The development of a web-enabled framework for probabilistic exposure assessments RR763

Health and Safety
Executive
The development of a web-enabled
framework for probabilistic exposure
assessments
Prepared by the Health and Safety Laboratory
for the Health and Safety Executive 2010
RR763
Research Report
Health and Safety
Executive
The development of a web-enabled
framework for probabilistic exposure
assessments
Nick Warren & Richard Cotton
Health and Safety Laboratory
Harpur Hill
Buxton
Derbyshire
SK17 9JN
This report describes the development of a web-based probabilistic model (PROWESE) for predicting the
statistical distribution of systemic exposure (dose) to chemicals following occupational use.
Model outputs include:
(1) confidence intervals for percentiles taken from the distribution of systemic exposure (measured in
micrograms/kg/day);
(2) confidence intervals for the proportion of workers meeting a minimum Margin of Exposure (with respect
to an appropriate toxic threshold); and
(3) graphical output to allow visualisation of the dose distribution. By replacing single worst-case values
with distributions representing real variation or uncertainty in exposure parameters, the model enables more
realsitic exposure assessment.
This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents,
including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily
reflect HSE policy.
HSE Books
© Crown copyright 2010
First published 2010
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the copyright owner.
Applications for reproduction should be made in writing to:
Licensing Division, Her Majesty’s Stationery Office,
St Clements House, 2-16 Colegate, Norwich NR3 1BQ
or by e-mail to [email protected]
ii
CONTENTS
1
INTRODUCTION..........................................................................................1
2 FUNCTIONALITY ........................................................................................2
2.1
Types of assessment................................................................................2
2.2
Using the model........................................................................................2
2.3
Model outputs...........................................................................................3
3 TECHNICAL BASIS ....................................................................................5
3.1
Monte Carlo algorithm ..............................................................................5
3.2
Calculation of systemic exposure .............................................................6
3.3
Distributions..............................................................................................7
4 FURTHER DEVELOPMENT........................................................................9
4.1
Extending the framework to cumulative exposures ..................................9
4.2
Maintenance.............................................................................................9
REFERENCES..................................................................................................11
GLOSSARY ......................................................................................................12
APPENDIX 1: DEFAULT DISTRIBUTIONS .....................................................14
APPENDIX 2: EXAMPLE OF A PROBABILISTIC ASSESSMENT .................18
iii
iv
EXECUTIVE SUMMARY
Summary
Existing methods for assessing occupational risks from chemical exposure are generally
deterministic and incorporate variability and uncertainty in an ad hoc manner, often through the
use of conservative worst-case values. Probabilistic exposure assessments, where worst-case
values are replaced with distributions representing real variation or uncertainty in the quantities,
offer an opportunity for more informed risk assessment.
This report describes the development of a web-based probabilistic model (PROWESE) for
predicting the distribution of systemic exposure (dose) to chemicals following occupational use.
HSE users require no specialist software with all computations performed by HSL's MATLAB1
web server. The model may be accessed through the HSE/HSL intranet at:
http://hslintranet/prowese
Specific features of the model include:
•
•
•
separate quantification of variability and uncertainty using 2-dimensional Monte
Carlo algorithms;
acute (single day) and chronic systemic exposure assessments;
options for parametric (log normal) and non-parametric characterisations of dermal
and inhalation exposures;
•
correlated external exposures;
•
correlated physiological parameters; and
•
standard distributions for variation in the efficacy of PPE and RPE.
Model outputs include:
•
•
•
confidence intervals for percentiles taken from the distribution of systemic exposure
(measured in µg kg-1 day-1);
confidence intervals for the proportion of workers meeting a minimum Margin of
Exposure (with respect to an appropriate toxic threshold); and
graphical output to allow visualisation of the dose distribution.
Recommendations
•
•
•
A second phase of development should be undertaken to extend the web-based
framework to calculate cumulative systemic exposure to a single chemical from
multiple sources, for example occupational exposure and exposure to consumer
products.
Probabilistic exposure assessments should be conducted alongside conventional
deterministic assessments required under the Biocidal Products Directive (98/8/EC)
in order to promote the methodology and improve acceptance.
Access to the model is currently limited to HSE staff, however no further
development would be required to allow full public access. HSE and HSL should
explore possible opportunities for cost recovery through commercialisation.
v
vi
1
INTRODUCTION
Existing methods for assessing occupational risks from chemical exposure are generally
deterministic; that is they use single values for exposure and toxicity and provide single value
estimates of risk e.g. a margin-of-safety or toxicity-exposure ratio. Deterministic methods
incorporate variability and uncertainty in an ad hoc manner, often through the use of
conservative worst-case values. Probabilistic exposure assessments, where worst-case values are
replaced with distributions representing real variation or uncertainty in the quantities, provide
distributions for systemic exposure and offer the opportunity for more informed risk assessment.
Several software packages exist for general purpose probabilistic modelling but whilst these
packages are user-friendly and flexible they become clumsy when implementing more complex
algorithms. Script based models developed using mathematical/statistical languages such as
1
MATLAB provide a platform for developing simulations of almost any level of complexity but
require a high degree of familiarity with the programming language. This provides a significant
obstacle to their use by exposure assessors who are not generally mathematicians or
programmers. Furthermore, license costs, especially for advanced statistical software packages,
can be prohibitively expensive.
Clearly, it is imperative to use the most appropriate modelling techniques, as it is the exposure
assessment that helps drive the risk characterisation and introduction of the most appropriate
control strategies. In its role as the competent Authority (CA) for biocides (BPR) and the
Registration, Authorisation and Restriction of Chemicals (REACH), The Health and Safety
Executive believes that a probabilistic approach is the most scientifically appropriate
methodology. It therefore agreed that the Health and Safety Laboratory develop the first stage of
a PRObabilistic Web-based model for Estimating Systemic Exposure (PROWESE). This model
will enable exposure assessors to conduct complex probabilistic exposure assessments via a
user-friendly web browser interface and should facilitate wider adoption of these methods.
1
2
2.1
FUNCTIONALITY
TYPES OF ASSESSMENT
Two types of probabilistic systemic exposure assessments are supported by this web-based
system: acute and chronic. Acute assessments do not consider within and between-worker
variation in exposure. The calculated distribution represents the distribution of systemic
exposure for a random worker on a random day. It is important to appreciate that this is not the
distribution of exposure for every worker - indeed no single worker is likely to experience the
whole range of this distribution. Instead the distribution is an amalgamation of many narrower
individual distributions. Although this is probably the most common type of probabilistic
exposure assessment, proper interpretation of the output distribution limits its utility for risk
characterisation. For example, a 95th percentile of 10 λg/kg/day means that 5% of worker days
result in a systemic exposure greater than 10 λg/kg/day; it is not possible to infer that all
workers exceed this amount 5% of the time or that 5% of workers are habitually exposed above
this level. However, the distribution can be used to determine whether exposures are acceptable
against a criteria based upon a maximum proportion of worker-days producing systemic
exposures greater than a specified dose. Such criteria, which are not yet established for
occupational exposure to biocides, may be appropriate when considering acute health end
points.
The chronic assessment option performs a longitudinal probabilistic exposure assessment. This
takes account of the pattern of occupational use of the chemical over time, and calculates the
distribution of mean systemic exposure, averaged over the whole time period. The resultant
distribution is easily interpretable, e.g. a 95th percentile of 10 λg/kg/day means that 5% of
workers have mean systemic exposures greater than 10 λg/kg/day, and is suitable for
comparison with a No Observable Adverse Effect Level (NOAEL) for a chronic health
endpoint.
2.2
USING THE MODEL
The model may be accessed through the HSE/HSL intranet at:
http://hslintranet/prowese
HSE users require no specialist software with all computations performed by HSL's MATLAB1
web server. Before using the model users are required to complete an online registration in order
to set up an account and user profile. Users may then either conduct probabilistic exposure
assessments for any of the existing exposure scenarios stored within the online library, or create
their own new scenarios using a wizard. Complete user guidance is provided by the online help
system and consists of step-by-step instructions for entering exposure scenarios and running the
model, alongside pop-up help on specific features.
2
2.3
MODEL OUTPUTS
This section gives an overview of the model outputs. Appendix 2 presents a complete example
of a probabilistic exposure assessment for a biocide conducted using the web-based model.
2.3.1
Distribution of systemic exposure
For both acute and chronic assessments the main model output is an estimate and confidence
interval for an exposure percentile chosen by the user e.g. the 90th percentile of systemic
exposure. Furthermore, the current system provides the user with a Cumulative Distribution
Function (CDF) plot of systemic exposure illustrating the uncertainty in the whole of the
systemic exposure distribution (Figure A2.1). This plot also displays the estimate and
confidence interval for their chosen exposure percentile along with an estimate of the percentile
corresponding to a minimum Margin of Exposure (see section 2.3.2). A histogram of the
uncertainty distribution for the chosen percentile is also provided (Figure A2.1).
No formal recommendation for the selection of exposure percentiles or the level of confidence
is made in this report. It is suggested that appropriate default choices should be established
through a series of comparisons with deterministic assessments and in consultation with other
competent authorities.
2.3.2
Risk characterisation
For deterministic assessments the Margin of Exposure (MOE) is defined as the ratio of an
appropriate No Observable Adverse Effect Level (NOAEL) and the estimated systemic
exposure:
MOE = NOAEL (λg/kg/day) / systemic exposure (λg/kg/day)
For a probabilistic assessment the MOE can be defined in the same manner, though, as systemic
exposure is expressed as a distribution, it now takes the form of a distribution. The use of a 2dimensional Monte Carlo algorithm allows both variation and uncertainty in the MOE to be
evaluated. Note that variation and uncertainty in toxicity is not currently considered, save by
(typically) demanding an MOE greater than 100.
For acute exposure assessments an acute NOAEL should be compared with the distribution of
single day systemic exposures. For chronic assessments the distribution of long-term average
systemic exposures ought to be compared to an appropriate NOAEL derived from a chronic
toxicity study. The current system provides the assessor with an estimate (and confidence
interval) for the proportion of MOEs greater than a chosen minimum Margin of Exposure
(default 100) along with a CDF plot of the distribution of MOEs and a histogram of uncertainty
in the proportion.
A traffic light system summarises the assessment for the user:
• Green: the data provided give robust assurance that systemic exposures are adequately
controlled i.e. the upper confidence limit for the chosen percentile of exposure is less
than the level of concern.
• Amber: the data provided are insufficient to conclude whether systemic exposures are
adequately controlled i.e. the confidence interval for the chosen percentile of exposure
overlaps the level of concern.
3
• Red: the data provided suggest systemic exposures are unacceptable i.e. the lower
confidence limit for the chosen percentile of exposure exceeds the level of concern.
Although a summary of the uncertainties considered in the assessment is presented in the model
output, there is currently no facility to conduct any further uncertainty analysis to rank their
individual contributions. Such a facility could be added in the future.
4
3
3.1
TECHNICAL BASIS
MONTE CARLO ALGORITHM
PROWESE uses a 2-dimensional Monte Carlo routine to keep uncertainty and variability
distinct and ensure that the output of the probabilistic exposure assessment is properly
interpretable. Essentially, this nests a conventional Monte Carlo simulation for assessing
exposure variability within a second simulation that varies the input distributions according to
their level of uncertainty. The output is a collection of distributions for systemic exposure that
represent uncertainty in the distribution. The results can be presented graphically as multiple
cumulative distribution plots and used to determine confidence intervals for any percentile from
the outcome distribution. The basic structure of the 2-D Monte Carlo algorithm for acute
exposure is shown in Figure 1.
Step 1.1 Generate distributional parameters
according to specified uncertainties
Step 2.1: Sample exposure quantities from
specified distributions
Variability loop
1,000 iterations
Uncertainty loop
1,000 iterations
Step 2.2: Calculate systemic exposure
using deterministic exposure algorithm
Step 1.2 Retain distributions for variation in systemic exposure
Step 3.1: Extract values for chosen percentile of exposure from each
retained distribution
Step 3.2: Take 500th, 25th, and 975th ordered values as the estimate and
confidence limits for exposure percentile
Figure 1: Schematic of 2-dimensional Monte Carlo algorithm for acute exposures
For assessing chronic exposures, the algorithm is extended to include time (days) as a third
dimension, as depicted in Figure 2.
5
Step 1.1 Generate distributional parameters
according to specified uncertainties
Step 2.1: Generate random worker effects
for dermal and inhalation exposure
Variability loop
1,000 iterations
Step 3.1: Sample exposure quantities
from specified distributions
Uncertainty loop
1,000 iterations
91 days
Step 3.2: Calculate systemic exposure
using deterministic exposure algorithm
Step 2.2: Calculate mean
exposure for each worker
systemic
Step 1.2 Retain distributions for variation in mean systemic
exposure
Step 4.1: Extract values for chosen percentile of exposure from each
retained distribution
Step 4.2: Take 500th, 25th, and 975th ordered values as the estimate and
confidence limits for exposure percentile
Figure 2: Schematic of Monte Carlo algorithm for chronic exposures
Figures 1 and 2 depict 1000 iterations for the variability and uncertainty loops. These numbers
are only illustrative and should be considered as a minimum. The numbers of iterations are
chosen by the user and, except for preliminary style analyses, should be sufficient to ensure
reproducibility of the results. For chronic assessments, the length of the assessment should be a
whole number of weeks to ensure a balanced pattern of activity for patterns of use that are less
frequent than daily. With 90 days being a common duration for toxicity studies, 13 weeks (91
days) provides a comparable duration for the exposure assessment.
3.2
CALCULATION OF SYSTEMIC EXPOSURE
calculates systemic exposure to the active substance (a.s.) using the following
standard deterministic algorithm:
PROWESE
Systemic exposure (µg/kg/day) =
IntakeDermal + IntakeAir
Body weight
Where
Intake Air = Duration ! Concentration a.s ! RPE f ! Breathing rate ! Air concentration
IntakeDermal = Concentrationa.s. ! % absorption ! (Duration ! PDEHands ! PPEGloves + Duration ! PDEBody ! PPECoveralls )
6
In this algorithm potential dermal exposure (PDE) to the hands and body are expressed as rates
of exposure to the in-use formulation i.e. λg min-1. The protection factors afforded by personal
and respiratory protection equipment are represented by PPECoveralls, PPEGloves and RPEf
respectively.
3.3
DISTRIBUTIONS
PROWESE supports a range of distributions for describing variability in systemic exposure
parameters (Table 1). For the distributions of dermal and inhalation exposure, duration, dermal
absorption and chemical concentration, users supply the distributional parameters, whilst for
PPE/RPE protection factors, bodyweights, work rates and breathing rates, users select from a
collection of in-built distributions.
The treatment of uncertainty varies between exposure parameters. Uncertainty in the
distributions of dermal and inhalation exposure will, except in exceptionally data rich scenarios,
be one of the main sources of uncertainty in the assessment and is automatically calculated by
the model from the user input via either a parametric or ordinary bootstrap. Uncertainty in the
in-built distributions for variation in performance of PPE is also considered, however
uncertainty in the performance of RPE is not, pending further review of the evidence base. The
treatment of dermal absorption using a percentage absorbed is rudimentary and this treatment is
a major source of uncertainty in both deterministic and probabilistic assessments. There is an
option to model variation in dermal absorption using a uniform distribution though the
distinction between variation and uncertainty for dermal absorption is difficult. Uncertainties in
the distributions for the remaining parameters, e.g. bodyweight, breathing rates, level of
exertion and chemical concentration in the product, are not expected to contribute significantly
to uncertainty in systemic exposure and are not modelled. Appendix 1 contains further details of
the distributions used to model within/between worker variation, the efficacy of PPE/RPE and
physiological parameters.
For the assessment of chronic exposures the treatment of variability becomes more complex.
Consideration must be given as to whether each parameter in the exposure algorithm varies
within or between workers. Table 2 summarises the treatment of within and between-worker
variation in PROWESE.
7
Parameter
Potential body exposure1
Hand exposure1
Inhalation exposure1
Within/between worker
variation1,2
Correlation in external
exposures1
PPE protection factors2
RPE protection factors
2
Task duration1
Dermal absorption1
Active substance
concentration1
Body weight2
Breathing rate2
Work rate2
1
2
Variability
Log normal
Empirical
Log normal
Empirical
Log normal
Empirical
Fixed value
Fixed values
Uncertainty
Parametric or non-parametric
bootstrap
Parametric or non-parametric
bootstrap
Parametric or non-parametric
bootstrap
Default Beta distribution or
Uniform
Not considered
Log normal
Uncertainty in regression parameters
Log normal
Not considered
Uniform distribution
Empirical
Fixed value
Uniform distribution
Fixed value
Uniform distribution
Log normal
Allometric scaling
Uniform distribution2
Not considered
Not considered
Not considered
Not considered
Not considered
Not considered
User supplied values
Built-in default distributions
Table 1: Options for treatment of variability and uncertainty
Exposure factor
Dermal and inhalation
exposure
Duration
PPE/RPE protection factors
Body weight
Work rate
Breathing rate
Chemical concentration
Dermal absorption
Treatment of within and between-worker variability
Variability split into within and between-worker components
according to user input using a lognormal random effects
model. A default distribution for the split between within and
between-worker variation may be used in the absence of
exposure data with repeat measurements.
All variation is assumed to be within worker i.e. all workers
have the same day-to-day distribution of exposure duration
All variation is assumed to be within worker i.e. all workers
have the same day-to-day distribution of protection factors
Between- worker variation only
All variation is assumed to be within-worker i.e. all workers
have the same day-to-day distribution of exertion rates
Calculated from body weight and work rates; varies both
between and within workers
Within-worker variation only i.e. all workers have the same
distribution
Within-worker variation only i.e. all workers have the same
distribution
Table 2: Treatment of within and between-worker variation in systemic exposure parameters
8
4
4.1
FURTHER DEVELOPMENT
EXTENDING THE FRAMEWORK TO CUMULATIVE EXPOSURES
It was originally envisaged that the web-based model for systemic exposure described in this
report would be the first phase in the development of a probabilistic model for cumulative
chemical exposure. The requirement for probabilistic methods for cumulative exposure
assessments was noted by the Committee on Toxicity's working group on risk assessment of
mixtures of pesticides and similar substances (WiGRAMP2, recommendations 11.5 and 11.7). If
commissioned, a second phase would develop a web-based tool for modelling cumulative
exposures to chemical agents arising through both occupational and consumer use. Calculation
of cumulative exposures should use a person-orientated modelling approach based around a
'lifestyle' model that allows the assessor to describe the activity patterns of individuals through
selecting exposure scenarios from a scenario database. By placing the at risk individual at the
centre of the system, person orientated modelling is readily adaptable to multiple sources of
exposure or even multiple chemicals.
A hierarchical approach is suggested using the current model to populate a scenario database
with systemic exposure (dose) distributions and accompanying confidence bounds and then
using a higher-level 'meta' exposure model to sample exposures from these distributions
according to frequencies generated by the lifestyle model. Splitting the modelling of cumulative
exposure into these two tiers would provide a much more flexible system as the lower tier
model(s) would not need to be run within the meta model. This would allow provision to be
made for including secondary (post application) exposure and dietary exposure via uploads
from other probabilistic models. A web-based platform similar to the current model but made
available to other government departments would further facilitate this. In such a system,
dietary exposure might be modelled as an every day event, occupational exposure as 5 or 6
events per week and consumer exposure scenarios as more occasional and sporadic events. A
major strength of the proposed system would be that no single model would have to directly
calculate occupational, consumer and dietary exposure so models for each type of exposure
could continue to be developed independently by different organisations. One obstacle to this
two-tier approach is that a common bodyweight ought to be used for all exposure events for the
same individual i.e. when sampling systemic exposures from occupational, consumer and
dietary exposure events the systemic exposures should all correspond to a common bodyweight.
This problem could be overcome by uploading information on the correlation between systemic
exposures and bodyweights from each lower- tier model.
4.2
MAINTENANCE
The web-based systemic exposure model is accessed through the HSE intranet but hosted by
HSL. HSE users require no specialist software or configuration changes with all computations
performed by HSL's MATLAB web server. With this delivery platform HSE incurs no software
license costs or other IT expenses - with all maintenance and future upgrades to the web-based
model rolled out automatically without a requirement for any impact testing. The hosting of
the model at HSL uses three servers: Bennu hosts the web application, Sol hosts the registration
and scenario databases, and MATLAB performs the simulations. All three servers are maintained
by HSL's Information Services as part of HSL's overall IT provision. An expected upgrade to
MATLAB during 2009 should lead to a substantial reduction in execution time of the model.
9
The Mathematical Sciences unit is currently working with HSE's Science Business Partners to
develop a maintenance and support programme for computational exposure models developed
at HSL which are recognised as a key facility and are eligible for funding under the Corporate
research budget. It is anticipated that this will provide a modest level of ongoing funding to
allow maintenance, error fixing and minor upgrades to both the web-based systemic model and
the Bayesian Exposure Assessment Toolkit (BEAT).
10
REFERENCES
[1] MATLAB. Version 2008b. Seattle: The Mathworks Inc.
[2] Committee on Toxicity (2002) Risk Assessment of Mixtures of Pesticides and similar
substances. Food Standards Agency report FSA/0691/0902.
[3] Health Survey for England (2006) National Centre for Social Research and University
College London
[4] Hamey P., Van der Jagt K. (2003) Development of Exposure algorithms and the estimation
of operator mixer/loader and applicator exposure using EUROPOEM operator exposure data.
Report submitted to ILSI Risk Sciences Institute Probabilistic worker exposure assessment
workshop, Brussels, Belgium.
[5] Garrod A.N.I., Rimmer, D.A., Robershaw, L., Jones, T. (1998) Occupational exposure
through spraying remedial pesticides. Ann. Occup. Hyg. 42:159-165.
[6] HSE (1999) Dermal exposure to non-agricultural pesticides. HSE guidance document
EH74/3 ISBN 0-7176-1718-1.
[7] Nelson T.J., Jayjock M.A., Colton C.E. (2000) How Protective are Respirator Assigned
Protection Factors: An Uncertainty Analysis. AIHAJ 61:388-393.
[8] Vaughan N., Rajan-Sithamparanadarajah B. (2005) Meaningful Workplace Protection
Factor Measurement: Experimental Protocols and Data Treatment. Ann. Occup. Hyg. 49:549561.
[9] Kromhout H, Symanski E, Rappaport SM. (1993) A comprehensive evaluation of
within- and between-worker components of occupational exposure to chemical agents.
Ann. Occup. Hyg. 37:253-270.
[10] Rappaport SM, Kromhout H, Symanski E. (1993) Variation of exposure between
workers in homogeneous exposure groups. AIHAJ 54:654-62.
[11] Symanski E, Maberti S, Chan W. A meta-analytic approach for characterizing the
within-worker and between-worker sources of variation in occupational exposure. Ann.
Occup Hyg 2006; 50; 343-357.
11
GLOSSARY
Beta distribution A family of continuous probability distributions defined on the interval [0,1]
parameterised by two shape parameters. Beta distributions can be bell or U-shaped and either
left or right skewed. Beta distributions are useful for modelling quantities that take values in a
defined interval with minimum and maximum values. The uniform distribution is a special case
of the Beta distribution where both shape parameters are set to one.
Bootstrap Bootstrap methods are computationally intensive methods of statistical analysis that
use simulation (specifically re-sampling of the original data to produce a number of new
samples each of the same size as the original) in order to calculate properties such as standard
errors and confidence intervals for a statistic derived from the data. It is often used as an
alternative to inference based upon distributional assumptions but also provides a simple
approach where analytical methods require complex formulas or rely on asymptotic
assumptions.
Cumulative distribution function The cumulative distribution function F(x) completely
defines the distribution of a random variable and represents the probability that the random
variable (quantity) takes a values less than or equal to x.
Log normal distribution A right-skewed distribution taking strictly positive values that is
frequently used to represent exposures (dermal, inhalation and biological monitoring data). Log
transforming data that is distributed according to a lognormal distribution provides a normal
distribution.
Margin of Exposure The Margin of Exposure (MOE) is the ratio of the No Observed Adverse
Effect Level to the estimated systemic exposure.
Monte Carlo simulation Monte Carlo simulation is a type of numerical algorithm that relies
upon repeated random sampling of quantities to calculate the result. Monte Carlo algorithms are
especially useful for modelling systems with substantial variability or uncertainty in inputs. In
this type of application, distributions are assigned to the input quantities of a model from which
random values are repeatedly sampled and entered into the model, thus obtaining a distribution
of outcomes. The models used within the Monte Carlo simulation can vary enormously in
complexity from simple algebraic expressions to much more complex computer models.
NOAEL The No Observed Adverse Effect Level is the highest dose of a substance that has
been established either through observation or experimentation to have no harmful effect on the
target organism (either humans or animals in the context of human health risk assessment).
Non-parametric Non-parametric statistical methods make no assumptions about the underlying
distribution from which data are drawn and are appropriate for situations where it is difficult to
verify the validity of common statistical assumptions, such as data being normally distributed,
or where standard distributions fail to provide a reasonable representation of the data.
Parametric bootstrap The parametric bootstrap is a variant on the ordinary bootstrap which is
useful for calculating the sampling uncertainty in a fitted parametric distribution without
recourse to complex analytical formulas. Instead of generating new samples through resampling the original data, new samples (of the same size as the original) are generated from the
fitted distribution, and the quantities of interest (e.g. the geometric mean or geometric standard
deviation) calculated for each sample.
12
Random effects model A type of statistical model used to analyse and represent data sets with
repeated measurements on the same unit or individual within a population. Each unit is
supposed to have their own baseline the deviates from the overall baseline by their random
effect with individual observations on a unit varying around that unit’s baseline. This partitions
variation into inter-individual (between-person) and intra-individual (within-person) variation.
Random effects models are frequently used in occupational and environmental settings to model
variation in exposure across a population.
Variability Variability describes variation of a quantity (exposure) spatially, temporally and
across populations. Variability is an intrinsic characteristic of an exposure scenario and cannot
be reduced, save by altering the scenario itself, through, for example, improved control of
exposure.
Uncertainty Uncertainty reflects a lack of precision or knowledge in (exposure) parameters or
inherent structural errors in a model. Some sources of uncertainty can be reduced through the
collection of more data or the application of more sophisticated methods of analysis.
13
APPENDIX 1: DEFAULT DISTRIBUTIONS
A1.1
Physiological parameters
Bodyweights
Body weights are represented by a mixture of two log normal distributions fitted to data on
approximately 10,000 UK male and female adults taken from the 2006 Health Survey for
England3 and summarised in Table 1.
GM
83 kg
68 kg
UK adult males
UK adult females
GSD
1.20
1.23
Table A.1: Geometric means (GM) and geometric standard deviations (GSD) for UK adults.
Level of exertion
Three levels of physical exertion may be modelled each represented by a uniform distribution:
at rest (20-50W), light exercise (50-100W), heavy exercise (100-150W).
Breathing rates
Correlated breathing rates are calculated from bodyweights and work rates using the following
equation:
0.74
&
BW
#
BR (litre/min) = (-0.0005 WR + 0.0852 WR + 13.544 WR + 347.9) '
$
!
% 75 "
3
2
14
A1.2
Distributions for Personal and Respiratory Protection Equipment
Personal Protection Equipment (PPE)
In deterministic exposure assessments the potential dermal exposure (PDE) is multiplied by a
penetration factor (or equivalently divided by the Protection Factor) to give the actual dermal
exposure (ADE). The obvious extension for a probabilistic exposure assessment is to replace the
single default value for penetration with a distribution. However there is some evidence e.g.
Hamey and Van der Jagt4, that at higher potential exposures comparatively less gets through i.e.
the protection factor of clothing increases. This is modelled using a power law relationship,
which may be represented on a log scale by:
log( ADEi ) = # + " $ log(PDEi ) + ! i
where εi, representing variation in the efficacy of the protective clothing, is normally distributed
with zero mean and standard deviation σ. In the case of β equal to 1 the actual dermal exposure
is proportional to potential dermal exposure and the distribution of penetration does not depend
upon the level of exposure (taking a lognormal distribution with a GM of eα and a GSD of eσ).
In PROWESE power law relationships are used for cotton coveralls, impermeable coveralls and
impermeable double layer clothing systems. In these three cases the power and variance
parameters (β and σ respectively) have been taken from Hamey and Van der Jagt4. For cotton
coveralls the intercept parameter (α) was chosen so that the 75th percentile of the penetration at
an external loading of 2,000 mg (approximately the median potential body exposure for
remedial biocides5) equalled 0.2, which corresponds to the default deterministic Protection
Factor of 5 for dry cotton coveralls. For impermeable and impermeable double layer coveralls
the intercept parameters were chosen so that the 75th percentiles of penetration at an external
loading of 10,000 mg (approximately the median potential body exposure for spraying of
antifoulants6) equalled 0.05 and 0.01 respectively, which correspond to the default deterministic
Protection Factors for these types of PPE.
Minimal clothing is treated somewhat differently. Minimal clothing represents shorts and Tshirt or something similar and the protection they offer is mainly determined by the spatial
distribution of dermal exposure over the body. A log normal distribution for the proportion of
potential dermal exposure deposited on the (uncovered) forearms, head and shins has been
calculated from patch samples on 313 records of dermal exposure extracted from the BEAT
database. This gave a median proportion of potential dermal exposure on uncovered parts of the
body of 0.44 (GSD = 1.8).
The protection offered by gloves is also represented by a lognormal distribution (GM 0.02, GSD
2.5) determined from a regression analysis of 231 data on seven scenarios also extracted from
the BEAT database. This dataset contains no paired measurements inside and outside of
protective gloves on the same individuals, but does contain a mix of potential and actual hand
exposures for every scenario, thereby allowing the average level of protection to be estimated.
Variation in the efficacy gloves was determined by the difference in variability between actual
and potential hand exposures.
For all types of PPE the distributions are truncated at a value of 1 to prevent actual dermal
exposure exceeding potential dermal exposure
15
Respiratory Protection Equipment (RPE)
Variation in Workplace Protection Factors for RPE is modelled as a lognormal distribution with
a GSD of 3.7 – the median variation in eight studies reported in Nelson et al.7. For each class of
RPE, the median Workplace Protection Factor has been calculated in order that the 5th percentile
of the distribution corresponds to the Assigned Protection Factor (APF) as conventionally
assumed6. As with other types of PPE, values are truncated at 1.
A power law representation allows the treatment of all types PPE/RPE to be summarised in a
common format (Table A.2).
Type of PPE
α (s.e.)
β (s.e.)
σ
5th PF
25th PF
50th PF
Suitable gloves
-3.9 (0.34)
1
0.9
11
27
50
Minimal clothing
Cotton coveralls
Impermeable
Impermeable double layer
-0.82 (0.04)
-0.04
-0.94
-2.55
1
0.7 (0.1)
0.7 (0.1)
0.7 (0.1)
0.6
1.05
1.05
1.05
1
1.81
7.22
362
1.5
51
202
1002
2
101
402
2002
-3.54
-4.45
-5.15
-5.84
1
1
1
1
1.3
1.3
1.3
1.3
4
10
20
40
14
36
72
143
34
86
172
344
RPE (APF 4)
RPE (APF 10)
RPE (APF 20)
RPE (APF 40)
1
2
At a potential dermal exposure of 2000 mg
At a potential dermal exposure of 10000mg
Table A.2: Parameter values for the distributions for the efficacy of PPE/RPE (including
standard errors)
Uncertainty
For gloves and minimal clothing there is an option of incorporating uncertainty in the median
Protection Factor based upon the standard error of the estimated parameter (normal
distribution). For cotton, impermeable and impermeable double layer coveralls, uncertainty may
be incorporated based upon the standard error of the power law parameter (β). For these types
of PPE, uncertainty in the intercept parameter (α) is not considered (being highly correlated
with uncertainty in β). Uncertainty is not currently considered at all for RPE.
16
A1.3
Within and between-worker variance in dermal and inhalation exposure
Several studies (Kromhout et al.9, Rappaport et al.10, Symanski et al.11) have presented
comprehensive evaluations of within and between worker variability in exposures, particularly
in inhalation exposure. These studies have facilitated the derivation of a default uncertainty
distribution for the proportion of total exposure variability represented by the between-worker
component. Briefly the procedure was as follows:
•
•
•
Log normal distributions were fitted to the range of within and between-worker
variance components of data grouped by job and across locations, as reported by
Symanski et al.11.
A Monte Carlo simulation sampled variance components from the fitted lognormal
distributions to generate a distribution for the proportion of total variability
contributed by the between worker component. This procedure assumed that the
variance components were uncorrelated, an assumption supported by the study of
Kromhout et al.9 .
A Beta distribution was fitted to the Monte Carlo output to represent uncertainty in
the proportion of total variability contributed by between-worker variance.
The resultant default distribution, Beta (2.3, 4.1), is shown in Figure A.1. It is apparent that
there is a tendency for the between worker variance component to be the smaller of the two
components, however the proportion varies very considerably between scenarios (median 34%,
inter-quartile range 22%-48%).
Figure A.1: Default uncertainty distribution for the proportion of total external exposure
variation contributed by between worker variance
17
APPENDIX 2: EXAMPLE OF A PROBABILISTIC ASSESSMENT
This appendix presents an example probabilistic assessment for Triadimefon, a new active
substance used in wood preservatives, under review by HSE in 2008/2009. The applicant has
put forward a number of products containing Triadimefon for consideration, including
industrial, professional and consumer uses. The probabilistic assessment presented here relates
to the application phase of a water-based product used in vacuum pressure impregnation of
timber.
Distributions for dermal and inhalation exposures have been derived from the data presented in
HSE guidance document EH74/3 (Dermal Exposure to non-agricultural pesticides4). As no
information is available from this study relating to within- and between-person variability in
exposure, a default value (with uncertainty) for the split of total variability into these
components has been adopted for the chronic assessment. The assessment assumes that workers
wear cotton coveralls, suitable gloves and no RPE. At the time of writing, the dermal absorption
value has been revised and agreed by HSE toxicologists, the NOAEL however, is that suggested
by the applicant.
Table A2.1 presents the probabilistic exposure assessment for Triadimefon with Figure A2.1
showing the distribution of long-term (chronic) systemic exposures. Table A2. No judgement as
to the acceptability of the exposures is given here.
Table A2.2 presents a further probabilistic assessment for Triadimefon using a non-parametric
(re-sampling) representation of dermal and inhalation exposure. Only an acute assessment is
presented as it is not possible to characterise within- and between –person variability using this
methodology. Although differences in the predicted distribution of systemic exposure between
the two methodologies are apparent, these differences are relatively small and lie well within the
calculated ranges of uncertainty.
18
Exposure parameter
Potential body exposure
(λl min-1)
Variability
Log normal, GM=39.8,
GSD=4.4, n=45
Uncertainty
Yes, parametric bootstrap
Actual hand exposure inside
gloves (λl min-1)
Inhalation exposure
(λl m-3)
Within/between worker
variation
Correlation in external
exposures
PPE protection factors
Log normal, GM=2.86,
GSD=5.2, n=50
Log normal, GM=0.79,
GSD=3.4, n=49
34% of variation between
worker
0.5, 0.5, 0.5
Yes, parametric bootstrap
Cotton coveralls (power law)
Yes
RPE protection factors
No RPE
-
Task duration (minutes)
Uniform [300, 480]
Dermal absorption
Active substance
concentration
Body weight (kg)
Breathing rate
Work rate (W)
8% (fixed value)
0.025% w/v
(fixed value)
Log normal, GM=78, GSD=1.20
Allometric scaling
Light exercise,
Uniform [50,100]
S y st e m ic E xp o su r e ( µg kg-1 day-1)
E st i m at e
c on f id e n c e in t e r v a l
Acute
50th percentile
0.74
75th percentile
1.7
95th percentile
6.2
Chronic
50th percentile
1.1
75th percentile
2.4
95th percentile
5.9
-1
-1
3400
NO A E L ( µg kg day )
M ar gi n of E xp o su r e
Estimate
confidence interval
Acute
50th percentile
4595
25th percentile
2000
5th percentile
548
Chronic
50th percentile
3090
25th percentile
1417
5th percentile
576
Yes, parametric bootstrap
Default Beta distribution
Not considered
Not considered
Not considered
Not considered
Not considered
Not considered
Not considered
95 %
0.4 - 2.1
0.8 - 5.5
2.9 - 21
0.5 -3.4
1.2 - 7.9
2.6 - 18
95%
1620 - 8500
620 - 4250
162 - 1170
1000 - 6800
430 - 2833
189 - 1308
Table A2.1: Probabilistic assessment for water-based vacuum impregnation using Triadimefon.
19
Figure A2.1: Cumulative distribution of chronic systemic exposure to Triadimefon.
20
Exposure parameter
Potential body exposure
(λl min-1)
Variability
Re-sampling from empirical
distribution
Uncertainty
Yes, bootstrap
Yes, bootstrap
Actual hand exposure inside
gloves (λl min-1)
Inhalation exposure
(λl m-3)
Correlation in external
exposures
PPE protection factors
Re-sampling from empirical
distribution
Re-sampling from empirical
distribution
0.5, 0.5, 0.5
Not considered
Cotton coveralls (power law)
Yes
RPE protection factors
No RPE
-
Task duration (minutes)
Uniform [300, 480]
Yes, bootstrap
Not considered
Dermal absorption
Active substance
concentration
Body weight (kg)
Breathing rate
Work rate (W)
8% (fixed value)
Not considered
0.025% w/v
Not considered
(fixed value)
Log normal, GM=78, GSD=1.20
Not considered
Allometric scaling
Not considered
Light exercise,
Not considered
Uniform [50,100]
S y st e m ic E xp o su r e ( µg kg-1 day-1)
E st i mat e
9 5%
c on f id e n c e in t e r v a l
Acute
50th percentile
0.83
0.5 - 2.2
75th percentile
1.6
0.9 - 5.0
95th percentile
5.7
2.1 - 18
3400
NO A E L ( µg kg-1 day-1)
M ar gi n of E xp o su r e
E st i m at e
9 5%
c on f id e n c e in t e r v a l
Acute
50th percentile
4096
1545 – 6800
25th percentile
2125
680 – 3778
5th percentile
596
189- 1620
Table A2.2: Probabilistic assessment for water-based vacuum impregnation using Triadimefon
using non-parametric (re-sampling) exposure distributions
21
Published by the Health and Safety Executive
01/10
Health and Safety
Executive
The development of a web-enabled
framework for probabilistic exposure
assessments
This report describes the development of a webbased probabilistic model (PROWESE) for predicting
the statistical distribution of systemic exposure (dose)
to chemicals following occupational use.
Model outputs include:
(1) confidence intervals for percentiles taken from
the distribution of systemic exposure (measured in
micrograms/kg/day);
(2) confidence intervals for the proportion of workers
meeting a minimum Margin of Exposure (with respect
to an appropriate toxic threshold); and
(3) graphical output to allow visualisation of the
dose distribution. By replacing single worst-case
values with distributions representing real variation
or uncertainty in exposure parameters, the model
enables more realsitic exposure assessment.
This report and the work it describes were funded
by the Health and Safety Executive (HSE). Its
contents, including any opinions and/or conclusions
expressed, are those of the authors alone and do
not necessarily reflect HSE policy.
RR763
www.hse.gov.uk