1. Paul Price The Dow Chemical Company March 16, 2010
Using Empirical Data on Toxicity Pathways in the Prediction of Responses at Low-doses
Paul Price
The Dow Chemical Company
March 16, 2010

2. Nature of the talk
Goal is to explore statistical and toxicological concepts in low-dose extrapolation
Integrate ideas from NAS reports
Toxicity in 21 Century
Science and Decisions - Advancing Risk Assessment
Issues
low-dose linearity or non linearity
A Gedanken experiment
Effect of pre-existing disease process
Creating room for mode of action arguments

3. The great divide
Toxicologists have traditionally favored the concept of thresholds (the dose makes the poison)
Historical confidence that biology favors thresholds (after all we all are alive and are exposed to thousands of chemicals daily)
Thresholds should be the default assumption in risk assessment
Classic toxicology believes that animal data are a good marker for thresholds
Nothing is going on at doses 1-10 fold below the animal NOEL

4. The great divide Statisticians are suspicious of thresholds
The value of data from animal studies is very dependent on the number of animals and noise-to-signal ratios
Animal tests have less statistical power then many toxicologists recognize
Proving the existence of thresholds takes “a lot” of data (distinguishing between a low effect and “no” effect)
Methodology used to deal with thresholds smacks more of policy than science (safety factors are statistically “icky”)

5. An animal study is performed
A toxicologist sees:
The apical effect at high doses
Precursors to the effect (but not the apical effect) at a lower dose
At the lowest dose and control sees no effect
Conclusion: there is no chance of the apical effect occurring at low doses

6. An animal study is performed
The statistician is given the data on the occurrence of the apical effect
X animals high dose, 0 and mid dose, 0 at low-dose, no background occurrence in controls
Fits apical data to multiple dose-response models, calculates lower limit to a robust benchmark dose
Draws a line from the lower confidence limit of the benchmark dose to zero
Conclusion:
The apical event will occur at low doses
Test enough animals and at any dose you will always find the apical effect

7. You did visit the same country, didn't you. President Robert F
You did visit the same country, didn't you? President Robert F. Kennedy speaking to two military advisors returning from Vietnam.

8. Can we bring these worlds together?
Toxicologist and statisticians were not looking at the same data
Toxicologists looks at precursor data and mentally did an statistical assessment of “contingent probability”
No apical effect without the precursor effect
No precursor effect at lowest dose
Therefore at the lowest dose no chance of apical effect
Statisticians only looked at data on occurrence of the apical effect (did not consider data on precursor effects)
Can these data be used in dose response in a quantitative fashion

9. Toxicity in the 21st Century
Base State (No dose related effect)
State D (Events 1-3 and Apical Effect)
State B (Events 1 and 2)
State C (Events 1-3)
State A (Event 1)
All toxic effects begin with perturbation of biological systems
The pathway leading to the apical toxic effect includes key events that can be measured
Key event is “necessary” but “not sufficient” to cause the apical effect
The probability for going from one event to the next is determined by “dose dependent transition probabilities”

10. Toxicity pathways
Base State (No dose related effect)
State D (Events 1-3 and Apical Effect)
State B (Events 1 and 2)
State C (Events 1-3)
State A (Event 1)
A multistage process is inherently a non-linear process
Each stage is defined by a
Each step is defined by an independent transition probability:
Linear with dose
Non linear with dose
Threshold

11. Low-dose linearity
If any transition is non-linear at low doses then the total dose response curve is non-linear (linearity is only as strong as its weakest link)
As the number of stages goes up the probability of linearity goes down
50% chance of a threshold per step in 5 stage pathway gives 97% overall chance of a threshold

12. Low-dose linearity
Assumption of linearity in dose-dependent transitions at each step in a pathway does not lead to an over all linear dose response
When there is no background rate and when transitions are dose dependent you get non-linearity

13. When can low-dose linearity occur?
There must be a background rate of the apical endpoint
When some individuals are at each interim stage (including the penultimate stage)
Some individuals are ready to be “pushed over” the last transition
When there is a dose-independent probability (stochastic) that an animal at an early stage can progress to the apical event

14. Carcinogenicity and low-dose linearity
Cancer is a disease
By definition carcinogens are chemicals that are assumed to be affecting a preexisting disease process
There are very few key events
Once a second mutation occurs some fraction of the mutations will result in cancer – dose independent process

15. Non-carcinogenic effects and low-dose linearity
Non-cancer adverse effects of a chemical may affect a preexisting disease process
Non-cancer adverse effects can cause independent adverse effects
A chemical can cause both

16. No disease interaction pathway
Base State (No dose related effect)
State D (Events 1-3 and Apical Effect)
State B (Events 1 and 2)
State C (Events 1-3)
State A (Event 1)
A chemical has been tested
Multiple dose groups
Three key events measured on pathway to apical effect
Animals are dosed
All events and apical effect measured at the terminal sacrifice

17. Assumptions
The occurrence of each event is contingent on the occurrence of prior effects.
Each event is necessary but not sufficient to cause subsequent effects.
Each step in the pathway is dose dependent (these dose dependencies may or may not have thresholds).
The events have background rates of zero.
Base State (No dose related effect)
State D (Events 1-3 and Apical Effect)
State B (Events 1 and 2)
State C (Events 1-3)
State A (Event 1)

18. Using transition probabilities (f1) in dose response modeling (10th Grade Probability Theory)
PBase State = 1- f1(d)
PA = f1(d)*(1- f2(d))
PB = f1(d)* f2(d)*(1- f3(d))
PC = f1(d)* f2(d)* f3(d)*(1- f4(d))
PD = f1(d)* f2(d)* f3(d)*f4(d)
Base State (No dose related effect)
State D (Events 1-3 and Apical Effect)
State B (Events 1 and 2)
State C (Events 1-3)
State A (Event 1)

19. Number of Animals in Each State in Different Dose Groups
A gedanken experiment
Number of Animals in Each State in Different Dose Groups
Dose Group
Dose
(d)
Base State A B C D
(Apical Effect) 1 15 25 2 30 23 3
100 5 10 4
300 19
1000 6
3000

20. Number of animals in each state (or prior state) in different dose groups
Base State A B C D
(Apical Effect) 1 15 25 2 30 3
100 20 5 4
300
1000 6
3000 23

21. Fraction of tested animals in each state (PA, PB, PC and, PD) in different dose groups
Base State PA PB PC PD 1 15 2 30
0.08 3
100
0.8
0.6
0.2 4
300
0.04 5
1000 6
3000
0.92

22. Probability of Apical Effect =F1(d)* F2(d)* F3(d)* F4(d)
Dividing P for a cell to a prior stage gives the transition probability at each dose
Dose group
Dose
F1(d)
F2(d)
F3(d)
F4(d)
Probability of Apical Effect
=F1(d)* F2(d)* F3(d)* F4(d) 1 15 - 2 30
0.08 3
100
0.8
0.75
0.33 4
300
0.05
0.04 5
1000
0.6 6
3000
0.92

23. Low-dose extrapolation for key event dose response
Data are not available on the occurrence of apical and key events at doses below 300 and values of transition probability cannot be measured
Lets assume no thresholds for the dose response for each step and estimate the response at lower doses by drawing a ling from the lowest dose producing the key event and zero

24. Probability of Apical Effect =F1(d)* F2(d)* F3(d)* F4(d)
Transition probabilities at lower doses
Dose group
Dose
F1(d)
F2(d)
F3(d)
F4(d)
Probability of Apical Effect
=F1(d)* F2(d)* F3(d)* F4(d) 1 15 - 2 30
0.08 3
100
0.8
0.75
0.33
=100/300*0.05 4
300
0.05
0.04 5
1000
0.6 6
3000
0.92

25. Probability of Apical Effect =F1(d)* F2(d)* F3(d)* F4(d)
Transition probabilities at lower doses
Dose group
Dose
F1(d)
F2(d)
F3(d)
F4(d)
Probability of Apical Effect
=F1(d)* F2(d)* F3(d)* F4(d) 1 15 - 2 30
0.08 3
100
0.8
0.75
0.33
0.017 4
300
0.05
0.04 5
1000
0.6 6
3000
0.92

26. Probability of Apical Effect =F1(d)* F2(d)* F3(d)* F4(d)
Transition probabilities at lower doses
Dose group
Dose
F1(d)
F2(d)
F3(d)
F4(d)
Probability of Apical Effect
=F1(d)* F2(d)* F3(d)* F4(d) 1 15
0.04
0.1
0.05
.003 - 2 30
0.08
0.2
.005 3
100
0.8
0.75
0.33
0.017 4
300 5
1000
0.6 6
3000
0.92

27. Probability of Apical Effect =F1(d)* F2(d)* F3(d)* F4(d)
Apical responses at low doses
Dose group
Dose
F1(d)
F2(d)
F3(d)
F4(d)
Probability of Apical Effect
=F1(d)* F2(d)* F3(d)* F4(d) 1 15
0.04
0.1
0.05
.03
6 E-7 2 30
0.08
0.2
.05
9 E-6 3
100
0.8
0.75
0.33
0.17
3 E-3 4
300 5
1000
0.6 6
3000
0.92

28. Results
LOAEL

29. Results

30. where N is the number of key events
Discussion
Option 3 is a power model that results from the assumption that dose affects multiple steps in the pathway. If:
PD = f1(d)* f2(d)* f3(d)*f4(d)
and f1(d) = D * S1
Then:
PD = D*S1* D*S2* D*S3* D*S4 or
PD =D4*S1*S2*S3*S4
R= KD4 or R= KD(N+1)
where N is the number of key events

31. Ok so what happens if a non-cancer effect interacts with a disease
Ok so what happens if a non-cancer effect interacts with a disease? Case 2

32. State D (Apical Effect of Disease)
Disease pathway
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1

33. Disease and chemical pathways
Base State (No dose related effect)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1
State A (Effect 1)
State B (Effects 1-2)
State C (Effects 1-3)
State D (Effects 1-3 and Apical Effect)

34. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1

35. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1

36. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1

37. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1

38. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1
Threshold

39. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1
Threshold

40. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1
Threshold

41. Non-linear dose response
When a chemical influences a disease outcome at high doses,
But at low-dose has a threshold or is strongly non linear at a step prior to the interaction with the disease process,
Low-dose linearity will not occur.

42. This is not a new concept!
This strategy applies to carcinogenic effects
Mode of Action work on carcinogens formaldehyde and vinyl acetate
Irritation is a key event with a threshold

43. Chemical disease interaction
Base State (No dose related effect)
State D (Effects 1-3 and Apical Effect)
State B (Effects 1-2)
State C (Effects 1-3)
State A (Effect 1)
Healthy Individual
State D (Apical Effect of Disease)
State B1
State C
State A1
Irritation (Threshold)

44. Summary
Data on key events can improve the modeling of dose response at low doses
Empirical data on precursor events that are essential but not sufficient to cause the apical effect can inform low-dose modeling
Interaction with a disease state does not necessarily imply low-dose linearity