Dose-Response Modeling for EPA’s Organophosphate CumulativeRisk Assessment: Combining
Information from Several Datasets toEstimate Relative Potency Factors
R. Woodrow SetzerNational Center for Computational Toxicology
Office of Research and DevelopmentU.S. Environmental Protection Agency
Background
• Food Quality Protection Act, 1996Requires 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 multi-chemical exposures.
• Non-interaction coincides with linear isoboles.
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:
1 2
1 2
1d d
D D
1
1
1n
n
dd
D D
For n chemicals:
:line
:hyperplane
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 StructureChemical
Study 1 Study 3Study 2
MF M MF F(in each Study X Sex) Mean, SD, N
Doses Compart. DS1 DS2 DS3 DS4
1
Brain X X X X
RBC X X X X
Plasma X X X X
… … … … … …
k
Brain X X X X
RBC X X X X
Plasma X X X X
Experimental Design
Chemical
Study 1 Study 3Study 2
MF M MF F
(in each StudyXSex:)
Doses Animals Compart. DS1 DS2 DS3 DS4
Di
1
Brain X
RBC X X
Plasma X X
… … … … … …
n
Brain X
RBC X X
Plasma X X
Distribution of # Doses
2
3
4
5
6
7
# Data Sets
# D
ose
Gro
ups
0 500 1000 1500
1312
1311
1077
265
28
7
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 MRID 2
Time 1.1 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.
Dose-Response and Potency: Approach 1
15000 500 1000
050
010
0015
0020
00
Dose
AC
hE A
ctiv
ity
exp
1 e m
lm Dose
B By A P P
potency
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
0.9ln
1Bk
Bkk
k
PP
BMDm
10.9ln 110.9ln 1
BIBII kI
k IBk
Bk k
PPBMD mm
BMD mPP m
Random Effects Model for BMD
• Log(BMD) = μlBMD+ EMRID + ETime in MRID
• μlBMD varies between sexes• EMRID ~ N(0,σMRID
2)• ETime in MRID ~ N(0,σTiM
2)• 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 si
2. Potency estimates () and variance components (2) maximize:
22 2 2 2
1 1
lnq q
i i ii i
L s lm s
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.
2 21
1
1q
i is
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?
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
Body ( C b)
Liver ( C l)
Metabolism ( V max , K m )
Urine ( ke)
Ingestion (Dose ×BW/24)
Q b
Q l
C a
• 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
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:
2
max
0.5 *
4
24 24;l b m e
l e b e l b
idose Dose S D
Dose S D Dose S
QQ K k VS D
BW Q k Q k QQ BW
DR with First Pass Metabolism
0 2 4 6 8 10
0
500
1000
1500
2000
Dose
0
2
4
6
8
10
Sca
led
Inte
rna
l Do
se
AC
hE A
ctiv
ity
S =20.20.001
D = 2
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)
Re
lati
ve
Po
ten
cy
0.001
0.01
0.1
1M
ALA
THIO
N
TE
TR
AC
HLO
RV
INP
HO
S
BE
NS
ULI
DE
TR
ICH
LOR
FO
N
PR
OFE
NO
FO
S
CH
LOR
PY
RIP
HO
SM
ET
HY
L
PH
OS
ALO
NE
DIA
ZIN
ON
TR
IBU
FO
SP
HO
SM
ET
DIC
HLO
RV
OS
PIR
IMIP
HO
SM
ET
HY
L
FE
NA
MIP
HO
S
CH
LOR
PY
RIF
OS
ETH
OP
RO
P
FO
ST
HIA
ZA
TE
NA
LED
AC
EP
HA
TE
AZI
NP
HO
SM
ET
HY
L
ME
TH
YLP
AR
ATH
ION
CH
LOR
ETH
OX
YF
OS
PH
OS
TE
BU
PIR
IM
ME
TH
IDA
TH
ION
DIM
ET
HO
AT
EF
EN
TH
ION
PH
OR
AT
E
ME
VIN
PH
OS
TE
RB
UF
OS
OX
YD
EM
ET
ON
ME
TH
YL
OM
ET
HO
AT
E
ME
TH
AM
IDO
PH
OS
DIS
ULF
OT
ON
DIC
RO
TOP
HO
S
Relative Potencies
Computing a MOE (Margin of Exposure)
Chem RPFExposure
(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 0.54
BMD10(A) = 0.08 mg/kg/day
MOE = 0.08 X 1000 μg/kg/day / 0.54 = 148
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.
Horizontal Asymptotes
0.0
0.2
0.4
0.6
0.8
FO
ST
HIA
ZA
TE
TR
IBU
FO
S
DIC
HLO
RV
OS
DIC
RO
TO
PH
OS
ME
TH
AM
IDO
PH
OS
OX
YD
EM
ET
ON
ME
TH
YL
TE
TR
AC
HLO
RV
INP
HO
S
NA
LED
ET
HO
PR
OP
AC
EP
HA
TE
FE
NA
MIP
HO
S
TR
ICH
LOR
FO
N
PH
OR
AT
E
ME
TH
YLP
AR
AT
HIO
N
BE
NS
ULI
DE
MA
LAT
HIO
N
TE
RB
UF
OS
AZ
INP
HO
SM
ET
HY
L
PH
OS
ALO
NE
PH
OS
ME
T
FE
NT
HIO
N
DIS
ULF
OT
ON
CH
LOR
PY
RIF
OS
ME
TH
IDA
TH
ION
ME
VIN
PH
OS
DIM
ET
HO
AT
E
PIR
IMIP
HO
SM
ET
HY
L
DIA
ZIN
ON
CH
LOR
PY
RIP
HO
SM
ET
HY
L
Direct Acting Require Activation
PB
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 << 10-6), so dose-additivity cannot hold exactly.
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.
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”.
Strict Sense Dose Additivity
Dose Chem. 27
Dos
e C
hem
. 47
0 20 40 60 80 100 120
0
5
10
15
0 5000 10000 15000
0
20
40
60
80
100
Dose Chem 27
Pct
. AC
hE A
ctiv
ity
00.05
0.10.15
0.20.25
0.3
Bra
in C
onc.
27
0 500 1000 1500 2000
0
20
40
60
80
100
Dose Chem 47
Pct
. AC
hE A
ctiv
ity
0
0.05
0.1
0.15
0.2
0.25
Bra
in C
onc.
47
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:
1 21 1
1 2 1 1 1 1
1 2 1 1
1
,
n
n
dd d
D f f D f f D
R d d f D
Broad Sense Dose Additivity
Dose Chem. 27
Dos
e C
hem
. 17
0 20 40 60 80 100 120
0.0
0.5
1.0
1.5
0 5000 10000 15000
0
20
40
60
80
100
Dose Chem 27
Pct
. AC
hE A
ctiv
ity
00.05
0.10.15
0.20.25
0.3
Bra
in C
onc.
27
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
20
40
60
80
100
Dose Chem 17
Pct
. AC
hE A
ctiv
ity
00.010.020.030.040.050.06
Bra
in C
onc.
17
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
Common Mode of Action?
Dose Chem. 17
Dos
e C
hem
. 300
0.0 0.5 1.0 1.5 2.0
0
2
4
6
8
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0
20
40
60
80
100
Dose Chem 17
Pct
. AC
hE A
ctiv
ity
00.010.020.030.040.050.060.07
Bra
in C
onc.
17
0 50 100 200 300
0
20
40
60
80
100
Dose Chem 300
Pct
. AC
hE A
ctiv
ity
05
1015202530
Bra
in C
onc.
300
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