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Critical approach of mathematical extrapolation Prof. Etienne Fournier (free translatiion not checked by the author.)

A critical study of inethods of assessment of the effects of low doses P. Etienne Fournier (1993) This paper sets out to be a consideration of the positions taken by experimental toxicologists and regulatory bodies for more than 40 years and on their necessary confrontation with the facts from hutnan observation conducted by clinical physicians and, preferably, by clinical toxicologists. One objective is apparent, in any case part of all the legislation - that of suppressing - in theory completely (objective 0), in praetice.in such a way as to become indiscernible, and at worst to reduce substantially - ailmeats connected with.the absorption of chemical products howeverr absorbed and the clinical course of cancer.. Let us admit that in the usual constitution of discussion panels, clinical toxicologists (representing internal medicine or working mediciae) although the only qualified observers, are practically excluded from the final report in favour off experimental toxicologists or analysts. This is not a paradox, since each of their contributions stresses actual facts including a strong probability of correlation N . Q between a known exposure and the too premature, too frequent jV and excessively atypical incidence of certain cancers. W From these comes the set of agreed procedures which are

t transcribed and quantified to achieve national and interAational regulation. Calculations in this matter are those of epidemiologists and biostatisticians and evaluation.of doses those of-analysts: A first logical., quasi-mathematical, relationship will be established: For one exposure to xl ppm in the air or for oral absorption of x2 mg/Kg/day, n cancers appear (in the context of the study: target population, - exposure tirae, time before appearance, & -). A second relationship, no less classical, normally follovs. it is defined in accordance with methods which avoid the essential bias of the number of these cancers observed in a reference population suffering no exposure to the target chemical hazard. In general, it results in a mortality coefficient implying excess mortality for a defined exposure . From the moment when the set of. interpretations begins, the most frequent being a major increase through a purely formal movement to sufficiently large numbers: For example, if Xhas observed.tWo fatal cancers in the target population and only one in the control population, Y can say that the SHII2 ratio is 200%. Whilst recognizing ~ immediately that this simple cutline is not only ~ unacceptable but is far from representing the reality of the ~ cancerous condition. ~ ~ ~ 0

a) Most common hormone-sensitive cancers currently treated are cured or benefit from a prolonged remission. Indeed the morbidity of cancer is exceptionally well-documented. b) The relative importance of cancers subject to hormonal influence has not ceased to grow and this group does not alvays have an obvious connection with toxic impregnation, with the exception of thyroid cancers, although an associated effect should be observed. c) Conversely, cancers appear in subjects. treated and cured by the use of radiation.or drugs primarily acting on DNA. d) Other pathological phenomena certainly recognized apart from the transmission of transplacental products, individual predispositions in individuals who are carriers of inherited cancers, identify genetic criteria in families where.;the _ preponderance of cancer amongst the causes of morbidity is important. This notion is particularly useful in the study of childhood cancers. This is found in an exaggerated manner -in subjects who are carriers of inherited abnormalities relating to the DNA and its repair, and who present a greater prevalence of cancers of the skin or blood ( leukaeatias and lytaphomas ). There are too few such families to identify from them response criteria to chemi.cal.products. And caffeine, the classical inhibitor of DNA repair, has no demonstrated in experimental carcinogenesis.

el The jtvout cotamon cancers of c2iemi.cal origjn are cancers of the lun$ due to chronic addiction to smoking uith constant e:.poeure to several grams of carcinogenic substanoes over the bronchial anicous Meatbr+sne, phot:oeensitive Skin cancors susceDtiblE to activation by cheia.ical products and oL the bladder atter excessively prolonged iatpregnation (aromatic amines). In all thrco cases cellular expoaura is massive and. prolonged_ AcbestoE cancers in the form of MPsothelivcna arc consparable with them becau.Se of a considerable accumulation of asbcetos fibrilla irreversibly accWaul•ated in the serous nteabra,ie. In fact, human cancPrs due to chemical produets (the "may cause human cancer" categoty) appeac after long periods of close and significant contact betveen a cellular type and t.he product itsplt or its sattabolites. The "one bit - one canc:er' hypothesis should therefore be quesLioned. This slogan is suspect because it is a Sloqan. It cannot simply be accepted. Clinicians have urv+x taken eteps to observe a cancer occurring after one single minimal contact, which certainly dv"s not mean that this method of occurrence cannot be suggested as one possible hypothesis. F.ach individu&l is free to express his views. But this firet attitude, an extreme one, is also one v2xic.ti prevents all subsequent 4

, ' discussion, since no individual has been totally protected from the sun or fumes. In advance we are all cancerous - which will perhaps be confirmed but in different vays. A better quantitative approach to the initial mutation phenomenon might be assessment involving tests on procarocytes of the 'mini.mctm concentration effective. In the usual literature, the biologist looks for an obvious effect which he calls positive and which he contrasts with doubtful or negative results. It vould•be interesting to test the molecules by specifying the threshold-concentration from observation of a rise in mutations compared with the spontaneous mutations of the original preparation_ Even if we do not know the cause'of-spontaneous mutations we may assume that they relate to a random process on the scale of a micro-organism vhich becomes a measurable constant for the population, and the deviation from'the constant may be a good experimental index for the effect of loW dose- concentrations (less thaan 1--9M). The same reasoning is proposed for organs and their cellular population_ Proaposed extrapolations . a) an3.ma1 references conditions, the logical stance would be to take experimentan Since no cancer due to a chemical product can have been observed in man in the purest imaginable environmental data supported by control animals reared under rigorous

conditions- water, food, air, accommodation and free of viral immunological reactions. Even If all is not yet perfect in the field of good laboratory practice, experimenters are nearing perfection. They also note that the spontaneous mortality, apparently inescapable, of such animals is largely of cancerous origin, and that the date of appearance of cancers depends on the species and the breed. N.B. 1 Epidemiologists, for their part, give us to understand that the prevalence of human cancers is a function of age: kA5, but this proposition has only modest consequences if the average lifespan varies little from one population to ano.ther.'Thus the variation from 70 to 75 years (considerable average variation) only increases the probability caused by 41.%. N.B.2 An extrapolation by linear or even semi-Zogarithmic function towards doses - or concentrations - considerably lower than those for which cancers have been observed in man or animals, leads to non observable rates of effect still comparable with the initial doses, generally very high (n mq/Kg/day)- over some forty years an abstract approach has developed based on hypotheses which at first were the interpretation of extremely simplistic elementary principles but which have evolved through the introduction of the biological knowledge accumulated during recent-years and the biology of DNA. W

Let us briefly recall them: First h_vnothCs.is: only one particular shock - production of a single radical OR* - causes DNA to explode (cellular death) or deforms it sufficiently for the cell to become uncontrollable (one hit one cancer). Apart from its fundamental drawbacks, the hypothesis ill applies to the absorption of chemical substances or to the effect of their metabolites. Avogadro's constant 6.02 1023 implies that the nanogram supports an average of 3 10 12 reactive poles. This is considerably more than can be supported by an organism if each cell absorbing a single reactive molecule were to become cancerous . Secp~hypo hesic: It refers to the most generally accepted knowledge of cancerisation, the current theory 'making to succeed' an initial stage which remains latent in successive phases of advancement. If the same molecule is initiator and promoter, the hypothesis of a multiple stage reaction is acceptable. Unfortunately our knowledge about promoters is still very hazy compared with what we know about initiators and complete carcinogens. If we admit that a very large number of molecules such as some phenols are promoters and that the human being always carries them, we are brought back to the previous stage. For initiators the current theory.would be that of

incomplete repairs leaving adduits???-mutations in place, becoming more and more numerous. For promoters a consensus without formal reason agrees somewhat shamefacedly to consider that they only act above a certain threshold. ThjXd hvoothesis: This results from knowledge of anticancerous genes - emerogenes. These can equally FTell be stimulated by both chemical products and pro-oncogenes. Similarly, damaged DNA excision-repair phenomena unite to predict the appearance of immortal cells with carcinogenic potential. The theory seeks a differential function between. the initiator effect and the-repairer effect. h hvflathesis: Coming finally to the in situ control of frQur,t formed cancer and its own evolution by metastases, attacks and phases of stabilization. The simple theory holds that once formed, the i.nitiated and promoted cell divides in an inescapable way. In this case, whatever the duration of a pathological division, the carrier of the cancerous mass should die within a few days or months, Which is effectively observed in acute forms. The actual phenomenon becomes at least doubly random - uncertainty about the progress uncertainty about regression - in so far as we are of gauging the different factors and measuring the cytokines which regulate the complete process_

Matbematical analysis of sequential and contradictory cellular phenomena calls on models of physio-pathological regulation. In respect of mathematical carcinogenesis, we are unfortunately at the point where the ancient Egyptian surveyors of a random expanse - the silt of the Nile - were, before fundamental data about plane geometry. But additional data is gradually appearing. Evaluation of resistance to a cancer has barely begun. For we already knflw that not all asbes-tos workers die of inesothelioma even if exposed to the maximum amount of dust. oa a simpler mode, not all the bacteria of the Ames systemm mutate when they divide in a milieu containing a reference carcinogen, but.it is clear that the random nature of the mutation is located at a level other than that of the non exposed population. The deregulation is explained by a coefficient of ntutageaesis: It is in hotnolog.ous terms that the coeff icients of morbidity (rarely recognized) and mortality (which are only valid for cancers which are often fatal) appear_ Uncertainty increases in the proximity of the coefficient 1 in as much as the first serious observation was that of the "healthy worker effect" which brings the coefficient to 0_8 during adult life. Hence faced the extraordinary by biologists conf us ion of demands and doctors who admit for nil risk, N that this N ~

is strictly spaaking unrealistic (Krewoki et al 1984). vhicil is not to say that to propose and tolerate au added acceptable r.is}s (between 10-5 and 10'8) makes more sea9e: 10-5 x 70 ycaars: about 6 ttours in terms of lifo Qxpect.ancy. The biologist acCustomed to margina of error othervise large has a poor gracp of the practical value of attitudee, vhich may be compared to a proposition of Pure Behavioral Act: Art. 1"the designated population ehould livp without sin". Should the risk of 51.nning be aqrezd to be 10'S or l0'8? Should attempts at QvalUatinq a carcinogcnic effect ha similarly rejected vholesala? The answer is certainly no, proviCed.:tLe limita of models are knovn. * N_B. I sxou1Q especially like to thank ProfessorG A.J. Valleroa and G. Thomas, who describrd to me the methods uFerl and thc limits of uce. a) The model with threshold (tolerance model) assumes that a subject exposed tv a dose (cumulative) of a carcinogen vill develop a cancerous tumour if the dose exceeds a thrweholQ called a tolerance_ Various approaches are suggested (see Appendix). These models are only valid for binary situations exe-TuCirig all interference from otner factors, eliednating the time tac(.or to the advantage of thee single cumulative Cose. Elemental toxicology, throughout life, p®rmits thesp calculations_ 1a X

These models are however little used, for it is rare that human observations concern more than three situations: A lot, a little, or no chemical product. Experiments on animals rarely involve more than three to four doses: one close to the maxiTUum dose more or less well tolerated (in the general sense) by the animal; another fairly low dose -;,& selected in the reasonable expectation that nothing will be observed; and one or two intermediate doses which are the only ones genuinely compatible with a sub-normal life expectancy_ In these conditions it is difficult to draw up a graph with a single point - or two - and the regulations most frequently allow for the lowest dose which shoWed no effect (NOEL). Nodels allovi.ng for the effect of time Time is a fundamental variable of carcinogenesis but its introduction necessitates a biological unity such as average life span or the extreme life expectancy of the species or ethnic group, or that of the appearance of perceptible phenomena of which cancers form a part. There is no consensus about the mechanism of the increase in the prevalence of cancer according to age (accumulation of errors, progressive chromosomal abnormality, perigenic abnormality of the histones, epigenetic abnormalities of cellular regulators (hormones, adenylcyclases, calcic mediators etc.), but an experimental gain is confirmed by 1/~

monitoring animals throughout their lives_ Little by little the notion is taking hold that in certain mammals the prevalence of cancerous mortality becomes preponderant in excess of 70%. In man the situation is evolving in the same direction although the part played by degenerative causes with cellular death remains high. If the average life span reaches 80 years cancerous morbidity should become considerable. N.B. This discussion is different from that about the sensitivity of elderly subjects to exposure to carcinogens. Models using time refer to empirical models called log- linear, of the type T (probability - distribution according to observation) + exp' (Bl Z + 6W) p. vector p. vector actual random variable of parameters of functions of a single dose or of regression (Lox) y (t:d) = yo (t) exp (o'Z(t))) and to models based on biological hypotheses: multi-hits, multi-stage. These already old models like those of Fisher and Bolloman (1951) have had the merit of taking parallel events into account (more than six cells transformed together - abandoned- ) or more DNA disorders (6-7 0 ~?

successive mutations on the same cell). The latter argument was essential to explain why the-incidence of many human cancers would grow with age to the power of 5 or 6. We acknowledge that currently the appearance of a cancer supposes at least two, and probably fewer than seven predisposing factors affecting one cell. The model derived f roai the work of Moolgavkar, Venzon and Knudson (1981) results in an- outline consisting of normal and intermediate cells and those proliferating out of control, capable of reproducing themselves as"they are, of leading to the later stages, or dying. Recent models associated vith validated experimental or epidemiological data, studies of absorption or metabolisms, encompass usable results for childhood and adult cancers_ Progress is therefore genuine with the possibility of comparing very closely connected different ethnic groups and /or chemical products. What about low doses? First, one cornment must be made. Extrapolation has almost always been from models kinown as tolerance models which presupposes the absence of effect below a certain dose. As continuous functions do not prevent extrapolation below this dose, mathematicians have noticed that according to the models, at origin the slope goes from 4 to infinity but if N what is knovn about carcinogenesis and the kinetics and 0 ~ ~ ~

metabolism of the chemical product are taken into account, the latter argument leads to linear methods of extrapolation tovards loW doses,.vhatever the model. It therefore seems essential to require biomathematicians to adopt a less contradictory attitude towards the significance, omission and evaluation of a threshold: Extrapolation from.what? If* it concerns cancers which are very rare in the general population, their appearance defines an absolute.risk and makes it possible to establish a dose/effect relationship from an accumulation even limited to exceptional cancers (absolute risk). If the number of cancers is greater than tbree this suffices in principle to define the risk in a human group and to research the part played by genetics and acquisition. The. essential problem is- the bringing together of cases, achieved through a toxicovigilance program examining scattered cases (speregic phencxaena). If it concerns common cancers the added risk from the chemical product is only relative. Multiplication of a relative risk by an appreciable factor is only possible with large size cohorts and comparable populations: 1000 people are needed to guarantee confirmation of a risk x 3.5, about 5000 for a risk x 2 and about 10,000 for a risk x 1_5. Now such investigations often undertaken in professional ~1~

pathology require guarantees of good epidemiological practice whose details are still under discussion, vbich means that many already published studies risk sufferinq from bias or procedural error and should be considered with caution. F.xpert consensus There are two kinds of expert consensus: a) The most frequently encountered kind brings together experts provided with secondhand documents or already drafted summaries. The conclusions of such meetings are simple and result in a genuine consensus. In other words everyone agrees to reduce the reference indicated by a factor of 1000 (10 for species, 100 for the highest rate without cancers, NoEL). we are in the habit of accepting a regulatory attitude from such information because the number of experimental cancers observed in the current anti-vivisectionist conditions (40 to 50 animals per group) corresponds to a high proportion, several cancers per hundred human beings. Such a prediction, which is very disturbing, justifies the two stages: recognition of an NEL rate (the observable term limiting confirmation by observation of 'an unlimited population) and moving to a rate said to be acceptable (10-1 x 10'Z) whilst knoving that this rate ought never be observed in the present environment of the general population.

b) the other expert attitude is described as the Delphi method based on the anonymity of contributors and the progressive interaction of a group of experts. The question defining the objective is.posed in successive "rounds" until the appearance of a convergence, a little like convergent sequences in mathematics_ Of course, the sequence may not converge, or may aim at two different and incompatible points, but it is a process used more or less consciously with regard to modern regulation. In practice, regulatory bodies are content vith an extremely crude dose-effect relationship, most commonly limited to comparison of the effects of two doses. It no longer concerns models. The reduction coefficients usually applied by groups of experts in chronic toxicology (1/100 NOEL if there is neither mutagenesis nor experimental carcinogenesis, 1/200 to 1/500 if there is only mutagenesis, 1/100 if there is carcinogenesis) well represent the average result of current considerations regarding cancer prevention. When part of the conclusion is disliked, they start again. This is a quasi-Delphi. Perhaps it would be useful to-afld to each product a real elemental model adapted to toxicokinetics and the experimental criteria of a corsolete carcinogen, an initiator, a promoter and its fate in the organism2 c) Other contributors will probably wish to discuss the ;~E

beneficial and adverse effects of low doses if reputedly toxic products are involved. This point, the traditional basis of homeopathy, has been evoked in the face of leucose graphs as a function of the radiation dose suggested by a slope which is slightly negative at origin_ The positive, negative or complex quality of the coefficients of representative functions permits the suggestion that models of'this type and the Belle group are forced to give a scientific basis to this type of reasoning. True cellular protection within narrow limits can be envisaged if the genes preventing cellular access or repair are more sensitive to the product than pro-oncogenes. Would a first reference be greater affinity, a larger number of identifiable adducts? The formation of antibodies is another possible effect of low doses. d) What has to be weighed is the risk of presence and the risk due to banning. We should at least admit that linear extrapolation toward the origin is a theoretical artefact, that numerous arguments are opposed to a simplification which eliminates the obvious idea of a tolerance-threshold, which animals demonstrate with not small doses administered throughout their lives without apparent adverse effect. What also has to be admitted is that the rates deemed, /1 ~-

acceptable vith a risk in the order of 10-6 are guarantees uhich it is especially advisable to veigh against the ri.sk associated with a ban on the product. In outline, three iliustrative cases may become apparent: the adverse risk (appearance of over-representation of cancers~ exceeds the adverse risk associated uith a ban, it is less, it is comparable. This point is alvays tackled belatedly vhen the regulatory bodies try to reverse a manifestly erroneous decision. In general conclusion: We have the means to bring together medical observation of human cancers and assessment of a cumulative exposure (concentration x years of exposure). We have the means to brit~g together the most detai3ed observation of animal cancers and a fairly precise assessment of an exposure (concentration or dose x months of exposure) of a very small animal population_ The concentrations used for anf3ma~,'s are usually clearly greater than those correspor~ding to ht~tan exposure _ We have experimental tests urith a semi-quantitative predi.ctive value regarding the #.nitiati.on, promotion and formation ot cancers. These tests refer to a range of concenttations usually much higher than the tvo previous concentrations. N O ~ V O ~ ~.

The experts do not agree on the simplest definitions: For example, the European term, Guide-Line, means an expression of a principle to be followed categorically_ in Japan it is interpreted as the minimum demand required and in the USA as a reference opery to discussion case by case_ And each body is primarily organized around its own doctrine which it refuses to modify on the grounds that the system has worked until now. Most of the regulations only accept the notion of a threshold if there is no argument in favour of genotoxicity. Nov the most obvious test, relating to a: very large population, that of B, Ames demonstrates from the evidence, that for most molecules tested rpthing,is observed below a concentration which has to be called the threshold concentration. Under these conditions, the "worldwide" extrapolation to low doses appears to be a purely intellectual exercise which does not rely on any biological argument but which has the merit of reminding us that the essential mathematical operation in the life sciences is the rule of three. other approaches Perhaps it would be more effective to move closer to the N analyses of the engineers in charge of the complex systems ~ which define the reliability-probability of a system which X W d'oes not break down within a given period or in the course ~ UT %I 06

of accomplishing a defined task - and operating safety, a complementary aspect of the risk of breakdovn: P (safety + risk) = I if we assume vhile simplify3.ng considerab3y that the sole animal risk (spontaneous and variable) in laboratory rodents is cancer, and that in man this risk predominates vith regard to the epidemiology of mortality and the evaluation of an "extra cost" of chemical-origin, it will be possible to individualize and evaluate a) cellular systems evolving in parallel (the global risk is the product of the risks on each element), b) systems evolving in series (the global risk ls the sum of the elemental risks) for high risks reaching several V of the-population, the orl:yy ones accessible to mathematical epidemiology. c) the mean time betveen failures (MTBF). Evaluation of small risks will remain difficult, precisely because the "chemical cause" for very low doses will never be the principal cause if not, it is this dose vhich has to be considered as the primary reference - but only as one element amongst scattered and' fragmented causes. Paris April 1993 References 0 N Armitage P., Do11 R. W The age distribution of cancer and a multistage theory of th e carchiogenesis Br , J. Cancer 1954; 8; 1-12 ; Ilirnbaum LS. Age-related changes in drug dispos9tion in: Zenser T.V.& Coe R.M. ed Cancer and aging Springer Verlag 1989 pp25-138 ;I

Crump K.S. Hoel D. G.,_ Langley C.H. Peto R. Fundamental carcinogenic processes and their applications forr low dose risk assessment Cancer Res 1976; 36 ; 2973-2979 . Hartley H.O., Sielken J.R., Estimation of safe doses in carcinogenic experiments Biometrics 1977 ;33 ;1-30 I.P.C.S. Principles for evaluating chemical effects on the aged population Env Health Crit. 144 1993 W.H. O. Geneva Moolgavkar S.H., Venzon D,j'. Two-event models for carcinogenesis: incidence curves for childhood and adult tumors Math Biosciences 1979 47, 55-77 Rai K. Van Ryzin J.A. - A generalized multi-hit dose response model for low-dose extrapolation Blonietrics 1981 ; 37 1; 341-352 Sankaranarayanan K. determination and evaluation of genetic risks to humans from exposure to chemicals . Prog Mut Res. 1982; 3 .; 289-321 Valleron Aj, Bignon J., Hughes J.M., Hesterberg T.W. & al Low dose exposure to natural and man-made fibres and the risk of cancer : towards a collaborative European epidemiology : 13r . J; Ind. Med . 1992 ;49 ; 606-614 . Valleron Aj . Thomas G. Methodology of carcinogenic risk assessment at low doses 1993 (to be published) Vijg J., Papaconstantinou J. Aging and longevity genes strategies for identifying DNA sequences controlling life span J. Geront . 1990, 45 (5), B179-B182 %-- J

Table 1. Tolerance dose response models Tolerance distribution: Model Probability of respo nse at dose d x2 oc+~llogd 1 - Lognormal Probit J 2 dx ((3 > 0) 0 2n Loglogistic Lo it 0 g I +e_(atai o9di (0 > ) Gamma Gamma multi-hi[ ade-xXk - J ~ dx (k 0 o r(k } > , a> 0) Extreme value Weibull 1-exp(-(3 dm) ((i > 0,m > 0) 1 2_

2.2.1. Empirical models 2.2.1.1. Log-Ilnear models Any probability distribution with support the positive real line may be postulated for T. It is thus obviously convenient to consider log-linear models, of the form : T - exp((c + (3 logd + aW) where W is a real random variable. Table 2 presents severai possibilities. Table 2. Log-linear models Distribution of W Distribution of T Normal Lognormal Exireme value Weibull Logistic Log-logistic More generally, one can consider the models : T = exp(PIZ + aW) where 0 is a p-vector of parameters and Z a p-vector of functions of dose alone. ?_ ~