Stochastic modelling applied Stochastic modelling applied to the estimation of intense to the estimation of intense

sweeteners intake.sweeteners intake.

Davide ArcellaDavide Arcella

National Research Institute for Food and Nutrition

(INRAN)

The EU directive which fixed Maximum Permitted Levels (MPL) for intense sweeteners for all Member

States also include the general obligation to establish national

systems for monitoring the intake of food additives, in order to evaluate

their use safety.

In the EU the most commonly used methods for the assessment of

exposure to these substances follow a deterministic approach based on

conservative assumptions.

The food products market changes very rapidly in relation to both

product formulation and consumer

preferences.

It is considered to be neither cost-effective nor necessary to

collect detailed data for every food chemical.

Present conservative methods serve us well but sometimes they

produce estimates of exposure which are biologically improbable.

These estimates of potential exposure may obscure the ability of regulators, industry and consumers

to determine which scenarios present a risk that is likely to occur and therefore need to be addressed

An important activity in the field of food safety is to develop and refine

always more efficient statistical methods to periodically estimate the risk of an excessive intake of

chemical substances.

Over the past years, to get a more realistic view of exposure to hazardous substances, risk managers are getting more interested in probabilistic

modelling.

A conservative approach tells us that a given intake is possible even

though available data show it is improbable.

The primary goal of the probabilistic approach is to describe the exposure distribution for the whole population under consideration quantifying the range of exposure and the likelihood of each exposure level.

The probabilistic approach:

allows the utilisation of all the available information on variability in:

•the proportion of foods containing the substance,

•the concentration of the substance present

•food consumption patterns.

allows to take into account all sources of variability and uncertainty in estimates of exposure.

36 104

172

241

309

377

445

514

5820

0.05

0.1

0.15

0.2

0.25

0.3

Freq.

36 104

172

241

309

377

445

514

582

g per day

36 104

172

241

309

377

445

514

5820

0.05

0.1

0.15

0.2

0.25

0.3

Freq.

36 104

172

241

309

377

445

514

582

g per day

Consumption

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

3.3

3.6

3.9

0

0.05

0.1

0.15

0.2

F

r

e

q

.

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

3.3

3.6

3.9

Residue mg/kg

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

3.3

3.6

3.9

0

0.05

0.1

0.15

0.2

F

r

e

q

.

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

3.3

3.6

3.9

Residue mg/kg

Food chemical residue

8

10 12 14 16 18 20 22 24 26

0

0.020.04

0.06

0.080.1

0.12

0.140.16

Freq.

8

10 12 14 16 18 20 22 24 26

kg

8 10 12 14 16 18 20 22 24 26

0

0.02

0.040.06

0.08

0.1

0.12

0.14

0.16

Freq.

8 10 12 14 16 18 20 22 24 26

kg

ResultBody weight

It must be noticed that simulations can be conducted in a wide variety of different ways using widely different data, assumptions and algorithms.

The models are only a simplified representation of real-world

system.

The structure of mathematical models employed to represent scenarios and phenomena of interest is often a key source of uncertainty.

Two different approaches can be used to perform simulations:

the parametric method (Monte Carlo) depends on the random samplings from probability distributions describing consumption and occurrence data.

the nonparametric method takes into account the consumptions and the levels of chemical occurrence in the simulations using random sampling of raw data.

Example - simulation techniques

For simplicity and accuracy when using a probabilistic simulation technique, input variables should be as independent as possible.

However, the presence of moderate to strong correlations or dependencies between input variables should be included in a model and discussed.

Example - Correlations or dependencies

Example A: dependency between the amount of food consumed and the body weight are correlated therefore it is better to use food consumption data standardised for the body weight.

Example B: dependency between intakes of different food categories for the same individual (e.g. high consumers of pears may be also high consumers of apples, both containing the same pesticide residue).Different methods can be used to generate correlated random variables.

Example C: dependency between events of food selection on a given day and on sequential days should be included.

Significant approximations are often an inherent part of the assumptions upon which a model is built. But uncertainty arises also from a basic lack of knowledge regarding the input variables.

There is therefore the critical need to test and validate probabilistic models against actual exposure data.

Validation criteria adopted in Validation criteria adopted in the Monte Carlo projectthe Monte Carlo project

Probabilistic models were considered valid when they provided exposure estimates that can be shown not to underestimate the true exposure but at the same time are more realistic than the currently used conservative estimates.

Databases of “true” intakes were generated for food additives, based on brand level food consumption and ingredient composition.

Food surveyFood survey

INRAN-RM-2001INRAN-RM-2001

Adolescents recorded on diaries, at brand level, all foods and beverages ingested over 12 days.

FOOD SURVEY

DATA ENTRY

ANTHROPOMETRICS MEASUREMENT COLLECTION

STANDARDIZATIONSTANDARDIZATIONSTANDARDIZATIONSTANDARDIZATION

INTERVIEWERS

SamplesSamples

3,982 students completed a screening questionnaire aimed at identifying females high consumers of the main sources of intense sweeteners, table-top sweeteners and sugar-free soft drinks.

The final randomly selected sample comprised 125 males and 108 females.

Female teenagers selected as high consumers of table-top sweeteners were finally 79.

Female teenagers selected as high consumers of sugar-free soft drinks were 75.

FOOD DIARY

BOBoccale

LALattina

TPTazza Piccola

TMTazza Media

TGTazza Grande

BLBicchiere da Liquore

BPBicchiere Piccolo

BGBicchiere Grande

BOWalky cup

FPFetta Piccola

FMFetta Media

FGFetta Grande

PPPorzione Piccola

PMPorzione Media

PGPorzione Grande

UNIT OF MEASURAMENTUNIT OF MEASURAMENTUNIT OF MEASURAMENTUNIT OF MEASURAMENT

THE DATA ENTRY SOFTWARE

CODES, FOOD PRODUCTS AND CODES, FOOD PRODUCTS AND PORTIONSPORTIONS

FOOD FOOD COMPOSITIONCOMPOSITIONFOOD RECIPESFOOD RECIPES FOOD LABELSFOOD LABELS

DATABASESDATABASESDATABASESDATABASES

TERMINALS (interviewers)

MASTER

Additives presence and concentration

a) All the labels of packaged products susceptible to contain intense sweeteners were collected and the food labels database present at INRAN was updated including all the sugar-free products consumed during the survey.

b) Producers were asked to declare the intense sweeteners concentration of all the products susceptible to contain intense sweeteners consumed within the survey.

No gross underestimation of intake occurred.

The energy intake to basal metabolic rate (EI/BMR) ratio was well above the cut-off point established by Goldberg et al. (1991) to identify energy under-reporting.

Results - data qualityResults - data quality

Percentage of consumers of the sugar-free products in the study

samples

Sugar-free products

Random males and females

(%)

Females high

consumers of sugar-free soft drinks

(%)

Females high

consumers of table-top sweeteners

(%)Sugar-free chewing gum and candies

69 95 94

Table-top artificial sweeteners

3 13 39

Sugar-free frizzy drinks, fruit juices and iced teas

6 20 18

Sugar-free mousse and yoghurts

6 0 11

Intake of intense sweeteners (mg/kg b.w.) in the sample of randomly

selected males and females (n=233).

Artificial sweetener

mean

95th percentil

eADI

Aspartame0.03

90.170 40

Acesulfame K

0.011

0.048  9

Saccharin0.00

10.000 5

Cyclamate0.01

40.049 7 

Intake of intense sweeteners (mg/kg b.w.) in the sample of females high consumers of sugar-free soft drinks

(n=75).

Artificial sweetener

mean

95th percentil

eADI

Aspartame0.09

10.298 40

Acesulfame K

0.043

0.246 9

Saccharin0.00

10.000 5

Cyclamate0.08

60.551 7

Intake of intense sweeteners (mg/kg b.w.) in the sample of females high consumers of table-top sweeteners

(n=79).

Artificial sweetener

mean

95th percentil

eADI

Aspartame0.17

20.859 40

Acesulfame K

0.041

0.265  9

Saccharin0.03

00.233 5

Cyclamate0.04

90.292 7 

consumption data are rarely collected at brand level.

food additives that are not strictly necessary for the process are added in some brands and not in others.

The nonparametric simulation method can be used to combine eating occasions assessed though food surveys with food additives concentrations values available at brand level.

Stochastic modelling applied to the estimation of intense

sweeteners intake

Stochastic modelling applied to the estimation of intense

sweeteners intake

Market share and brand loyalty are responsible for correlations between intakes on sequential days.

Market share: proportion of the consumption level of a brand with respect to all brands of the same product.

Brand loyalty: consumers’ tendency to repeat the purchase of a brand.

ExperimentObjective: validate the model for estimating the intake among high consumers. Additive: cyclamate.Source: soft drinks.Sample: 75 pre-screened females who stated to be high consumers of sugar-free beverages.Variable: average daily intake per kg body weightStatistics: 95th percentile.Number of sets: 10,000.Sensitivity analysis: inclusion\exclusion of information about market share - inclusion\exclusion of information about brand loyalty.

B

E

C

D

A

Day 12 H 13:30

Day 1 H 12:05

Day 1 H 18:05

Day 8 H 21:10

Day 3 H 17:25

A brand is assigned randomly by selecting uniformly from all available

brands.

No market share and

no brand loyalty

Brand A

Brand B

Brand C

Brand D

Brand E

D

E

C

E

E

Day 12 H 13:30

Day 1 H 12:05

Day 1 H 18:05

Day 8 H 21:10

Day 3 H 17:25

A brand is assigned by selecting from all available brands, with the

probability to select a given brand set equal to the Market Share (MS) for

that brand.

Market share but no brand loyalty

Day 12 H 13:30

Day 1 H 12:05

Day 1 H 18:05

Day 8 H 21:10

Day 3 H 17:25Each subject is first assigned a brand

to which he / she is assumed to be loyal. This brand is chosen on the basis of the defined Market Share

(MS) values.

Brand D

His / her probability to select Brand D from MS(D) becomes:

{MS(D) + [1 – MS(D)] x LF]}

Where LF = Loyalty Factor

Market share and brand loyalty

D

E

D

D

A

Day 12 H 13:30

Day 1 H 12:05

Day 1 H 18:05

Day 8 H 21:10

Day 3 H 17:25

Market share and Market share and brand loyaltybrand loyalty

Once the subject is assumed to be loyal to brand D, if theLoyalty Factor (LF) = 0.5,

his / her market share becomes:

Brand D

When LF = 1 the consumer always chooses the brand to which he / she is assumed to be loyal.When LF = 0 the consumer chooses each brand with a probability equal to its market share.

Mean of the daily average intake of cyclamate

1) No market share (27 brands) data and no loyalty factor2) Market share data and no loyalty factor3) Market share data and Loyalty Factor = 0.54) Market share data and Loyalty Factor = 1

This line is the “true”

intake

95th percentile of the daily average intake of cyclamate

1) No market share (27 brands) data and no loyalty factor2) Market share data and no loyalty factor3) Market share data and Loyalty Factor (average)4) Market share data and Loyalty Factor (high)

This line is the “true”

intake

Brand loyalty and market share influence results of a probabilistic model of human exposure to food additives.The probability of high intakes of intense sweeteners was in fact underestimated when they were not taken into account.

When no data regarding market share or brand loyalty are available it would be advisable to run the model under different theoretical scenarios and use the worse case scenario to obtain conservative intake distributions.

Conclusion

The numerical simulation techniques provide powerful tools that will take advantage from all the available knowledge (empirical data, experts judgments, etc.) in order to provide realistic estimates of exposure. The results, however, are only as good as the input data, algorithms and assumption.

• The impact of the assumptions should always be tested carefully and the results should be fully documented.

• A modelling tool must be structured so that all algorithms and assumptions inherent to the model can be identified and validated.

General conclusion

1) Cullen, A. C. and Frey, H. C. (2002) Probabilistic techniques in exposure assessment. A handbook for dealing with variability and uncertainty in models and inputs., Plenum Press, New York.

2) Petersen, B. J. (2000) Probabilistic modelling: theory and practice. Food Additives and Contaminants, 17, 591-9.

3) Leclercq, C., Arcella, D., Le Donne, C., Piccinelli, R., Sette, S. and Soggiu, M. E. (2003) Stochastic modelling of human exposure to food chemicals and nutrients within the "Montecarlo" project: an exploration of the influence of brand loyalty and market share on intake estimates of intense sweeteners from sugar-free soft drinks. Toxicology Letters, 140-141, 443-57.

4) Gauchi, J. P. and Leblanc, J. C. (2002) Quantitative assessment of exposure to the mycotoxin Ochratoxin A in food. Risk Analysis : An Official Publication of the Society For Risk Analysis, 22, 219-34.

5) Albert, I. and Gauchi, J. P. (2002) Sensitivity analysis for high quantiles of ochratoxin A exposure distribution. International Journal of Food Microbiology, 75, 143-55.

6) Frey, H. C. and Patil, S. R. (2002) Identification and review of sensitivity analysis methods. Risk Analysis : An Official Publication of the Society For Risk Analysis, 22, 553-78.

References

Research group Research group

Food Safety – Exposure AnalysisFood Safety – Exposure Analysis

Davide ArcellaDavide Arcella arcella@inran.itarcella@inran.it

www.inran.it/Ricerca/rischioalimentare

National Research Institute for Food and Nutrition

www.inran.it