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

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

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

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”)

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

An animal study is performed The statistician is given the data on the occurrence of the apical effect X animals affected @ 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

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.

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

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”

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

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

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

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

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

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

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

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)

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)

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

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

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

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

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

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

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

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

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

Results LOAEL

Results

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

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

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

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)

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

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

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

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

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

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

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

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.

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

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)

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