Bayesian Decision Analysis (BDA): A Tool
for Incorporating Professional Judgment
and Modeling into Exposure Control
Banding
Paul Hewett Ph.D. CIH
Exposure Assessment Solutions, Inc.
Copyright 2006 Exposure
Assessment Solutions, Inc.
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Abstract
Bayesian statistical methods have recently been applied to industrial
hygiene decision making. This technique, called Bayesian Decision
Analysis (BDA), provides a mechanism for explicitly incorporating
professional judgment into the statistical analysis and interpretation of
occupational exposure data. The analysis goal is to determine with
high accuracy whether the SEG exposure profile can be classified as a
Control Band Category 0, 1, 2, 3, or 4 exposure (using the AIHA
exposure categories). The output of BDA is a set of three "decision
charts": one summarizing professional judgment, the second
representing the analysis of the exposure data, and the third
representing a combination of professional judgment and data analysis.
Each chart depicts the probability that the true exposure profile is in
each of the five exposure control band categories. BDA automatically
provides feedback regarding the accuracy of the professional
judgment: if the professional judgment-based decision chart and the
data-based decision charts are substantially different then it is likely
that the basis for the professional judgment was faulty.
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Bayesian Decision Analysis (BDA): A Tool for
Incorporating Professional Judgment and Modeling into
Exposure Control Banding
I.
II.
III.
IV.
V.
VI.
Scenario
AIHA & UK/ILO Control Banding Models
Intro to Bayesian Decision Analysis
Incorporating Professional Judgment
Incorporating Exposure Modeling
Feedback
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I. Scenario
Dimethyl Death
„
„
OEL (TLV) = 1 ppm
R-phrases: R48/20 Æ Hazard Band C
Two Similar Exposure Groups:
SEG1
„ SEG2
„
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Assume the following for the SEG1:
„
„
„
<100 ml are used per batch
the liquid has a medium vaporization
potential
the task is performed inside a ventilated
enclosure
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Assume the following for the SEG2:
„
„
„
>900 ml but less than 1 L quantities are
used per batch
the liquid has a medium vaporization
potential
the task is performed inside a ventilated
enclosure
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Example (Traditional) IH Survey
During a baseline exposure assessment for
SEG1, an IH collected the following full-shift
measurements from an SEG:
„
„
„
„
x = {0.20, 0.05, 0.10} ppm
n=3
gm = 0.1 ppm
90%CI( 0.03, 0.32 )
gsd = 2.0
90%CI( 1.5, 21 )
The sample 95th percentile was 0.31 ppm
but with a 95%UCL of 20 ppm
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The point estimate of the 95th percentile is <
50% of the limit.
Exposures appear to be a Category 2
exposure.
However, the 95%UCL(X0.95) is considerably
greater than the OEL.
What would you do?
„
„
Make a decision ?
Collect more data ?
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Our IH concludes:
„
„
This SEG (operation) is well-controlled (i.e.,
Category 2) with just the existing dilution
ventilation.
Although the 95%UCLs were excessive, our IH
took into account his extensive past experience
with this type of operation.
His recommendations:
„
„
Further sampling is not necessary.
Routine surveillance samples should be collected
using the established schedule for well-controlled
operations
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Questions
Is the SEG in compliance?
„
What is the definition of “compliance”?
Š All measurements < OEL
Š True 95th percentile < OEL
„
Can the confidence level for a decision composed
of Data Analysis + Professional Judgment be
quantified?
Is there a way to combine Professional
Judgment and Data Analysis into an objective
and transparent Decision Making Process?
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II. AIHA and UK/ILO Control Banding
Models
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The AIHA Model uses “Exposure Control
Banding”
AIHA Exposure Control Ratings for TWA OELs
„
Which control zone is appropriate?
Exposure Control
Ratings *
Cutoff (%OEL)
0
X0.95 < 1%
1
1% > X0.95 < 10%
2
10% > X0.95 < 50%
3
50% > X0.95 < 100%
4
X0.95 > 100%
Confidence level
High
Medium
Low
* Adapted from Tables 5.2 and 6.2; rating 0 taken from 1991 version
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Example Control Category Follow-up
(Exposure Control Banding)
Exposure Control
Category**
Recommended Control
0 (<1% of OEL)
No action
1 (<10% of OEL)
general HazCom
2 (10-50% of OEL)
+ chemical specific HazCom
3 (50-100% of OEL) + exposure surveillance, medical surveillance, work
practices
4 (>100% of OEL)
+ respirators & engineering controls, work practice
controls
5 (Multiples of OEL;
e.g., based on
respirator APFs)
+ immediate engineering controls or process
shutdown, validate respirator selection
** - Decision statistic = 95th percentile
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SEG1
gm = 0.1 ppm
gsd = 2.0
90%CI( 0.03, 0.32 )
90%CI( 1.5, 21 )
5
4
GSD
3
2
2
1
0
3
4
1
0.001
0.01
0.1
1
GM
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UK and ILO “Control Banding”:
Hazard group vs. target exposure range
Hazard Group
(w/ examples)
Target airborne concentration
range
Particulate
Vapors
A - Skin and eye irritants
>1-10 mg/m3
>50-500 ppm
B - Harmful on single exposure
>0.1-1 mg/m3
>5-50 ppm
C - Severely irritating & corrosive;
skin sensitizers
>0.01-0.1 mg/m3
>0.5-5 ppm
D - Very toxic on single exposure;
reproductive hazard
<0.01 mg/m3
<0.5 ppm
E - Carcinogens, asthmagens
Seek specialist advice
S: skin and eye contact
Prevent or reduce skin and/or eye
exposure
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SEG1
gm = 0.1 ppm
gsd = 2.0
90%CI( 0.03, 0.32 )
90%CI( 1.5, 21 )
5
4
GSD
3
D
2
A
B
C
NR
1
0.01
0.1
1
10
100
1,000
GM
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Comments
The category cutoffs and ranges for the AIHA
Exposure Control Band model is substancespecific and correspond to regimens of
Actions.
The UK/ILO Control Banding model is used
solely for determining if exposures tend to be
in the target Control Band.
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III. Intro to Bayesian Decision Analysis
(BDA)
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Bayesian Decision Analysis (BDA)
An adjunct or alternative to the calculation
and interpretation of traditional statistics.
The goal of BDA is to estimate the probability
that the true exposure profile falls into a
particular category, or Exposure Rating.
BDA can explicitly incorporate professional
judgment.
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Foundation of BDA:
Bayes’ Theorem
Posterior
Likelihood
Prior
Correction Factor
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Modified Bayes’ Equation
Popi = all combinations of G and D within the ith
Exposure Control Category.
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References
Hewett, P. et al.: Rating Exposure
Control Using Bayesian Decision
Analysis. Journal of Occupational and
Environmental Health, in press (2006).
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BDA Summary
Input: professional judgment + data
Output: Decision Charts
„
„
Prior decision distribution - represents our
professional judgment regarding the probability of
each of the five Exposure Ratings.
Likelihood decision distribution - the set of
probabilities of each Exposure Rating calculated
using only the collected data.
„
Posterior decision distribution - the set of
probabilities of each Exposure Rating calculated
using Bayes’ equation.
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IV. Incorporating Professional
Judgment
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Prior Decision Distribution
Categorical
„
Assign an a priori
probability to each
Exposure Rating zone
Decision Probability
Prior
1
0.6
0.8
0.6
0.4
0.17
0.17
0.03
0.03
0.2
0
0
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2
3
Exposure Rating
4
26
Basis for the Prior Decision Distribution
„
„
„
„
„
„
Past data from this or similar SEGs
Personal experience with this SEG or job
Peak readings from a direct reading
instrument
Recommendations from other IHs
Physical / chemical modeling calculations
Expert system recommendations
Š e.g., UK/ILO Control Banding model
„
and so on …
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SEG1 data:
x = {0.20, 0.05, 0.10} ppm
OEL = 1 ppm
Substance: Dimethyl Death
AIHC Exposure Categories
„
„
„
„
„
4
3
2
1
0
:
:
:
:
:
X0.95 > 1ppm
0.5ppm < X0.95 < 1ppm
0.1ppm < X0.95 < 0.5ppm
0.01ppm < X0.95 < 0.1ppm
X0.95 < 0.01ppm
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SEG2 data:
x = {2.0, 0.5, 1.0} ppm
OEL = 1 ppm
Substance: Dimethyl Death
AIHA Exposure Categories
„
„
„
„
„
4
3
2
1
0
:
:
:
:
:
X0.95 > 1ppm
0.5ppm < X0.95 < 1ppm
0.1ppm < X0.95 < 0.5ppm
0.01ppm < X0.95 < 0.1ppm
X0.95 < 0.01ppm
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V. Incorporating Exposure Modeling
or an Expert System
Example: Let’s use the UK/ILO Control
Banding “expert system” to inform our
Professional Judgment.
The UK/ILO Control Banding predicts the
range of probable exposures, as function of
three exposure determinants:
„
„
„
Quantity
Dustiness or vaporization potential
Level of control
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Example: UK/ILO Control Banding Predicted exposures for both SEG1 and SEG2
Control
Approach
Exposure Predictor Band (ppm)
ml – lo
ml – med,hi
L, m3 – lo
m3 – med
L – med,hi
m3 – hi
General
ventilation
<5
5-50
50-500
>500
Local Exhaust
<0.5
0.5-5
5-50
5-500
Containment
<0.05
0.05-0.5
0.5-5
0.5-5
Quantity – ml, L, m3
Vaporization potential – lo, med, hi
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A typical “Control Banding” Posterior
Decision Chart ? ? ? ?
Decision Probability
0.996Prior
1.000
1
0.8
0.6
0.4
0.2
0.000
0.001
0.000
0.001
0.000
0.001
D
C
B
A
Exposure Rating
0.000
0.001
0
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SEG1 data:
x = {0.20, 0.05, 0.10} ppm
OEL = 1 ppm
Substance: Dimethyl Death
R-phrases: R48/20
Hazard Band C
„
„
„
„
„
NR: X0.95 > 500ppm
A : 50ppm < X0.95 < 500ppm
B : 5ppm < X0.95 < 50ppm
C : 0.5ppm < X0.95 < 5ppm
D : X0.95 < 0.5ppm
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SEG2 data:
x = {2.0, 0.5, 1.0} ppm
OEL = 1 ppm
Substance: Dimethyl Death
R-phrases: R48/20
Hazard Band C
„
„
„
„
„
NR: X0.95 > 500ppm
A : 50ppm < X0.95 < 500ppm
B : 5ppm < X0.95 < 50ppm
C : 0.5ppm < X0.95 < 5ppm
D : X0.95 < 0.5ppm
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VI. Feedback
The Prior and the Likelihood Decision
Charts may not agree.
This could be considered feedback.
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What if my Initial
Rating was AIHA
Category 4 but the BDA
analysis of the data
suggest Category 2?
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What if my Initial
Rating was AIHA
Category 2, and I
collect one
measurement, which
was 90% of the OEL?
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Contact Information
Paul Hewett PhD CIH
Exposure Assessment Solutions, Inc.
[email protected]
304.685.7050
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