The basic thesis of the Crawford and Wilson article (1) is the well known theory of low-dose linearity sometimes called the incremental dose-incremental effect theory. Drs. Wilson, Crawford and Heitzmann make a good presentation out of this long known theory of toxicological action and its possible application to noncarcinogenic endpoints. They are to be commended for a thoughtful and clear presentation. The invited summary and commentaries to this article published in the Volume 6, No. 1 of the BELLE Newsletter of March 1997 have also done a fine job presenting the main important points of the several theoretical and experimental arguments that can be made either for or against the thesis from Dr. Wison's group at Harvard. Constructive criticism helps the field of risk assessment advance and this is what we saw in the preceeding BELLE Newsletter - a Hegelian sequence of scientific thesis, antithesis and synthesis.

In this subsequent invited commentary I wish to emphasize several points made by prior commentaries, extend these points in some cases and hopefully add some hopefullynew thoughts to the fray that is dose-response relationships in the low and experimentally untestable range.

1. The two critical assumptions of the low-dose linearity theory.
Both Drs. Myron Pollycove and Robert Sielken, Jr. identified and presented the best counter argument to the incremental dose incremental effect theory. In Dr. Sielken's commentary he states "First, the background dose and the "pollutant" are assumed to have exactly the same mechanism of action (that is the background dose and the pollutant dose are additive in the dose-response relationship)." Sielken later writes "Second, the authors assume that the dose-response relationship is monotonic (strictly increasing in dose)." It is exactly these two critical assumptions that cannot be demonstrated to be true in many cases. In most cases of chemical pollution we do not know the exact mechanism of toxicological action at a high level of scientific sophistication and certainty. All we have are our current, experimentally limited, scientific models and hypotheses. The assumption that the dose-response curve is monotonic is even less tenable. Why not assume that the dose response relationship is nonmonotonic? A more complete theory of low dose-response relationships would include hormetic responses, no responses at all and positive monotonic responses. Examples of all three of these cases will now be given. As example of a hormetic response, very low doses of either TCDD or phenobarbital to rats decrease the number of rat hepatic foci from that of concurrent control groups; higher doses of TCDD or phenobarbital increase the number of hepatic foci (2). In the NCTR 2-acetylaminofluorene megamouse experiment, the incidence of urinary bladder cancer showed no significant effect over a certain dose range and then increased at higher doses (60ppm-150ppm) (3). This is an example of no significant biological response. In the same experiment the incidence of liver cancer was linearly related to the dose of 2 acetylaminoflurorene over the entire dose range (3). This is an example of a positive monotonic response.

In summary, one should conclude that these two critical assumptions (same mechanism, monotonic increase) pertaining to low dose dose-response relationships have not been proven to be true or justified in their utilization by Dr. Wilson's group.

2. Mathematical form of the dose-response relationship
Selecting the form of the mathematical equation determines what type of low dose response is obtained in the environmentally important often experimentally untestable low dose region. Of this situation Dr. Dale Hattis

writes "If I have any complaint about their summary and their more extensive earlier paper (Crawford and Wilson, 1996), it is that they have chosen a mathematically tractable power law dose response formulation for their illustrations, rather than something like a probit which is more directly interpretable in terms of lognormal variability in susceptibilities to toxic action (and/or) a lognormal distribution of functional reserve capacities in our diverse human population." Nonlinear transition or sequential-cascade type equations are one alternative to power or power series equations. Nonlinear transition equations often have an upper bound or asymptote and a transition point about which the curve may be symmetrical or nonsymmetrical. Examples of these types of equations include log normal cumulative, logistic dose response, sigmoid, gaussian cumulative, and cascade type equations built on chemical reaction kinetics. These types of equations can give lower slopes or even no practical slope at all in the very low dose regions. The equation for a sigmoid curve with an intercept is y=a+b/(1+exp(-(x-c)/d)), where a is the y intercept, and the values for b, c, and d control the sigmoidal shape of the curve. Nonlinear transition equations do not model hormetic responses well; but hormetic responses can often be modeled by power series equations such as a quadratic or cubic equation.

Sequential-cascade type models (such as the Moolgavkar type of model in the carcinogenesis area) (4) offer a lot of advantages. Sequential-cascade models contain multiple stages and the overall process is modeled somewhat like a sequential chemical reaction (i.e. A ---> B --> C --> D --> E --> F). In the carcinogenesis area they can explain the difficult problem of why cancer does not occur in most human organs at higher frequencies and at earlier ages. As there are many exogenous mutagens as well as continual DNA damage from endogenous activated oxygen species produced during intermediary metabolism, one wonders why some men and women can reach their eighties without cancer in any organ while mice and rats sometimes have a difficult time avoiding cancer during the first two years of their much shorter lifespan. As well summarized by Dr. Myron Pollycove "From this point of view, the problem of cancer seems to be not why it occurs, but why it occurs so infrequently." The slowness of cancer to develop in humans may be due to our multiple, highly efficient defense and repair mechanisms. These defending and repairing factors should be included in any holistic mathematical model of the time and dose dependence of human cancer. Because defense and repair mechanisms exist, sequential-cascade types of models are attractive because they can include the considerable biological complexity of defense and repair capabilities that we already know about.

3. An example of the dose-response relationships for 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) - induced hepatic microsomal enzyme induction and hepatocellular carcinomas in female rats.
TCDD's induction of the microsomal enzyme aryl hydrocarbon hydroxylase (AHH) in female rat liver has been studied by Kitchin and Woods (5) in experiments utilizing 10 different TCDD doses. TCDD induced hepatocellular carcinomas in female rats were quantified in a Dow Chemical Company study utilizing 3 different TCDD dose published by Kociba et al. (6). As both experimental studies included measurements of how much TCDD was present in the livers of TCDD treated rats, both dose response curves can be plotted on a common x axis of the rat hepatic TCDD concentration (pg of TCDD per g of liver) (Figure 1). Once this is done, the two dose response relationships in Figure 1 appear to be fairly similar in shape. Indeed the data of Figure 1 suggests that there may be two parallel curves for TCDD - a lower dose curve for hepatic AHH enzyme induction and a higher dose curve for hepatocellular carcinoma. What limits this scientific interpretation of possible parallelness from being more throughly tested is that lethality limits the amount of TCDD that can be given to experimental rats. Thus, the full possible curve of TCDD induced hepatocellular carcinoma can never be experimentally observed because the rats will die of TCDD poisoning before developing tumors. Thus, the percentage of rats developing TCDD induced hepatocellular carcinoma is limited by TCDD's lethality.



The ideas offered by Dr. Wilson's group are germane to both cancer and noncancer endpoints. Let us see how well these ideas do with these particular TCDD data sets which contain both cancer and noncancer endpoints. With log transformed dose the AHH data can be well fit by a sigmoid type of equation (r² = 0.9972); a power law equation as suggested by Dr. Wilson's group does not fit this data as well (for the equation y = a + bx^c, the r² = 0.9375). Attempting to fit different equations to the four available hepatocellular carcinoma data points of Kociba et al. study is basically futile as far too many equations fit the very limited number of data points well including linear, quadratic, power, nonlinear transition equations etc. We have waited nearly 20 years for a better experimental study of the low dose range of TCDD-induced tumors in experimental animals, but the best study is still the 1978 study of Kociba et al. (6). As this type of experimental work is difficult, expensive, time consuming and not in current favor with federal granting agencies, it may be a very long time indeed before a superior dose response rodent study of TCDD induced hepatocellular carcinoma eventually becomes available.

In the meantime one can speculate that the mechanisms of the two different TCDD effects (AHH enzyme induction and liver tumors) may be mechanistically related and that their dose-response relationships may be similar as well. Therefore, it is an attractive alternative to use the available AHH enzyme induction data to select mathematical equations for dose response extrapolation and then use these equations to make predictions or extrapolations about what the dose response curve for liver tumors might be like. This could be a useful approach in experimental design of future TCDD cancer experiments and/or TCDD risk assessment.

Based on regression analysis of both the untransformed and log transformed AHH enzyme activity and hepatocellular carcinoma data sets, I wish to offer the following ideas or interpretations to the BELLE dose-response forum:

(A) A power equation is not a good choice for either version of the AHH data set, although the power equation is among the best simple equations for fitting to some degree of quality both this AHH data set and many other biological data sets. The selection of mathematical equations is the most critic issue in low dose risk assessment.

(B) Nonlinear transition equations fit the AHH data set better than power or power series type of equations. This generalization is true for both untransformed and log transformed TCDD dose. In general, nonlinear transition equations have been underutilized by the risk assessment community even though nonlinear transition equations have several attractive features (7).

( C ) Among nonlinear transition equations it is difficult to justify the preference of one nonlinear transition equation over another. However, for this AHH data set the log normal cumulative (r² = 0.9977, r² = 0.9974 for the untransformed and log transformed dose, respectively) and the logistic dose response (r² = 0.9972, r² = 0.9971 for the untransformed and log transformed dose, respectively) equations do particularly well. Among the 14 nonlinear transition equations tested, most fit the data points very well and 12 out of 14 nonlinear transition equations had r² > 0.9925.
(D) A good experimental study of TCDD-induced hepatocellular carcinoma might require as many as about 8 very carefully chosen doses of TCDD. Such an elaborate 8 dose-response study of TCDD induced hepatocellular carcinomas could advance the art and practice of TCDD risk assessment. Any additional experimental studies of 4 or less TCDD doses will have little or no hope of adding to our present day scientific knowledge or improving mathematical modeling of TCDD-induced hepatocellular carcinoma.

(E) Using a mathematical equation selected by a data analysis of a surrogate biomarker, hepatic AHH induction, rather than by data analysis of the hepatocellular carcinoma incidence data itself, may be a defendable risk assessment practice. For example the log normal cumulative, logistic dose response or sigmoid equation could be used to model the dose response relationship for TCDD-induced hepatocellular carcinomas. This basis of mathematical equation selection is about as good as other practices that we currently utilize in risk assessment.

Conclusion
It is difficult to make progress in the area of low dose extrapolation regardless of whether one takes an experimental, theoretical or mixed approach. The considerable difficulty of making real progress, the lack of funding in the dose-response area and the reticence of humans and regulatory institutions to change may be the three chief reasons that we as a society have not advanced faster in this scientific area in the recent past. However, real progress is still possible based on new experimental studies of a high level of quality over a considerable part of the dose-response range. For example, the TCDD and AHH data set argues against the use of the power law as a dose response extrapolation method. Similarly, theoretical model construction and mathematical studies of substantial sophistication can be done to advance the current state-of-the-art in risk assessment. Moolgavkar type models are examples of progress being made via the construction of theoretical models in the carcinogenesis field. Because the current cost of computing systems keeps coming down, the overall prospects for improvements in the low dose environmental world may be brighter in the theoretical camp than in the experimental camp right now. One could not end this commentary much better than to draw attention to David Hoel's concluding sentence "What should be said is that low-dose linearity is speculative and it is a reasonable assumption for public health purposes in those instances where there is no scientific evidence to the contrary."

References
1. Crawford, M. And Wilson, R. 1996. Low dose linearity: The rule or the exception? Human and Ecological Risk Assessment 2(2): 305-330

2. Pitot, H.C., Goldsworthy , T.L., Morgan S., Kennan, W., Maronpot, R., and Campbell, H.A. 1987. A method to quantitate the relative initiating and promoting potencies of hepatocarcinogenic agents in their dose-response relationships to altered hepatic foci. Carcinogenesis 8: 1491-1499

3. Farmer, J.H., Kodell, R.L., Greenman, D.L. and Shaw, G.W. 1979. Dose and time response models for the incidence of bladder and liver neoplasms in mice fed 2-acetylaminofluorene continuously. Journal of Environ. Pathology and Toxicol. 3, 55-68.

4. Moolgavkar, S.H. 1986. Carcinogenesis modeling. From molecular biology to epidemiology. Ann. Rev. of Public Health 7, 151-169.

5. Kitchin, K.T. and Woods, J.S. 1979. 2,3,7,8-Tetrachlorodibenzo p-dioxin (TCDD) effects on hepatic microsomal cytochrome P-448 mediated enzyme activities, Toxicology and Applied Pharmacology 47: 537-546

6. Kociba, R.J., Keyes, J.E., Beyer, J.E., Carreon, R.C.,Wade, C.E., Dittenber, D.A., Kalnins, R.P., Frauson, L.E., Park, C.N., Barnard, S.D., Hummel, R.A. and Humiston, C.G. 1978. Results of a two-year chronic toxicity and oncogenicity study of 2,3,7,8-tetrachlorodibenzo-p dioxin in rats. Toxicology and Applied Pharmacology 46: 279-303

7. Kitchin K.T., and Brown, J.L. 1996. Dose-response relationship for rat liver DNA damage caused by 1,2-dimethylhydrazine. Toxicology 114: 113-124.


RESPONSE TWO
Bernard L. Cohen
Physics Department
University of Pittsburgh
Pittsburgh, PA 15260
Tel: 412-624-9245
Fax: 412-624-9163
email: blc+@pitt.edu

I hope it is clear to all that the paper on "Low Dose Linearity..." by Heitzmann and Wilson (hereafter H-W) has absolutely no relevance to the current debate in the radiation health effects community over use of the Linear-No Threshold (L-NT) paradigm.. H-W points out that, if we know the slope of the dose-response relationship at the high end of the region of background radiation, what mathematicians call "analytic continuation" requires that the dose-response relationship for small amounts of incremental radiation, such as that caused by our technology, must be linear with this same slope. This has no relationship to the slope used in current practice based on L-NT which is derived by drawing a straight line from the well established dose vs response data points at high doses down to the origin. For example, that procedure obviously gives a positive slope indicating that low level radiation is harmful, whereas in the low dose region where H-W is applicable, the slope may well be negative as expected from hormesis considerations. There is certainly no evidence contradicting this possibility and there is a substantial body of evidence supporting it. If that slope is indeed negative, H-W requires that the dose-response relationship for low level incremental radiation, such as exposures from the nuclear industry, also have a negative slope, which means that these exposures are protective against cancer.


RESPONSE THREE
John T. Barr
162 Brandywood Dr., Easley, SC 29640

Those who support their belief in the philosophy of low dose linearity by the assumption of additivity of effects from background and ambient exposure indulge in circular reasoning of the most obvious type. The very assumption of universal low dose additivity of effects denies the existence of a no-effect level. That unproved assumption is then used to demonstrate its own accuracy.

Perhaps it is not surprising that this fatal flaw in regulatory philosophy is supported primarily by nonbiological scientists and by regulators seeking to justify their own conservative regulatory policies. It is most unfortunate that these supporters fail to heed the advice of Heitzmann and Wilson that "it is important --to have some understanding of the underlying biological mechanism(s)." They offer no supporting experimental evidence, but nevertheless insist that their philosophy be examined yet again. Perhaps the "remarkably little attention" that they say their philosophy has received to date is not for want of examination, but for want of acceptance by the mainstream of science.

There are other fatal flaws of the linearity philosophy such as total lifetime dose, which even the EPA confesses it cannot justify on a scientific basis, and the ignoring of the concepts of dose to target organ and latency, both of which require some knowledge of biological mechanisms.

I and more than 99% of my colleagues who received significant exposures to vinyl chloride 25 or more years ago are living proof of the existence of sequential thresholds which must be exceeded before clinical effects are found. First, there must be sufficient exposure for the vinyl chloride to be absorbed through the lungs and transported to the liver. Next, the detoxification capacity of the liver must be overwhelmed. Then the defense mechanisms of the arterial wall cells must be defeated. Finally the immune system as a whole must fail. In our case less than 1% of the most heavily exposed persons developed angiosarcoma in their livers. This occurred with an average latency period of about 25 years, ranging from about 16 to over 40 years. This time does not seem to be dose dependent.

It is unthinkable that all of the biological evidence demonstrating the necessity of no-effect levels be disregarded, and most especially the great body of evidence developed by the CIIT, and that brought forth by BELLE itself in recent years. Both organizations distribute regularly summaries of findings that even a layman can understand. We should not be deterred from our support of these very valuable endeavors by yet another bit of wishful thinking.