Exposure assessments are central to any Industrial Hygiene program as Hygienists spend huge amounts of time classifying exposure profiles. However, it can be difficult to be sure when the right classification has been made, particularly when a hygienist’s individual judgment is required. This challenge is further exacerbated when working with small data sets. Fortunately, Bayesian decision analysis (BDA) is a form of statistical analysis of occupational exposure data that allows hygienists to select the most appropriate exposure category, even with limited data. BDA results in easy to interpret “decision charts”, permits the user to mathematically incorporate prior information and professional judgment into the analysis, and can handle non-detects. It can also be used to select the most appropriate level of respiratory protection for those difficult to control exposure scenarios. Presentation covers the basic methodology, assumptions and cautions, and will include several examples drawn from the chemical and pharmaceutical industries. Watch this webinar and learn: A basic understanding of BDA methodology. Ability to apply BDA, and use the resulting “decision charts” to make IH decisions. An understanding of the relationship between BDA and the AIHA exposure assessment model. An introduction to quantifying “professional judgment” using a Prior Decision Chart. An appreciation of the advantage that BDA has over the calculation of standard statistics and confidence intervals.

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Monica Melkonian, MS, CIH
Product Manager- Industrial
Hygiene
- THE BASICS OF BDA METHODOLOGY
- BDA DECISION CHARTS
- BDA AND THE AIHA EXPOSURE MODEL
- QUANTIFYING PROFESSIONAL JUDGMENT
Paul Hewett, owner, Exposure
Assessment Solutions Inc

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ADVANTAGES OF BDA
• Can set a plausible parameter space
• Output is a set of Decision Charts
• Can incorporate Professional Judgment
• Best applied to small datasets
• Provides feedback
• Consistent with …
AIHA Exposure Banding Model
EU Control Banding Model
pharmaceutical Control Banding or PB-OEL Models
• Can be applied to datasets that contain non-detects
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AIHA EXPOSURE ASSESSMENT
Start
Basic Characterization
Exposure
Assessment
Unacceptable
Exposure
Uncertain
Acceptable
Exposure
Reassessment
Control
Further Information
Gathering
The exposure assessment
and management program
of most companies is based
on the AIHA approach.
Category 0, 1, 2 or 3
Category 4 or 5

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AIHA EXPOSURE CONTROL BANDING MODEL
Exposure Control
Category Cutoff (%OEL) Confidence level
0 X0.95 < 1%
High
Medium
Low
1 1% < X0.95 < 10%
2 10% < X0.95 < 50%
3 50% < X0.95 < 100%
4 X0.95 > 100%
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TYPICAL ACTIONS
Exposure Control Category Recommended Actions
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
practice analysis
4 (>100% of OEL) + respirators & engineering controls, work practice
controls, validate respirator selection
Multiples of OEL (e.g.,
based on respirator
APFs)
+ immediate engineering controls or process shutdown,
validate respirator selection
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• The goal of an exposure assessment is to select the
exposure category that most likely contains the true
95th percentile.
• The resulting “actions” will then be risk-based …
that is, proportional to the expected degree of risk,
as indicated by the exposure category.
• How do we pick the correct exposure category and
certainty level?
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EXPOSURE ASSESSMENT GOAL

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THE “DATA DRIVEN” APPROACH
• Collect a large n dataset.
• Calculate the “sample” 95th percentile (X0.95)
plus the 95%LCL and 95%UCL.
• Compare sample X0.95 to the category cutoffs
Which category does it fall in?
• Determine a certainty level.
Compare LCL and UCL to category cutoffs.
• With large n little to no judgment is necessary. Nearly
all IHs will reach the same decision.
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EXAMPLE
• An IH collected 17 representative measurements
and calculated standard statistics (OEL=1):
gm = 0.12 and gsd = 2.0
x0.95 = 0.38
38% of the OEL; suggests a Category 2 exposure profile
95%LCL = 0.26 and 95%UCL = 0.67
Category 3 is also a possibility. Categories 1 and 4 can be
eliminated from consideration.
Final Rating : Category 2, Medium Certainty
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How do we pick a category and certainty level
… when we have only a few measurements?
• n=1; x = {0.05} (OEL=1)
• n=2; x = {0.05, 0.2}
X0.95 = 0.50 ( 95%LCL=0.16, 95%UCL=1.5x1010 )
• n=3; x = {0.05, 0.2, 0.1}
X0.95 = 0.31 ( 95%LCL=0.16, 95%UCL=20 )
• Which category: 0, 1, 2, 3, or 4 ?
10
PICKING A CATEGORY

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PICKING A CATEGORY
• x = {<0.1, 0.2, <0.1} (OEL=1)
X0.95 = ?
• x = {<0.05, 0.2}
X0.95 = ?
• x = {<0.05} or {<0.25} or {<0.75}
X0.95 = ?
• Which category: 0, 1, 2, 3, or 4 ?
11
…when some or most of the measurements are
non-detects?

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BAYESIAN DECISION ANALYSIS (BDA)
• An adjunct to the calculation and interpretation of
traditional statistics.
• The goal of BDA is to estimate the probability that
the true 95th percentile exposure falls within a
particular category, or Exposure Rating.
• BDA can explicitly incorporate professional judgment.
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ADVANTAGES
• Best suited for small datasets
• Can handle non-detects
• Professional judgment can be
incorporated
• Encourages the improvement
of professional judgment
• The output is a set of easy to
interpret “decision charts”
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x = {0.05, 0.2, 0.1}

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BDA DECISION CHARTS
• Prior decision chart
 Represents our professional judgment
regarding the probability of each of the
five Exposure Ratings.
• Likelihood decision chart
 The set of probabilities of each exposure
rating calculated using only the collected
data.
• Posterior decision chart
 The set of probabilities of each exposure
rating, updated using the information
from the prior decision chart.
x = {0.05, 0.2, 0.1}

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• In order to apply Bayesian analysis to industrial
hygiene “decision making” we need the following:
A model for classifying occupational exposure profiles into
exposure categories.
e.g., the AIHA Exposure Control Banding Model
A distributional model
e.g., the lognormal model
A decision statistic
e.g., the 95th percentile
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BDA DECISION MAKING

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When n is small, confidence intervals are often
extremely broad.
• X = {0.20, 0.05, 0.10} (OEL=1)
• n = 3
• gm = 0.1 95%LCL = 0.03, 95%UCL = 0.32
• gsd = 2.0 95%LCL = 1.5, 95%UCL = 21
• x0.95 = 0.31 95%LCL = 0.16, 95%UCL = 20
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CONFIDENCE INTERVALS

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Exposure Rating 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%
An “Exposure Rating” represents a population of
exposure profiles.
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EXPOSURE RATINGS

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GM
0.0001 0.001 0.01 0.1 1
GSD
20
10
PARAMETER SPACE (OEL =1)
0 1 2 3 4
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GM
0.001 0.01 0.1 1
GSD
5
4
3
2
1
0 1 2 3 4
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KEY CONCEPT: Parameter Space with a plausible
upper limit for the true GSD (OEL=1)
KEY CONCEPTS

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GM
0.001 0.01 0.1 1
GSD
5
4
3
2
1
0 1 2 3 4
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KEY CONCEPT: Decision
Charts

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Bayes’ Theorem –
The foundation of Bayesian statistics
Posterior Likelihood Prior
Correction Factor
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BAYES’ THEOREM

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Applied to all lognormal distributions within parameter space
22
BAYES’ THEOREM
KEY CONCEPT: Populationi = AIHA exposure category
(i.e., all combinations of geometric mean (G) and geometric
standard deviation (D) within the ith exposure category)

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DECISION CHARTS
• Example Prior Decision Distributions
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.05
0.2
0.5
0.2
0.05
Prior
Exposure Rating
0 1 2 3 4
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
Non-informative prior
Informative prior:
Category 2, Medium Certainty
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GENERIC “PRIOR DECISION CHARTS”
• Professional Judgment prior
When the user picks an Initial Rating and Certainty
Level a recommended Prior Decision Chart is
loaded.
The default category probabilities represent a
“best guess” as to what a generic prior should look
like.
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Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.6
0.2 0.15
0.04 0.01
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.5
0.25
0.18
0.05 0.02
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.4
0.3
0.21
0.06 0.03
Non-informative prior “decision
chart”
IR=Initial
Rating
CL=Certainty
Level
IR=Category 0
CL=low
IR=Category 0
CL=medium
IR=Category 0
CL=high
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
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Non-informative prior “decision
chart”
IR=Category 1
CL=low
IR=Category 1
CL=medium
IR=Category 1
CL=high
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.3
0.4
0.18
0.07 0.05
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.25
0.5
0.16
0.06 0.03
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2
0.6
0.14
0.04 0.02
IR=Initial
Rating
CL=Certainty
Level

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Non-informative prior “decision
chart”
IR=Category 2
CL=low
IR=Category 2
CL=medium
IR=Category 2
CL=high
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
IR=Initial
Rating
CL=Certainty
Level Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.07
0.23
0.4
0.23
0.07
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.05
0.2
0.5
0.2
0.05
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.03
0.17
0.6
0.17
0.03

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Non-informative prior “decision
chart”
IR=Category 3
CL=low
IR=Category 3
CL=medium
IR=Category 3
CL=high
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
IR=Initial
Rating
CL=Certainty
Level Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.05 0.07
0.18
0.4
0.3
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.03 0.06
0.16
0.5
0.25
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.02 0.04
0.14
0.6
0.2

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Non-informative prior “decision
chart”
IR=Category 4
CL=low
IR=Category 4
CL=medium
IR=Category 4
CL=high
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
IR=Initial
Rating
CL=Certainty
Level Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.03 0.06
0.21
0.3
0.4
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.02 0.05
0.18
0.25
0.5
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.01 0.04
0.15 0.2
0.6

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X={ 0.20, 0.05, 0.10 }
Likelihood
Exposure Rating
0 1 2 3 4
1
0.8
0.6
0.4
0.2
0
0 0.002
0.66
0.229
0.109
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EXAMPLE LIKELIHOOD DECISION CHART

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EXAMPLE POSTERIOR DECISION CHARTS
Posterior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.001
0.865
0.12
0.014
Posterior
Exposure Rating
0 1 2 3 4
1
0.8
0.6
0.4
0.2
0
0 0.002
0.66
0.229
0.109
Using the
non-informative prior
Using the
informative prior
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PRIOR
LIKELIHOOD
POSTERIOR
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.2 0.2 0.2 0.2 0.2
Prior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.05
0.2
0.5
0.2
0.05
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.002
0.66
0.229
0.109
Posterior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.001
0.865
0.12
0.014
Posterior
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.002
0.66
0.229
0.109
NON-INFORMATIVE INFORMATIVE

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EXAMPLE APPLICATIONS OF BDA
• General analysis of occupational exposure
data
• Reach a decision when n is small
• Leverage professional judgment
• Provide feedback
• Assist in respirator selection
• Analyze censored datasets
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GENERAL ANALYSIS OF OCCUPATIONAL EXPOSURE DATA
• OEL=0.2 mg/m3
• n = 4
• x = {0.015, 0.008, 0.006, 0.016}
mg/m3
• In principle, BDA can be applied
to any sample size (but is
limited here to n<250).
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REACH A DECISION WHEN N IS SMALL
• OEL=1 ppm
• n = 1
• x = 0.05 ppm
• BDA can be applied to sample
sizes as low as n=1.
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REACH A DECISION WHEN N IS SMALL
• OEL=1 ppm
• n = 1
• x = 0.99 ppm
• “Yes, the measurement is <OEL.
But I strongly suspect that the
exposure profile is not
acceptable.”
• BDA leads to the same
conclusion.
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LEVERAGE PROFESSIONAL JUDGEMENT
• OEL=1 ppm
• n = 1
• x = 0.05 ppm
• Professional judgment can
sharpen the decision.
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PROVIDE FEEDBACK
• OEL=1 ppm
• n = 3
• x1 = 0.25 ppm
• x2 = 0.50 ppm
• x3 = 1.00 ppm
• The Prior is inconsistent with the
Likelihood.
• BDA can be used to help improve
professional judgment.
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ASSIST IN RESPIRATOR SELECTION
• OEL=1 ppm
• n = 3
• x1 = 0.99 ppm
• x2 = 0.50 ppm
• x3 = 2.0 ppm
• Decision = Category 4
• BDA can be used to guide PPE
selection.
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ANALYZE CENSORED DATASETS
• OEL=1 ppm
• n = 1
• x < 0.05
• LOD = 0.05
• BDA can be applied to censored
datasets, even datasets that are
100% censored and have
different detection limits.
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Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.003
0.393
0.253
0.352
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.05
0.804
0.13
0.012
0.005
ONE SAMPLE EXAMPLES (OEL=1)
• X = {0.005} ppm
• X = {0.01} ppm
• X = {0.05} ppm
• X = {0.25} ppm
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.394
0.542
0.059
0.004
0.001
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Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0.000
0.394
0.459
0.082
0.064

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OEL = 1 PPM
• X = {0.49} ppm
• X = {0.75} ppm
• X = {0.99} ppm
• X = {1.5} ppm
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.000
0.056
0.351
0.593
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0.000
0.013
0.189
0.798
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0 0.002
0.012
0.986
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0 0.006
0.048
0.946
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LARGE SAMPLE EXAMPLE
• An IH collected 17 representative measurements
and calculated standard statistics (OEL=1):
X0.95 = 0.38 95%LCL = 0.26 and 95%UCL = 0.67
Final Rating : Category 2, Medium Certainty
• When n is large the BDA
results and standard
statistical analysis generally
lead to the same decision.
Likelihood
Exposure Rating
0 1 2 3 4
DecisionProbability
1
0.8
0.6
0.4
0.2
0
0 0
0.79
0.201
0.009
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ASSUMPTIONS
• The lognormal distribution is a reasonable
approximation of the true exposure profile.
• The true exposure profile falls somewhere
within Parameter Space.
If the true GSD approaches or exceeds 4 the
decision probabilities for the upper categories
may be underestimates (and can potentially
mislead).
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CAUTIONS
• BDA does not give us a “data driven” decision
from a small n dataset.
• BDA simply gives us a different way to look at
the data, in terms of …
exposure categories and
decision probabilities that the true 95th percentile
falls within a category.
45

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CAUTIONS
• Training is necessary to properly use the BDA
method and interpret the decision charts.
• Management should agree on …
the company risk management goals
the decision statistic
the use of the AIHA exposure rating method
how BDA fits into the overall program.
46

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• BDA is new “decision making” tool for IHs.
• Use it in conjunction with your other tools:
graphs and goodness-of-fit tests
descriptive statistics
compliance statistics.
• Do the BDA results suggest a different interpretation
of your dataset?
• Which interpretation is most likely correct? The BDA
interpretation or that reached using your current
data analysis tools?
SUMMARY
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48. Enterprise EHS Software Solutions
WATCH THE WEBINAR
48
If you want to listen to the presentation
that goes alongside this deck, you can
do so for free here:
http://www2.medgate.com/bayesian-webinar