Dose-Response Modeling for EPA’s
Organophosphate Cumulative
Risk Assessment: Combining
Information from Several Datasets to
Estimate Relative Potency Factors
R. Woodrow Setzer
National Center for Computational Toxicology
Office of Research and Development
U.S. Environmental Protection Agency
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.”
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.
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)
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 multichemical exposures.
• Non-interaction coincides with
linear isoboles.
Dose Chem 2
Isoboles Example: 2 chems
Dose Chem 1
Dose-Response for NonInteractive 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:
d1 d 2
  1 :line
D1 D2
For n chemicals:
d1

D1

dn
 1 :hyperplane
Dn
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(k1x1+k2x2)
 Typically, pick one chemical as index (say
1 here) and express others in terms of
that.
 Then RPF for 2 is k2/k1
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)
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
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 < 10%
Database of
Acetylcholine Esterase
Data
• 33 chemicals
• 80+single-chemical studies
• 3 compartments (brain, rbc, plasma)  2
sexes
• multiple durations of exposure,
subchronic to chronic
• total >1655 dose-response relationships
(~ 1300 retained)
Data Structure
Chemical
Study 1
F
Study 2
M
F
M
(in each Study X Sex)
Doses
1
…
k
Compart.
Study 3
F
M
Mean, SD, N
DS1
DS2
DS3
DS4
Brain
X
X
X
X
RBC
X
X
X
X
Plasma
X
X
X
X
…
…
…
…
…
Brain
X
X
X
X
RBC
X
X
X
X
Plasma
X
X
X
X
Experimental Design
Chemical
Study 1
F
Study 2
M
F
Study 3
M
F
M
(in each StudyXSex:)
Doses
Animals
Compart.
DS1
DS2
Brain
1
Di
…
DS4
X
RBC
X
X
Plasma
X
X
…
…
…
Brain
n
DS3
…
…
X
RBC
X
X
Plasma
X
X
# Dose Groups
Distribution of # Doses
7
7
6
28
5
265
4
1077
3
1311
2
1312
0
500
1000
# Data Sets
1500
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.
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)
Hierarchical Structure of
BMD Estimate
• Multiple studies carried out at different times
by different laboratories, using different
analytic methods, reporting results in different
units.
BMD Estimate
MRID 1
Time 1.1
MRID 2
Time1.2
Time 2.1
Time 2.2
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).
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.
1500
500
1000
 exp  lm  Dose

y  A   PB   1  PB  e m


potency
0
AChE Activity
2000
Dose-Response and
Potency: Approach 1
0
500
1000
Dose
1500




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
< 3):
• set PB  0
• refit to dataset
• drop highest dose
Potency Measure
• Absolute potency is BMD calculated from
fitted model:
• Relative Potency:
• IF PBI = PBk
Estimate dose-response
for each dataset:
Random Effects Model for
BMD
•
•
•
•
•
Log(BMD) = μlBMD+ EMRID + ETime in MRID
μlBMD varies between sexes
EMRID ~ N(0,σMRID2)
ETime in MRID ~ N(0,σTiM2)
Error variance proportional to (predicted)
mean of AChE activity at that dose;
constant of proportionality varied among
MRIDs.
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:
q
q
i 1
i 1
L   ln  si2   2     lmi   2
2
2
s


i

Combine Potency (more)
• Variances for ln(potency) estimates:
1
q

i 1

1
si2   2

• 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.
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 doseresponse curve in the low-dose
region?
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.
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
Body ( C b )
Qb
Urine ( k e )
Ingestion (Dose ×BW/24)
Liver ( C l )
Metabolism ( V max , K m )
Ql
Ca
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:
Stage 2: Same as Before
• But reparametrized:
 1 PB  BMR 


log 

1

P

B
 idose 

iBMD


m
y  A  PB  1  PB  e





2000
DR with First Pass
Metabolism
10
S =
2
0 .2
0 .0 0 1
8
6
1000
4
D = 2
500
2
0
0
0
2
4
6
8
10
S caled Internal D ose
A C hE A ctivity
1500
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)
Dose Response
AChE (U/G)
15
10
5
0
0.0
0.4
0.8
1.2
Dose (mg/kg/day)
Benchmark Dose: Fitting
One Dataset at a Time
F
M
0.01
0.10
1.00
BMD
Benchmark Dose:
Combining Datasets
F
M
0.01
0.10
BMD
1.00
Overall Quality of Fit:
Residuals
Residuals
5
0
-5
-10
0.0
0.2
0.4
0.6
Inhibition
0.8
AC M
HL A
ORLA
CH
V THI
O
LO
TR BEN INPH
RP P IC SU ON
H
YR RO LO LI S
IPH FE R DE
O N FO
PH SMEOFON
O S TH S
D A LO Y L
N
TRIAZIN
PIR
IBU O E
P
D
IM IC HO FON
I PH H S S
O LORM E
CHFEN SM E VOT
LO A M T H S
RP IPH YL
FOETH YRIFOS
ST OP OS
HIA RO
AZ
ME INP A N ZATP
CHTHY HOCSEPALEDE
LO LP M HA
PH RETARAETHTE
O H T YL
MESTE OXYHION
TH B U FO
IDA PIR S
DIM
ET TH IM
FE HO ION
NT AT
OX
MEPHO HIO E
YD
EM T VIN RA N
ET ER PH TE
ME O ONMBUF OS
TH M E ET OS
AM TH HY
O L
DIS IDO
DIC U PATE
L
RO FO HOS
TO TO
PH N
OS
TE
TR
Relative Potency
Relative Potencies
1
0.1
0.01
0.001
Computing a MOE
(Margin of Exposure)
A (Index)
1.00
Exposure
Eq.
(μg/kg/day) Exposure
0.2
0.2
B
0.1
1.0
0.1
C
1.2
0.2
0.24
Chem
RPF
Total Equivalent Exposure
0.54
BMD10(A) = 0.08 mg/kg/day
MOE = 0.08 X 1000 μg/kg/day / 0.54 = 148
Distribution of Total
MOEs
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.
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
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.
CHLORPYRIPHOSMETHYL
DIAZINON
PIRIMIPHOSMETHYL
DIMETHOATE
MEVINPHOS
METHIDATHION
CHLORPYRIFOS
DISULFOTON
FENTHION
PHOSMET
PHOSALONE
Direct Acting
AZINPHOSMETHYL
TERBUFOS
MALATHION
BENSULIDE
METHYLPARATHION
PHORATE
TRICHLORFON
FENAMIPHOS
ACEPHATE
ETHOPROP
NALED
TETRACHLORVINPHOS
OXYDEMETONMETHYL
METHAMIDOPHOS
DICROTOPHOS
DICHLORVOS
TRIBUFOS
PB
FOSTHIAZATE
Horizontal Asymptotes
0.8
Require Activation
0.6
0.4
0.2
0.0
Should We Expect DoseAdditivity? (Not Exactly!)
• Low-dose shoulder significantly
improves fit in a substantial number of
chemicals. At best, expect doseadditivity in terms of target dose.
• Horizontal asymptotes differ significantly
among chemicals (P << 10-6), so doseadditivity cannot hold exactly.
Beginnings of A
Theoretical Approach
• Through mathematical analysis
and in silico experiments, ask:
 What features determine the shape
of individual chemical doseresponse curves, and
 what are the features of chemicals
(if any) that lead to deviations from
dose-additivity in cumulative
exposures.
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”.
AChE Inhibition Scheme
ks
kI
E+I
kd
ka
EI
kr
E = AChE
I = OP-like inhibitor
Bound EI
100
80
60
40
15
20
0
0
5000
10000 15000
0.2
0.15
0.1
0.05
0
Pct. AChE Activity
Brain Conc. 47
Dose Chem 27
0.25
100
80
60
Dose Chem. 47
0.3
0.25
0.2
0.15
0.1
0.05
0
Pct. AChE Activity
Brain Conc. 27
Strict Sense Dose
Additivity
10
5
40
20
0
0
0
500
1000 1500 2000
Dose Chem 47
0
20
40
60
80
Dose Chem. 27
100
120
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:
d1
d2
 1

D1 f 2  f1  D1  
R  d1 , d2   f1  D1 
dn
 1
1
f n  f1  D1  
DR for 50-50 Mixture
From
RPFs
From
PBPK
100
80
60
40
1.5
20
0
0
5000
10000 15000
Pct. AChE Activity
Brain Conc. 17
Dose Chem 27
0.06
0.05
0.04
0.03
0.02
0.01
0
100
80
60
Dose Chem. 17
0.3
0.25
0.2
0.15
0.1
0.05
0
Pct. AChE Activity
Brain Conc. 27
Broad Sense Dose
Additivity
1.0
0.5
40
20
0.0
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Dose Chem 17
0
20
40
60
80
Dose Chem. 27
100
120
DR for 50-50 Mixture
From RPFs
“Berenbaum”
From
PBPK
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
100
80
8
60
40
6
20
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Pct. AChE Activity
Brain Conc. 300
Dose Chem 17
30
25
20
15
10
5
0
100
80
60
Dose Chem. 300
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Pct. AChE Activity
Brain Conc. 17
Common Mode of
Action?
4
2
40
20
0
0
0
50 100
200
Dose Chem 300
300
0.0
0.5
1.0
Dose Chem. 17
1.5
2.0
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.