Analyzing Left Censored Exposure Monitoring Data

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Analyzing Left Censored Exposure Monitoring Data

• Paul Wambach, CIH
• Department of Energy
• Office of Illness and Injury Prevention Programs

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Occupational Exposure Monitoring

• Personal monitoring representative of workers
  actual exposure
• Within worker variability
• Between worker variability
• Skewed data

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Detection Limits

• Instrument detection limit
• Significantly different from lab blanks
• Quantitation limit
• Achieves specified precision (i.e. 10)
• Laboratory reporting limit
• Accounts for day-to-day variation in media,
  interferences and instrument performance

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AIHA A Strategy for Assessing and Managing
Occupational Exposures

• Appendix VI
• Descriptive statistics (non-parametric)
• Inferential statistics (parametric)
• Mean and confidence interval
• Tolerance limits and exceedance tests
• Goodness-of-fit
• Probability Plotting
• Shapiro and Wilk Test (W-test)

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AIHA A Strategy for Assessing and Managing
Occupational Exposures

• Appendix VIII Analysis of Censored Data
• Maximum Likelihood Estimates (MLE) is the best
  parametric method
• Order statistics is the best non-parametric
  method but requires large sample size ( 59 for
  95-95 UTL).

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Methods for Left Censored Data

• ORNL Technical Report "Statistical Methods and
  Software for the Analysis of Occupational
  Exposure Data With Non-Detectable Values",
  ORNL/TM-2005/52
• Maximum Likelihood Estimates (MLE) for lognormal
  data
• Kaplan-Meier (KM) estimates for non-parametric
  data
• Order statistics for non-parametric upper
  tolerance limits

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MLE for Left Censored DataMetrics Inferred from
a Model
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Kaplan-Meier Product Limit EstimatesDescriptive
Statistics from Censored Data
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The R Foundation for Statistical
Computinghttp//www.r-project.org/
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Go to http//www.hss.energy.gov/HealthSafety/IIPP/
sand/index.htmlFollow the steps on the left
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Type help (sand) for overview and help menu
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More Instructions

• A PDF Document with help menus and examples is
  posted at the web site.
• Technical report with full details on the methods
  and computer code is also posted at the web
  site.

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Data from Table IV3 AIHA Book
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Save AsText (Tab delimited)(aihand.txt)
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R Commandaihandlt-readss(aihand,L5)

• Filename is case sensitive
• L the OEL being used to interpret the data
• Produces a csv file with all metrics
  aihandout.csv

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Open aihandout.csv with Excel
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Alternative Command IH.summary(aihand,L5)
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Probability Plotting

• First Command pndlt-plend(aihand) creates a data
  frame
• Second commandqq.lnorm(pnd)creates a Q-Q line
  fit plot from the data frame

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Mean Estimates and Confidence Intervals

• EX - The Maximum Likelihood Estimate of the
  arithmetic mean (parametric)
• LCLc-95 - 95 lower confidence limit
• UCLc-95 - 95 upper confidence limit
• KMmean - The Kaplan-Meier (KM) estimate of the
  arithmetic mean (non-parametric)
• KLCL-95 - 95 lower confidence limit
• KUCL-95 - 95 upper confidence limit

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Tolerance Limits

• Obs95 - The observed 95th percentile of the data
  set
• Est95 - The MLE of the 95th percentile
• LXpa9595 - The geometric 95-95 lower confidence
  limit
• UXpa9595 - The geometric 95-95 upper tolerance
  limit (UTL)
• NpUTL9595 - The non-parametric estimate of the
  95-95 UTL

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Exceedance Tests

• Fex-xx - The MLE of the percent of values
  exceeding the specified limit
• FeLCL-95 - 95 lower confidence limit
• FeUCL-95 - 95 upper confidence limit
• Fnp-xx - The product limit estimate (PLE) of the
  percent of values exceeding the specified limit
• FnLCL-95 - 95 lower confidence limit
• FnUCL-95 - 95 upper confidence limit

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Measures of Goodness-of-Fit

• Rsq - The square of the Pearson correlation
  coefficient for the data and standard normal
  same scale as W-test
• Interpret using Table IV.5 in AIHA book
• If n gt 50 and Rsq lt 0.95 use non-parametric
  estimates
• NonDet - The percentage of results that were
  non-detects
• If greater than 80 use non-parametric estimates.
  

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aihand Data Set

• NonDet 20
• Rsq 0.97
• EX 2.7
• LCLa_95 2.3
• UCLa_95 3.2
• Est95 4.6
• LXpa959 3.5
• UXpa9595 6.1
• Fax_5 3.2
• FaLCL_95 0.4
• FaUCL_95 15

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138 Beryllium Exposure MeasurementsUnitsµg/m3
OEL0.2

• NonDet 33
• Rsq 0.85
• KMmean 0.14
• KLCL_95 0.10
• KUCL_95 0.18
• NpUTL9595 0.8
• Fnp_0.2 14.5
• FnLCL_95 9.8
• FnUCL_95 20.4

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Mean Exposure Level

• Arithmetic mean exposure is most closely related
  to dose
• Lifetime dose Mean Level x Time
• Dose Rate Mean level while working
• Job exposure matrix method used in retrospective
  health studies
• MLE generally considered best method for
  estimating the mean

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Example Job Exposure MatrixSanderson WT,
Petersen MR, Ward EM. Estimating historical
exposures of workers in a beryllium manufacturing
plant. Am J Ind Med. 2001 Feb39(2)145-57.
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Hypothesis Testing

• Null Hypothesis (Ho) 5 or more of exposures
  exceed the OEL.
• Alternative Hypothesis (Ha) Less than 5 of
  exposure exceed the OEL.
• Accept Ha if 95-95 UTL is less than the OEL or
  UCL of percent exceeding is less than 5.
• Confidence interval is important not the central
  estimate.

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Sample Size Issues

• Very Large 59
• Non-parametric methods provide answers
• Large sample size often results from combining
  data so that distribution assumptions can be
  difficult to justify
• Large 15 58
• Non-parametric estimates of the 95th percentile
  will not achieve 95 confidence.
• MLE estimates provide answers

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Sample Size Issues (cont.)

• Small 6 14
• MVUE and Lands Exact methods recommended for
  complete data
• If non-detects are occurring consider collecting
  more samples
• Very Small lt 6
• Bayseian Decision Analysis?
• Who controls the Priors?

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Small Sample Size with Complete Data

• Use the spreadsheet that comes with the AIHA book
• SAND package includes Lands exact method for
  percent exceedance

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Very Large Data Sets

• Usually result from combining data from many
  exposure groups or over a long period of time
• Public Health Surveillance
• CDC Ongoing collection and analysis of data
  with dissemination to those responsible for
  prevention
• Secondary use of data collected for another
  purpose
• LaMontagne AD, et al. Exposure databases and
  exposure surveillance promise and practice. AIHA
  J. 2002 Mar-Apr63(2)205-12.

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DOE Beryllium-associated Worker Registry

• Summarizes Beryllium health and exposure
  monitoring data
• http//www.hss.energy.gov/HealthSafety/IIPP/hservi
  ces/beregistry.pdf

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Non-Parametric Exceedance TestsSurveillance
versus Assessment
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Contact Information

• Paul Wambach, CIH
• U.S. Department of Energy
• Office of Illness and Injury Prevention Programs
• Phone [phone]
• Email
• Paul.Wambach_at_hq.doe.gov