Bayesian Decision Analysis (BDA): A Tool for … · Title: Microsoft PowerPoint - RT233 Thu - P...

Bayesian Decision Analysis (BDA): A Tool for Incorporating Professional Judgment and Modeling into Exposure Control Banding

Paul Hewett Ph.D. CIHExposure Assessment Solutions, Inc.

AbstractBayesian 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 thirdrepresenting 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.

Bayesian Decision Analysis (BDA): A Tool for Incorporating Professional Judgment and Modeling into Exposure Control Banding

I. ScenarioII. AIHA & UK/ILO Control Banding ModelsIII. Intro to Bayesian Decision AnalysisIV. Incorporating Professional JudgmentV. Incorporating Exposure ModelingVI. Feedback

I. Scenario

Dimethyl DeathOEL (TLV) = 1 ppmR-phrases: R48/20 Hazard Band C

Two Similar Exposure Groups:SEG1SEG2

Assume the following for the SEG1:<100 ml are used per batchthe liquid has a medium vaporization potentialthe task is performed inside a ventilated enclosure

Assume the following for the SEG2:>900 ml but less than 1 L quantities are used per batchthe liquid has a medium vaporization potentialthe task is performed inside a ventilated enclosure

Example (Traditional) IH SurveyDuring a baseline exposure assessment for SEG1, an IH collected the following full-shift measurements from an SEG:

x = {0.20, 0.05, 0.10} ppmn = 3gm = 0.1 ppm 90%CI( 0.03, 0.32 )gsd = 2.0 90%CI( 1.5, 21 )

The sample 95th percentile was 0.31 ppmbut with a 95%UCL of 20 ppm

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 ?

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

QuestionsIs the SEG in compliance?

What is the definition of “compliance”?All measurements < OELTrue 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?

II. AIHA and UK/ILO Control Banding Models

The AIHA Model uses “Exposure Control Banding”

AIHA Exposure Control Ratings for TWA OELsWhich control zone is appropriate?

10% > X0.95 < 50%2

X0.95 > 100%4

50% > X0.95 < 100%3

1% > X0.95 < 10%1 High

Medium

X0.95 < 1%0

Confidence levelCutoff (%OEL)Exposure Control

Ratings *

* Adapted from Tables 5.2 and 6.2; rating 0 taken from 1991 version

Example Control Category Follow-up (Exposure Control Banding)

+ immediate engineering controls or process shutdown, validate respirator selection

5 (Multiples of OEL; e.g., based on respirator APFs)

No action0 (<1% of OEL)

general HazCom1 (<10% of OEL)

+ respirators & engineering controls, work practice controls

4 (>100% of OEL)

+ exposure surveillance, medical surveillance, work practices

3 (50-100% of OEL)

+ chemical specific HazCom2 (10-50% of OEL)

Recommended ControlExposure Control Category**

** - Decision statistic = 95th percentile

SEG1gm = 0.1 ppm 90%CI( 0.03, 0.32 )gsd = 2.0 90%CI( 1.5, 21 )

GM0.001 0.01 0.1 1

0 1 2 3 4

UK and ILO “Control Banding”:Hazard group vs. target exposure range

VaporsParticulate

Target airborne concentration rangeHazard Group

(w/ examples)

Prevent or reduce skin and/or eye exposure

Seek specialist advice

<0.01 mg/m3

>0.01-0.1 mg/m3

>0.1-1 mg/m3

>1-10 mg/m3

S: skin and eye contact

E - Carcinogens, asthmagens

<0.5 ppmD - Very toxic on single exposure;

reproductive hazard

>0.5-5 ppmC - Severely irritating & corrosive;

skin sensitizers

>5-50 ppmB - Harmful on single exposure

>50-500 ppmA - Skin and eye irritants

GM0.01 0.1 1 10 100 1,000

SEG1gm = 0.1 ppm 90%CI( 0.03, 0.32 )gsd = 2.0 90%CI( 1.5, 21 )

D C B A NR

CommentsThe category cutoffs and ranges for the AIHA Exposure Control Band model is substance-specific 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.

III. Intro to Bayesian Decision Analysis (BDA)

Bayesian Decision Analysis (BDA)An adjunct or alternative to the calculation and interpretation of traditional statistics. The goal of BDA is to estimate the probabilitythat the true exposure profile falls into a particular category, or Exposure Rating.BDA can explicitly incorporate professional judgment.

Foundation of BDA:Bayes’ Theorem

Posterior Likelihood Prior

Correction Factor

Modified Bayes’ Equation

Popi = all combinations of G and D within the ithExposure Control Category.

References

Hewett, P. et al.: Rating Exposure Control Using Bayesian Decision Analysis. Journal of Occupational and Environmental Health, in press (2006).

BDA SummaryInput: professional judgment + dataOutput: 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.

IV. Incorporating Professional Judgment

Prior Decision DistributionCategorical

Assign an a prioriprobability to each Exposure Rating zone

Exposure Rating0 1 2 3 4

ility 1

0.80.6

0.40.2

0.030.17

0.170.03

Basis for the Prior Decision DistributionPast data from this or similar SEGsPersonal experience with this SEG or jobPeak readings from a direct reading instrumentRecommendations from other IHsPhysical / chemical modeling calculationsExpert system recommendations

e.g., UK/ILO Control Banding modeland so on …

SEG1 data:x = {0.20, 0.05, 0.10} ppm

OEL = 1 ppmSubstance: Dimethyl DeathAIHC Exposure Categories

4 : X0.95 > 1ppm3 : 0.5ppm < X0.95 < 1ppm2 : 0.1ppm < X0.95 < 0.5ppm1 : 0.01ppm < X0.95 < 0.1ppm0 : X0.95 < 0.01ppm

SEG2 data:x = {2.0, 0.5, 1.0} ppm

OEL = 1 ppmSubstance: Dimethyl DeathAIHA Exposure Categories

4 : X0.95 > 1ppm3 : 0.5ppm < X0.95 < 1ppm2 : 0.1ppm < X0.95 < 0.5ppm1 : 0.01ppm < X0.95 < 0.1ppm0 : X0.95 < 0.01ppm

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:

QuantityDustiness or vaporization potentialLevel of control

Example: UK/ILO Control Banding -Predicted exposures for both SEG1 and SEG2

Exposure Predictor Band (ppm)Control

Approach

0.5-50.5-50.05-0.5<0.05Containment

5-5005-500.5-5<0.5Local Exhaust

>50050-5005-50<5General ventilation

m3 – him3 – medL – med,hi

ml – med,hiL, m3 – lo

ml – lo

Quantity – ml, L, m3

Vaporization potential – lo, med, hi

Exposure RatingD C B A NR

ility 1

0.80.6

0.40.2

0.001 0.001 0.001

A typical “Control Banding” Posterior Decision Chart ? ? ? ?

0.000 0.000 0.000

OEL = 1 ppmSubstance: Dimethyl DeathR-phrases: R48/20Hazard Band C

NR: X0.95 > 500ppmA : 50ppm < X0.95 < 500ppmB : 5ppm < X0.95 < 50ppmC : 0.5ppm < X0.95 < 5ppmD : X0.95 < 0.5ppm

SEG1 data:x = {0.20, 0.05, 0.10} ppm

OEL = 1 ppmSubstance: Dimethyl DeathR-phrases: R48/20Hazard Band C

NR: X0.95 > 500ppmA : 50ppm < X0.95 < 500ppmB : 5ppm < X0.95 < 50ppmC : 0.5ppm < X0.95 < 5ppmD : X0.95 < 0.5ppm

SEG2 data:x = {2.0, 0.5, 1.0} ppm

VI. Feedback

The Prior and the Likelihood Decision Charts may not agree.This could be considered feedback.

What if my Initial Rating was AIHA Category 4 but the BDA analysis of the data suggest Category 2?

What if my Initial Rating was AIHA Category 2, and I collect one measurement, which was 90% of the OEL?

Contact Information

Paul Hewett PhD CIHExposure Assessment Solutions, Inc.phewett@oesh.com304.685.7050

Bayesian Decision Analysis (BDA): A Tool for … · Title: Microsoft PowerPoint - RT233 Thu - P...

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