Transcript Development, validation and application of stochastic

National Research Institute
for Food and Nutrition
(INRAN)
Stochastic modelling applied to
the estimation of intense
sweeteners intake.
Davide Arcella
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.
Consumption
Food chemical residue
0.3
0.3
0.2
0.2
0.25
0.25
FF
rr
ee
qq
..
F
0.2
0.2
0.15
0.15
rr
0.15
0.15
ee
26
26
24
24
22
3.9
3.9
3.6
3.6
3.3
3.0
2.7
2.7
2.4
2.1
2.1
1.8
1.5
Result
20
18
18
14
14
12
12
10
10
88
16
16
kg
kg
1.2
Residue
Residue mg/kg
mg/kg
Body weight
FF
r
ee
qq
..
0.9
0.9
582
514
445
377
309
309
241
172
104
104
36
36
00
gg per
per day
day
0.16
0.16
0.14
0.14
0.12
0.12
0.1
0.08
0.08
0.06
0.06
0.04
0.04
0.02
0.02
0
0.05
0.05
0.6
0.6
.
0.05
0.05
0
0.1
0.1
q
0.1
0.1
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.
Example - simulation techniques
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 - Correlations or dependencies
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 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 the
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 survey
INRAN-RM-2001
Adolescents recorded on diaries, at
brand level, all foods and beverages
ingested over 12 days.
INTERVIEWERS
STANDARDIZATION
FOOD
SURVEY
ANTHROPOMETRICS
MEASUREMENT
COLLECTION
DATA
ENTRY
Samples
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
125 males and 108 females.
Female teenagers selected as high
of table-top sweeteners were finally
Female teenagers selected as high
of sugar-free soft drinks were 75.
comprised
consumers
79.
consumers
FOOD DIARY
UNIT OF MEASURAMENT
BL
Bicchiere da Liquore
BP
Bicchiere Piccolo
BG
Bicchiere Grande
PP
Porzione Piccola
BO
Boccale
TP
Tazza Piccola
BO
Walky cup
TM
Tazza Media
PM
Porzione Media
PG
Porzione Grande
LA
Lattina
TG
Tazza Grande
FP
Fetta Piccola
FM
Fetta Media
FG
Fetta Grande
THE DATA ENTRY SOFTWARE
DATABASES
CODES, FOOD PRODUCTS AND PORTIONS
FOOD RECIPES
FOOD
COMPOSITION
FOOD LABELS
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 sugarfree 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.
Results - data quality
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.
Percentage of consumers of the sugarfree products in the study samples
Sugar-free
products
Random
males and
females
(%)
Females high Females high
consumers of consumers of
sugar-free
table-top
soft drinks
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
percentile
ADI
Aspartame
0.039
0.170
40
Acesulfame K
0.011
0.048
9
Saccharin
0.001
0.000
5
Cyclamate
0.014
0.049
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
percentile
ADI
Aspartame
0.091
0.298
40
Acesulfame K
0.043
0.246
9
Saccharin
0.001
0.000
5
Cyclamate
0.086
0.551
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
percentile
ADI
Aspartame
0.172
0.859
40
Acesulfame K
0.041
0.265
9
Saccharin
0.030
0.233
5
Cyclamate
0.049
0.292
7
Stochastic modelling applied to the
estimation of intense sweeteners intake
 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.
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.
Experiment
Objective: 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 weight
Statistics:
95th percentile.
Number of sets: 10,000.
Sensitivity
analysis:
inclusion\exclusion
of
information about market share - inclusion\exclusion
of information about brand loyalty.
No market share and
no brand loyalty
Brand A
E
Day 1
H 12:05
C
Day 1
H 18:05
A
Day 3
H 17:25
D
Day 8
H 21:10
B
Day 12
H 13:30
Brand B
Brand C
Brand D
Brand E
A brand is assigned randomly by
selecting uniformly from all available
brands.
Market share but
no brand loyalty
Brand A
E
Day 1
H 12:05
C
Day 1
H 18:05
E
Day 3
H 17:25
E
Day 8
H 21:10
D
Day 12
H 13:30
Brand B
Brand C
Brand D
Brand E
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 and
brand loyalty
Day 1
H 12:05
Brand A
Brand B
Day 1
H 18:05
Brand C
Brand D
Brand E
Each 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
Day 3
H 17:25
Day 8
H 21:10
His / her probability to select
Brand D from MS(D) becomes:
{MS(D) + [1 – MS(D)] x LF]}
Where LF = Loyalty Factor
Day 12
H 13:30
Brand D
Brand A
Market share and
brand loyalty
Once the subject is assumed to be
loyal to brand D, if the
Loyalty Factor (LF) = 0.5,
his / her market share becomes:
Brand B
E
Day 1
H 12:05
D
Day 1
H 18:05
A
Day 3
H 17:25
D
Day 8
H 21:10
D
Day 12
H 13:30
Brand C
Brand D
Brand E
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
This line is
the “true”
intake
1)
2)
3)
4)
No market share (27 brands) data and no loyalty factor
Market share data and no loyalty factor
Market share data and Loyalty Factor = 0.5
Market share data and Loyalty Factor = 1
95th percentile of the daily average intake of
cyclamate
This line is
the “true”
intake
1)
2)
3)
4)
No market share (27 brands) data and no loyalty factor
Market share data and no loyalty factor
Market share data and Loyalty Factor (average)
Market share data and Loyalty Factor (high)
Conclusion
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.
General 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.
References
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.
National Research Institute
for Food and Nutrition
www.inran.it
Research group
Food Safety – Exposure Analysis
Davide Arcella
[email protected]
www.inran.it/Ricerca/rischioalimentare