected by both outcomes. However, when taking into account morbidity in addition, as done by using DALY, we can observe that males from 45-64 years old were the most affected by the outcome. Indeed, if the outcome induces a fatality, this population group will lose a higher number of years lived compared to their expected life expectancy. In addition, cases which survive but with sequelae, will live longer with a disability caused by the outcome, compared with the population group 65-84 years old (Figs. 4 and5). Therefore, for decision making, such as making further recommendations, DALY is more relevant.

Another advantage of using DALY to express the risk is its unit: reporting results in years is easier for the public to understand than a dimensionless output such as RR or population attributable fraction. DALYs are expressed in the same unit as life expectancy, which is widely known by the public and used in the mass media. Another study found 17 DALY per 100,000 people per year in Denmark (calculated from 394 DALY per 100,000 people per year when consuming or not red meat minus 377 DALY per 100,000 people per year without red meat intake) [START_REF] Berjia | Burden of diseases estimates associated to different red meat cooking practices[END_REF]. A Norway study cited by Thomsen et al. in 2018 estimated approximately 40 DALY per 100,000 people attributable to the consumption of red meat [START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF].

The CVD DALY for the French population attributable to the consumption of red meat was estimated to be 21 [95% CI = 12-32] DALY per 100,000 people per year corresponding to 12,960 [95% CI = 7,330-19,360] DALY per year. This is 1% of the total DALY estimated by the Institute for Health Metrics and Evaluation for the French population (IHME, 2018).

Our study highlighted a higher effect of the consumption of red meat on CVD mortality than on CRC, for the oldest age class, both in terms of number of deaths and DALYs (Figs. 4 and 5). This is so even if the number of YLD was excluded from the CVD. This exclusion was done because the relation between the consumption of red meat and the occurrence of CVD, including both full recovery and occurrence of the disease leading to fatalities, was either found to be not significant [START_REF] Kaluza | Processed and unprocessed red meat consumption and risk of heart failure: prospective study of men[END_REF]2015;[START_REF] Micha | Red and processed meat consumption and risk of incident coronary heart disease, stroke, and diabetes mellitus: a systematic review and meta-analysis[END_REF], or mortality and occurrence were mixed up in the estimation of RR [START_REF] Bechthold | Food groups and risk of coronary heart disease, stroke and heart failure: a systematic review and dose-response meta-analysis of prospective studies[END_REF][START_REF] Kaluza | Red meat consumption and risk of stroke: a metaanalysis of prospective studies[END_REF][START_REF] Micha | Red and processed meat consumption and risk of incident coronary heart disease, stroke, and diabetes mellitus: a systematic review and meta-analysis[END_REF][START_REF] Yang | Red meat consumption and the risk of stroke: a dose-response meta-analysis of prospective cohort studies[END_REF]. Consequently, without scientific quantitative evidence, only DALY for cardiovascular death were estimated. This could be then considered as higher than the estimate in the present paper. Based on the GBD-compare-tool [START_REF] Ihme | GBD compare/ Viz Hub[END_REF], which determines the number of DALY by risk, year, country, gender and age class, we could address the number of burden of disease attributable to CVD associated with the consumption of red meat under the assumption that red meat consumption induced disease before death. In the estimates of the GBD study, the YLD made up 21% and 27% of the total DALY, for males and females, respectively, whatever the source of illness. Based on this information, it was then possible to recalculate the number of DALY due to CVD including both morbidity and mortality: the median estimate of the mean was 17 DALY per 100,000 people per year for French males and 10 per 100,000 people per year for French females associated with the consumption of red meat. Unfortunately, to our best knowledge, there is no existing quantification of the DALY attributable to the consumption of red meat on CVD in the literature, to compare with our results.

The burden of CRC and CVD attributable to the consumption of red meat can be compared with other burdens of illness and risk factors in France. It was shown that the consumption of red meat induced 11 DALY per 100,000 people per year for CRC and 13 DALY per 100,000 people per year for French males for CVD. These values are comparable to the burden caused by sexually transmitted infections excluding HIV/AIDS (11 DALY per 100,000 people) but they are lower than those observed for liver cancer due to alcohol (160 DALY per 100,000 people) [START_REF] Ihme | GBD compare/ Viz Hub[END_REF]. In addition, we can compare the DALYs attributable to CRC and CVD due to the consumption of red meat (4% and 1% respectively) with other risk factors.

For example, the GBD-compare-tool estimated a higher risk factor contribution of tobacco (CRC: 8.5%; CVD: 18%) and alcohol (CRC: 28.19%; CVD: 12.3%) for both diseases [START_REF] Ihme | GBD compare/ Viz Hub[END_REF].

The use of the DALY metric also enabled making consumption scenarios. It confirmed that the recommendation to consume less than 500 grams per week of red meat, issued by the authorities (ANSES, 2016;[START_REF] Hcsp | Avis relatif à la révision des repères alimentaires pour les adultes du futur Programme national nutrition santé 2017-2021[END_REF], would be enough to prevent the risk of CRC attributable to red meat consumption. This estimate is also in line with the study of [START_REF] Norat | Meat consumption and colorectal cancer risk: dose-response meta-analysis of epidemiological studies[END_REF], in which a decrease of CRC risk was estimated (7%-24%) in case the intake was lowered to 70 g/week of red meat [START_REF] Norat | Meat consumption and colorectal cancer risk: dose-response meta-analysis of epidemiological studies[END_REF]. However, to prevent CVD attributable to the consumption of red meat, the consumption by the oldest individuals should be under 65 grams per day.

In this study, quantifiable and unquantifiable uncertainties were taken into account, and their effects on the model outputs were assessed (Table 4 and Fig. 6), as recommended by international organizations (FAO/WHO, 1999).

The quantification of the uncertainty took into account the fitted distribution of red meat intake, the proportion of red meat consumers, RR and the disability weight. However, the study also highlighted some difficulties in tackling uncertainty and variability. For instance, RR, identified as a source of uncertainty in our model due to model parameter estimation [START_REF] Frey | Quantitative analysis of uncertainty and variability in environmental policy making[END_REF][START_REF] Krewski | Characterization of uncertainty and variability in residential radon cancer risks[END_REF] within a random effect model meta-analysis [START_REF] Vieira | Foods and beverages and colorectal cancer risk: a systematic review and meta-analysis of cohort studies, an update of the evidence of the WCRF-AICR Continuous Update Project[END_REF], included also individual susceptibility variability. Indeed, a family history of colorectal cancer, the presence of adenomatous polyps, previous colorectal cancers, and infectious diseases such as Crohn's disease and ulcerative colitis, increase the risk of CRC [START_REF] Haggar | Colorectal cancer epidemiology: incidence, mortality, survival, and risk factors[END_REF]. In addition, diabetes, high cholesterol and high blood pressure are not always taken into account in the statistical estimation, and induce a variability in the RR of the CVD estimation [START_REF] Abete | Association between total, processed, red and white meat consumption and all-cause, CVD and IHD mortality: a meta-analysis of cohort studies[END_REF][START_REF] O'donnell | Cardiovascular risk factors. insights from framingham heart study[END_REF]. Nevertheless, the estimation of RR is generally implemented in risk-benefit models as a source of uncertainty [START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF].

Disability weights also combined variability and uncertainty. Some authors classify it as only variability [START_REF] Havelaar | Disease burden in The Netherlands due to infections with Shiga toxin-producing Escherichia coli O157[END_REF], the confidence interval representing the variability of the severity of the disability, but others implement it as an uncertainty [START_REF] Boué | Development and application of a probabilistic risk-benefit assessment model for infant feeding integrating microbiological, nutritional, and chemical components[END_REF][START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF].

Another source of uncertainty comes from the hypotheses made when building the study.

Indeed, the duration of each stage of colorectal cancer, the proportion of cases with sequelae, and the life expectancy, were implemented as deterministic values. The effect of these data on the output could not be assessed since they were considered as fixed. The hypothesis that the CRC had a dose-response without any threshold, i.e., effective starting from any consumption greater than zero grams (implicit when assuming a log-linearity of the doseresponse), was considered as leading to an overestimation of the outcome. Furthermore, for both outcomes, recent studies have also shown that the dose-response is non-linear, which might underestimate or overestimate the outcome for lower consumption. The same conclusion was drawn about the hypothesis that the life expectancy of the French population was constant over time. Due to the lack of data, no conclusion was possible about the influence of some of the assumptions, such as: children under three years old did not suffer from either outcome, the consumption habits of individuals over 80 years old were identical to those of individuals from 65 to 79 years old, and, RR and disability weight were assumed to be the same for both genders and age classes. The CVD burden of disease may be underestimated because the consumption of red meat was only associated with mortality due to CVD. The CRC burden of disease was also underestimated because stoma was considered as the only sequelae taken into account in the quantification of the disability of colorectal cancer. We assumed no change in the outputs stemming from a change in food habits, because the level of consumption of red meat did not vary much from 2005 to 2013. However, the estimation provides a snapshot of the effect of the consumption of red meat without considering any previous change in it in the population over the years. On the other hand, the CRC burden of disease was overestimated because the sequelae were considered as effective until the end of the life of a CRC survivor. In addition, the effect of exposure is not visible immediately, which induces an additional uncertainty [START_REF] Nauta | Meeting the challenges in the development of risk-benefit assessment of foods[END_REF]. Some studies have assumed a period of 8 years of latency between the exposure and the outcome for CRC [START_REF] Grundy | Cancer incidence attributable to red and processed meat consumption in Alberta in 2012[END_REF] and 10 years for CVD [START_REF] Milner | Health effects of adopting low greenhouse gas emission diets in the UK[END_REF], while in our study, the latency was taken to be 6-7 years.

Nonetheless, despite the inherent uncertainty due to the biological data and particularly the epidemiological data, the results obtained in this study can be interpreted as showing that some differences in the burden of disease were observed, such as between the highest and lowest intakes, as well as between the youngest and oldest populations.

In further studies, this burden will be balanced by the microbiological risks and nutritional benefits of red meat in a broader risk-benefit assessment. Indeed, red meat is also a source of microbiological foodborne illnesses. In 2017, it was estimated that pig and beef meat were responsible for 6.2% of the total outbreaks of such illnesses (ECDC/EFSA, 2018). On the other hand, red meat has beneficial aspects, due to its nutrients, especially iron, which is one of the major nutritional deficiency in the world [START_REF] Kassebaum | The Global Burden of Anemia[END_REF].

In conclusion, the effects of the consumption of red meat on the risk of CRC and CVD have been estimated and expressed in DALYs. The study estimated 19 [95% CI = 8-33] DALY per 100,000 people per year for CRC and 21 [95% CI = 12-32] DALY per 100,000 people per year for CVD, associated with the consumption of red meat. As done previously [START_REF] Cardoso | Portuguese preschool children: Benefit (EPA+DHA and Se) and risk (MeHg) assessment through the consumption of selected fish species[END_REF]Hoekstra et al., 2013a;Hoekstra et al., 2013b;[START_REF] Thomsen | A probabilistic approach for risk-benefit assessment of food substitutions: A case study on substituting meat by fish[END_REF][START_REF] Thomsen | Investigating the risk-benefit balance of substituting red and processed meat with fish in a Danish diet[END_REF][START_REF] Verhagen | Application of the BRAFO tiered approach for benefit-risk assessment to case studies on dietary interventions[END_REF][START_REF] Wikoff | Benefitrisk analysis for foods (BRAFO): Evaluation of exposure to dietary nitrates[END_REF], the present work will be included in a more comprehensive risk and benefit assessment.

  expectancy at the mean age of the class, current age at diagnosis, incidence of the outcome, length of outcome stage and the proportion of permanent sequelae are deterministic inputs in the model. -Data with uncertainty exclusively, such as the proportion of red meat eaters estimated through a beta probability distribution, or the 5-year net survival rate after CRC built with a normal distribution on the natural logarithm of the data (Cowppli-Bony et al., 2016).-Input with variability and uncertainty separated and quantifiable. For red meat consumption, the variability comes from the different levels of consumption of red meat for the different individuals in a given age class and gender. Uncertainty is due to the gap between the real and the estimated quantity of red meat consumed, obtained with a gamma distribution. The separation of uncertainty and variability was carried out using the function mcdata in the package mc2d of R (version 3.4.0).

Table 4 .

 4 Assumptions made in the model development and their influence on the output. * (=) no change/ little effect, (+) likely overestimation, (-) likely underestimation, (+ +) overestimation with certainty, (--) underestimation with certainty, (+/-) no possible conclusion ** Effect for age class 3-24 years old Data for colorectal cancer incidence and population were from 2012 and data from incidence of cardiovascular deaths were from 2013 and 2014, but consumption data dated from 2005 to 2007

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 4 .Fig. 5 .Fig. 6 .Fig

 123456 Fig. 1. Flowchart of the risk assessment model of colorectal cancer and cardiovascular disease in France per year, by age class and gender. White rectangles with dashed line correspond to the "Inputs", full line to "Intermediate calculation". Dark grey rectangles correspond to the "Intermediate output" and light grey rectangles correspond to the final output. (a) Only taken into account for colorectal cancer. (2 column fit)

Table 1 :

 1 Descriptions of and sources of information for inputs.

	Input	Description	Notation for input	Obtained from
	Current age	Mean age of the class		-
	French population	Population in France		INSEE, 2013
	data	Life expectancy at the mean age of the class		INSEE, 2014
	Individuals of the study	Quantity of red meat consumed by red meat eaters		ANSES, 2014
		Proportion of red meat eaters		ANSES, 2014
	Colorectal cancer	Incidence of colorectal cancer		Binder-Foucard et al., 2013
		5-year net survival proportion after colorectal cancer		Cowppli-Bony et al.,
		Mean Relative Risk Residual error of logarithm of RR Length of the outcome stage diagnosis and treatment	Ԑ	WCRF/IARC, 2017a WCRF/IARC, 2017a Soerjomataram et al.,
		remission		Soerjomataram et al.,

Input Notation for input Gender Model implementation per age class Unit Type 3-24 25-44 45-64 65-84 > 85 Current age

		Both	13.5	34.5	54.5	74.5	92.5	Years	D
	French	Male	8,720,840	8,071,902	8,147,229	4,196,602	546,978	Number	D
	population data	Female	8,389,958	8,203,441	8,559,150	5,286,389	1,251,801
		Male	78.73	79.48	81.43	86.48	95.87	Years	D
	Female Male Female Male Female K(772,107 Colorectal 85.2 Individuals of the study =(2.21,4.66 × 10 DE * =(2.58,6.94 × 10 DE * K(695,61 * Male 0.27	85.52 =(2.55,3.87 × 10 DE * =(2.71,6.63 × 10 DE * K(330,39 * 5.63	86.63 =(2.47,4.19 × 10 DE * =(2.82,6.63 × 10 DE * K(404,27 * 80.27	89.39 =(2.81,5.61 × 10 DE * =(2.59,6.43 × 10 DE * K(138,10 * 318.26	96.57 =(2.81,5.61 × 10 DE * =(2.59,6.43 × 10 DE * K(138,10 * 436.96	g/day Number Number	U and V U D
	cancer	Female	0.42	6.09	53.85	180.69	295.94	per 100,000

* K(546,73 * K(477,61 * K(168,22 * K(168,22 *

  TS×+, OP *

	Ԑ	Both Both Both			1.12 W(0, 5.69 × 10 DE * 1.08			Number Number Years	D U D
		Both			3.92			Years	D
		Both			1.267			Years	D
		Both			0.25			Years	D
	Cardiovascular	Both Both Both Both Both Both Both Both Male	0.33	2.13	0.083 W(0.288, 1.85 × 10 D+ * W(0.049,2.15 × 10 D+ * W(0.049, 2.15 × 10 D+ * W(0.451,1.71 × 10 D+ * W(0.54,1.53 × 10 D+ * 13 W(0.095, 1.87 × 10 D+ * 20.37	106.85	648.6	Years Mean Mean Mean Mean Mean Percentage Mean Number per	D U U U U U D U D
	disease	Female	0.2	1.15	9.12	95.63	876.63	100,000	D
		Both			1.15			Number	D
	Ԑ	Both			W(0, 4.65 × 10 DE *			Number	U

  Here, W n.[.lm(8,9 is the number of people who died after a diagnosis of CRC attributable to red meat consumption, W Z[r.lm(8,9 is the number of people who survived with sequelae after a diagnosis of CRC attributable to red meat consumption, and W l[!.lm(8,9 is the number of people who totally recovered after a diagnosis of CRC attributable to red meat consumption.

	W Zql.lm(8,9 = :X lm (` (8,9 ! oooooooooooooooo × W (8,9 ; -W n.[.lm(8,9
	(8)
	W Z[r.lm(8,9 = W Zql.lm(8,9 × Xf#s
	(9)
	W l[!.lm(8,9 = W Zql.lm(8,9 -W Z[r.lm(8,9
	In addition, W (8,9 is the number of individuals taken into account, in accordance with the
	French population statistics, and Xfpcd (8,9 is the 5-year net survival rate after a diagnosis of
	CRC.

  Here, f indicates the stage of the illness, tuvw lm(8,9 ! xyx the disability adjusted life years

	10)
	tuvw lm(8,9 ! xyx = W n.[.lm(8,9 × :∑ tt (Z Z :∑ tt (Z Z ;• + W Z[r.lm(8,9 × :v} (8 -~u(8 -tt €• ; × { Z[r + :W Z[r.lm(8,9 + × { (Z ; + W n.[.lm(8,9 × |v} (8 -~u(8 -W l[!.lm(8,9 ; × :∑ tt (Z Z × { (Z ;
	(11)
	tuvw lm(8,9 ! x'€ = W lm(8,9 ! x'€ × :v} (8 -~u(8 ;

of CRC due to red meat consumption, tt (Z the duration of stage s, { (Z the disability weight at stage s as taken from GBD Cancer Collaboration (2017), ~u(8 the current age at diagnosis of colorectal cancer, v} (8 the life expectancy at age 5, and { Z[r the disability weight of sequelae. For each age class, the mean age was calculated considering the current age at the moment of diagnosis of CRC. Life expectancy was estimated from mortality tables (INSEE, 2014), taking into account the mean age of the age class. The estimation of the DALY for CVD (tuvw lm(8,9 ! x'€ ) only took into account mortality, i.e. YLL, calculated from epidemiological data:

Table 3 .

 3 Number of DALYs calculated for colorectal cancer and cardiovascular disease for each scenario of consumption for males and females 45 to 64 years old and 65 to 84 years old.

	Calculated for 100,000 people per year in combinations of age, gender and intake. The value
	is represented with its 95% confidence interval.

proportionally, since a linear RR dose-response was used in the model. For both age classes and outcomes, males were more at risk, whatever the quantity consumed. However, for CRC

  DALY per year for the French population. Similar estimates were obtained by the Institute for Health Metrics and Evaluation for CRC, which calculated 17 DALY per 100,000 people per year of the attributable part of a diet high in red meat in France[START_REF] Ihme | GBD compare/ Viz Hub[END_REF].

	This study estimated 19 [95% CI = 8-33] DALYs per 100,000 people per year for CRC
	attributable to the consumption of red meat, corresponding to 12,170 [95% CI = 5,260-
	21,170]