Dose-Response%20Modeling%20for%20EPA

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Dose-Response Modeling for EPAs Organophosphate
CumulativeRisk Assessment Combining Information
from Several Datasets toEstimate Relative
Potency Factors

• R. Woodrow Setzer
• National Center for Computational Toxicology
• Office of Research and Development
• U.S. Environmental Protection Agency

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Background

• Food Quality Protection Act, 1996
• Requires EPA to take into account when setting
  pesticide tolerances
• available evidence concerning the cumulative
  effects on infants and children of such residues
  and other substances that have a common mechanism
  of toxicity.

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Cumulative Risk (per FQPA)

• The risk associated with concurrent exposure by
  all relevant pathways routes of exposure to a
  group of chemicals that share a common mechanism
  of toxicity.

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Identifying the Common Mechanism Group OP
Pesticides

• U. S. EPA 1999 Policy Paper
• Inhibition of cholinesterase
• Brain
• Peripheral Nervous System (e.g., nerves in
  diaphragm, muscles
• Surrogate/indicator (plasma, RBC)

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Synergy?

• Berenbaum (1989) described lack of interaction in
  terms of the behavior of isoboles Loci of
  points in dose space that have the same
  response in multi-chemical exposures.
• Non-interaction coincides with linear isoboles.

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Isoboles Example 2 chems
Dose Chem 2
Dose Chem 1
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Dose-Response for Non-Interactive Mixture

• For a two-chemical mixture, (d1, d2),
• if D1 is the dose of chem 1 that gives response
  R, D2 is the dose of chem 2 that gives response
  R, then all the mixtures that give response R
  satisfy the equation

line
For n chemicals
hyperplane
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Special Case

• When fi(x) f(ki x) chemicals in a mixture act
  as if they were dilutions of each other
• Isoboles are linear and parallel
• Dose-response function for mixture is
  f(k1x1k2x2)
• Typically, pick one chemical as index (say 1
  here) and express others in terms of that.
• Then RPF for 2 is k2/k1

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Strategy of Assessment

• Use dose-response models to compute relative
  potency factors (RPFs, based on 10 inhibition of
  brain AChE activity BMD10) for oral exposures
  NOAELs to compute RPFs for inhalation and dermal
  exposures.
• Probabilistic exposure assessment, taking into
  account dietary, drinking water, and residential
  exposures on a calendar basis.
• Final risk characterization based on distribution
  of margins of exposure (MOE)

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OP CRA Science Team

• Vicki Dellarco
• Elizabeth Doyle
• Jeff Evans
• David Hrdy
• Anna Lowit
• David Miller
• Kathy Monk
• Steve Nako

• Stephanie Padilla
• Randolph Perfetti
• William O. Smith
• Nelson Thurman
• William Wooge
• Plus Many, Many Others

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Oral Dose-Response Data

• Brain acetylcholinesterase (AChE) (as well as
  plasma and RBC)
• Female and male rats
• Subchronic and chronic feeding bioassays
• Always multiple studies for compounds
• Often multiple assay methods
• Ultimately, 33 OPs included
• Usually 10 animals per dose group/sex
• Control CVs lt 10

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Database of Acetylcholine Esterase Data

• 33 chemicals
• 80single-chemical studies
• 3 compartments (brain, rbc, plasma) ? 2 sexes
• multiple durations of exposure, subchronic to
  chronic
• total gt1655 dose-response relationships ( 1300
  retained)

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Data Structure
Chemical
(in each Study X Sex) (in each Study X Sex) Mean, SD, N Mean, SD, N Mean, SD, N Mean, SD, N
Doses Compart. DS1 DS2 DS3 DS4
1 Brain X X X X
1 RBC X X X X
1 Plasma X X X X

k Brain X X X X
k RBC X X X X
k Plasma X X X X
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Experimental Design
Chemical
(in each StudyXSex) (in each StudyXSex) (in each StudyXSex) (in each StudyXSex) (in each StudyXSex) (in each StudyXSex) (in each StudyXSex)
Doses Animals Compart. DS1 DS2 DS3 DS4
Di 1 Brain X
Di 1 RBC X X
Di 1 Plasma X X
Di
Di n Brain X
Di n RBC X X
Di n Plasma X X
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Distribution of Doses
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Exposure Duration

• Preliminary data analysis showed that subchronic
  feeding studies reached steady state after about
  3 weeks
• Multiple time points within a study were treated
  as independent, nested within study.
• Only time points with more than 3 weeks of
  exposure were included.

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Issues for Modeling

• Use as much of the acceptable data as possible
• Different units/analytic methods used
• Expect responses to differ among compartments,
  maybe sexes
• Generally small number of dose levels in a single
  data set (limiting the number of parameters that
  can be identified)

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Hierarchical Structure of BMD Estimate

• Multiple studies carried out at different times
  by different laboratories, using different
  analytic methods, reporting results in different
  units.

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Two Modeling Approaches

1. Model individual data sets, combining estimates.
2. Model the combined studies for each chemical ?
   compartment. Combined estimate is the estimate
   of the mean parameter (current revised risk
   assessment).

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Modeling Individual Datasets

• Fit a model to each dataset, estimating BMD (and
  estimated standard error) each time.
• Model all three compartments and both sexes
• Use the global two-stage method (Davidian and
  Giltinan, 1995 138-142) twice, once for each
  level of variability.

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Dose-Response and Potency Approach 1
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Sequential Approach to Fitting

• Fit full model to all data using generalized
  nonlinear least squares (gnls)
• If no convergence or inadequate fit,
• Repeat (until good fit or remaining doses lt 3)
• set PB ? 0
• refit to dataset
• drop highest dose

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Potency Measure

• Absolute potency is BMD calculated from fitted
  model
• Relative Potency
• IF PBI PBk

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Estimate dose-response for each dataset
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Random Effects Model for BMD

• Log(BMD) µlBMD EMRID ETime in MRID
• µlBMD varies between sexes
• EMRID N(0,sMRID2)
• ETime in MRID N(0,sTiM2)
• Error variance proportional to (predicted) mean
  of AChE activity at that dose constant of
  proportionality varied among MRIDs.

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Combine Potency Estimates

• Combine estimates in two stages among times
  within study and among studies
• At each stage, suppose q individual estimates lmi
  with variances si2. Potency estimates (?) and
  variance components (?2) maximize

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Combine Potency (more)

• Variances for ln(potency) estimates
• This implements the Global Two-Stage method of
  Davidian and Giltinan, (1995)
• This method could apply to any single statistic
  or parameter, or vector statistic with simple
  modification.

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Problems

• Estimate of m depends on PB. Particularly a
  problem when we cannot estimate PB.
• Would like a formal test of whether PBs differ
  among chemicals.
• Is there a shoulder on the dose-response curve in
  the low-dose region?

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Solution

• Fit the same model to multiple related datasets,
  allowing information about DR shape to be shared
  across datasets
• Develop a more elaborate model that takes into
  account some of the biology to give a better
  description of the lower dose behavior.

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Stage 1 A simple PBPK Model

• Two compartments Liver and everything else.
• Oral dosing, assume 100 into the portal
  circulation
• Only consider saturable metabolic clearance and
  first order renal clearance.
• Run to steady state

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Stage 1 (more)

• Solve the system of differential equations
  implied by the model for steady state.
• The concentration of non-metabolized parent OP in
  the body (idose) as a function of administered
  oral Dose rate is

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Stage 2 Same as Before

• But reparametrized

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DR with First Pass Metabolism
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Hierarchical Model

• All datasets for a chemical fitted jointly using
  nlme in R.
• S and D varied only among chemicals
• A varied among sex data set
• PB varied between sexes
• BMD random (same model as before)

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Dose Response
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Benchmark Dose Fitting One Dataset at a Time
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Benchmark Dose Combining Datasets
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Overall Quality of Fit Residuals
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Relative Potencies
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Computing a MOE (Margin of Exposure)
Chem RPF Exposure (µg/kg/day) Eq. Exposure
A (Index) 1.00 0.2 0.2
B 0.1 1.0 0.1
C 1.2 0.2 0.24
Total Equivalent Exposure Total Equivalent Exposure Total Equivalent Exposure 0.54
BMD10(A) 0.08 mg/kg/day MOE 0.08 X 1000
µg/kg/day / 0.54 148
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Distribution of Total MOEs
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1. Combining Estimates

• Keeps dose-response modeling simple
• Delays problems about heterogeneity (sexes,
  compartments, studies, etc.) until after the
  modeling.
• Number of dose levels in the smallest dataset
  limits the model used, have to drop data sets
  with too few doses for the selected model.

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2. Combining Datasets

• Dose-response modeling is (substantially)
  complicated
• Heterogeneity issues addressed in the modeling
• Overall number of dose levels (among other
  things) limits the model used

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Is PB a High-Dose Effect?

• Maybe, but could also be a consequence of
  multiple binding sites with different functions,
  or other aspects of the kinetics of AChE
  inhibition such as variation in aging among
  chemicals, which could manifest effects at lower
  doses as well.

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Horizontal Asymptotes
0.8
Direct Acting
Require Activation
0.6
PB
0.4
0.2
0.0
NALED
DIAZINON
PHORATE
PHOSMET
TRIBUFOS
FENTHION
ACEPHATE
TERBUFOS
ETHOPROP
BENSULIDE
MALATHION
MEVINPHOS
PHOSALONE
FENAMIPHOS
DISULFOTON
DICHLORVOS
DIMETHOATE
FOSTHIAZATE
TRICHLORFON
DICROTOPHOS
METHIDATHION
CHLORPYRIFOS
METHAMIDOPHOS
AZINPHOSMETHYL
METHYLPARATHION
PIRIMIPHOSMETHYL
OXYDEMETONMETHYL
TETRACHLORVINPHOS
CHLORPYRIPHOSMETHYL
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Should We Expect Dose-Additivity? (Not Exactly!)

• Low-dose shoulder significantly improves fit in a
  substantial number of chemicals. At best, expect
  dose-additivity in terms of target dose.
• Horizontal asymptotes differ significantly among
  chemicals (P ltlt 10-6), so dose-additivity cannot
  hold exactly.

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Beginnings of A Theoretical Approach

• Through mathematical analysis and in silico
  experiments, ask
• What features determine the shape of individual
  chemical dose-response curves, and
• what are the features of chemicals (if any) that
  lead to deviations from dose-additivity in
  cumulative exposures.

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Example A Toy OP Model

• Three compartments brain, liver, everything else
• Constant infusion into the liver
• Metabolic clearance in the liver,
  Michaelis-Menten kinetics (Vmax, Km)
• AChE inhibition in the brain uses same scheme as
  Timchalk, et al. (2002) Ki, Kr, Ka.
• Sample the 5-dimensional parameter space to make
  example chemicals.

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AChE Inhibition Scheme
ks
kI
ka
E I
EI
Bound EI
kd
kr
E AChE I OP-like inhibitor
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Strict Sense Dose Additivity
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Evaluating Berenbaum Dose-Response

• So, if f1(x) is the dose-response function for
  chem 1, etc., then for any given dose (d1,d2), we
  can find the response by finding D1

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DR for 50-50 Mixture
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Broad Sense Dose Additivity
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DR for 50-50 Mixture
From RPFs
Berenbaum
From PBPK
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Dose-Additivity Dogma

• What happens when two chemicals that are
  identical except for Ki are combined? (Same mode
  of action?)
• Chem 17 Ki 11.04
• Chem 300 Ki 0.01, other parameters the same
• Potency of 17 relative to 300 (ratios of BMD10)
  is 4.25

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Common Mode of Action?
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Future Work

• OPCRA Dose-response modeling is complete,
  tolerances being reassessed now.
• Toy Models
• Explore other combinations
• Can we duplicate real OP dose-responses without
  two sites on AChE?
• Activation
• Consequences for DR shape of metabolic clearance
  in the blood.