Benchmark Dose Modeling – Dichotomous Models
Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for Environmental Assessment, U.S. EPA
Dichotomous Models Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, - - PowerPoint PPT Presentation
Benchmark Dose Modeling Dichotomous Models Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for Environmental Assessment, U.S. EPA Disclaimer The views expressed in this presentation are those of the author(s) and do
Allen Davis, MSPH Jeff Gift, Ph.D. Jay Zhao, Ph.D. National Center for Environmental Assessment, U.S. EPA
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Description
where incidence increases with dose Example Endpoints
Model Inputs
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Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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0.2 0.4 0.6 0.8 1 50 100 150 200 Fraction Affected dose 10:50 04/25 2014
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>10% for precursor effects)
developmental studies)
BMRs. 7
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10% Added Risk 0.10 =P(d) – P(0) ; if P(0)=.50 P(d) = 0.10 + P(0) = 0.10 + 0. 50 = 0.60 10% Extra Risk 0.10 =[P(d) –P(0)]/[1-P(0)]; if P(0) = .50 P(d) = 0.10 x [1 - P(0)] + P(0) = (0.10 x 0.50) + 0.50 = 0.55 The dose will be lower for a 10% Extra risk than for a 10% Added risk if P(0) > 0
0.60 0.55 0.50
P(0) Probability of Response , P(Dose) P(d)
Dose-response model Dose Extra risk Added risk
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Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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Biological Interpretation Examples:
(Hill model)
Policy Decision U.S. EPA’s IRIS program uses the multistage model for cancer data
Otherwise However, in the absence of biological or policy-driven considerations, criteria for final model selection are usually based on whether various models mathematically describe the data 11
Model name Functional form # of Parametersa Low Dose Linearity Model fits
Multistage 1+n Yes, if β1 > 0 No, if β1 = 0 All purpose Logistic 2 Yes Simple; no background Probit 2 Yes Simple; no background Log-logistic 3 No All purpose; S-shape with plateau at 100% Log-probit 3 No All purpose; plateau S-shape with plateau at 100% Gamma 3 No All purpose Weibull 3 No ”Hockey stick” shape Dichotomous Hill 4 Yes Symmetrical, S-shape with plateau
a Background parameter = γ. Background for hill model = v × g
Model name Functional form # of Parametersa Low Dose Linearity Model fits
Multistage 1+k Yes, if β1 > 0 No, if β1 = 0 All purpose Logistic 2 Yes Simple; no background Probit 2 Yes Simple; no background Log-logistic 3 No All purpose; S-shape with plateau at 100% Log-probit 3 No All purpose; plateau S-shape with plateau at 100% Gamma 3 No All purpose Weibull 3 No ”Hockey stick” shape Dichotomous Hill 4 Yes Symmetrical, S-shape with plateau
a Background parameter = γ. Background for hill model = v × g
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freedom (DF) (in BMDS, DF is increased by 1 for p-value calculation)
penalization (EPA’s Statistical Working Group may modify this approach in the future) 14
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50 100 150 200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 22:08 06/25 2009 BMD BMDL Multistage
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50 100 150 200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 22:05 06/25 2009 BMD BMDL Multistage
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0.2 0.4 0.6 0.8 1 50 100 150 200 Fraction Affected dose Weibull Model with 0.95 Confidence Level 10:16 03/04 2010 BMDL BMD Weibull
Gamma, Weibull, Hill, Log- Logistic, or Log-Probit models
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Gamma, Weibull, Hill, Log- Logistic, or Log-Probit models
0.2 0.4 0.6 0.8 1 50 100 150 200 Fraction Affected dose Weibull Model with 0.95 Confidence Level 10:25 03/04 2010 BMDL BMD Weibull
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misconstrued to have more biological meaning than appropriate
models in BMDS; other software packages (i.e., PROAST) can consider covariates for all data types 19
Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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actual responses
model for cancer endpoints), a cut-off value of p = 0.05 can be used 22
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P = 0.94
Dose (mg/m3) N Incidence 50 20 180 20 4 300 32 13 750 12 12 1200 12 12
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0.2 0.4 0.6 0.8 1 200 400 600 800 1000 1200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 13:08 08/18 2010 BMD BMDL Multistage
Dose (mg/m3) N Incidence 50 20 180 20 4 300 32 13 750 12 6 1200 12 5
P = 0.0526 26
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 400 600 800 1000 1200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 14:10 11/03 2010 BMD BMDL Multistage
Dose (mg/m3) N Incidence 50 20 180 20 4 300 32 13 750 12 6
P = 0.3676 27
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 100 200 300 400 500 600 700 Fraction Affected dose Multistage Model with 0.95 Confidence Level 14:07 11/03 2010 BMD BMDL Multistage
Dose (mg/m3) N Incidence 50 20 180 20 4 300 32 13 750 12 6 1200 12 5
P = 0.9094 28
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 400 600 800 1000 1200 Fraction Affected dose Dichotomous-Hill Model with 0.95 Confidence Level 14:11 11/03 2010 BMDL BMD Dichotomous-Hill
cases of metabolic saturation (e.g., dose-response shape will be linearized)
indication that this dose metric is the metric of interest (i.e., Cmax vs. AUC) 29
(often advantageous if PBPK model is constantly updated or changed)
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√(𝑜∗𝑞(1−𝑞))
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50 100 150 200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 22:08 06/25 2009 BMD BMDL Multistage 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50 100 150 200 Fraction Affected dose Multistage Model with 0.95 Confidence Level 22:05 06/25 2009 BMD BMDL Multistage
Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
38
Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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multistage vs. log-probit)
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Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
42
Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
43
Yes
Have all models & model parameters been considered?
No No No
Consider combining BMDs (or BMDLs)
and least complexity (i.e., lowest AIC)?
parameter options, and run models
Are they sufficiently close? Use BMD (or BMDL) from the model with the lowest AIC START
Yes No
Use lowest reasonable BMDL
Yes Yes Yes
Data not amenable for BMD modeling
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– Background response – Background dose
– Background response – Background dose
– Quantal-Linear (power = 1) – Background response – Background dose
– Background response – Background dose
– Background response
– Background response – Background dose
– Background response – Background dose 47
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Scaled Residual
(local fit) Goodness-of-fit p-value (global fit)
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55.2
160.271
0.2788
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55.2 94.7
160.271 158.884
0.2788 0.5802
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55.2 94.74 111.50
160.271 158.884 157.776
0.2788 0.5802 1.000
0.004
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smaller, the better)
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55.2 94.74 111.50
160.271 158.884 157.776
0.2788 0.5802 1.000
0.004
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the Wizard subdirectory not contain any non-alphanumeric characters
(C:\Users\name\BMDS240)
must be in the same directory as the BMDS executable 94
Excel 2003
click “Macro Security”
tab and click “Trust Center Settings”
to “Disable all macros with notification” or “Enable all macros”
tab and click “Trust Center Settings”
“Disable all macros with notification” or “Enable all macros” 95
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