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Risk Analysis in Environmental and Occupational Health September 1, 1987 Uncertainties in Predicting Human Risks Edmund Crouch 1. Background Information It is useful to bear in mind a few sobering facts about total populations at risk, and the normal total risk of death and of dying of cancer. For the U.S., the total population is about 240 million, while the annual number of deaths is about 2 million per year and the annual number of cancer deaths is about 400 thousand. These figures imply an annual average total risk of death of about 10-2 (1 percent per year), and a lifetime risk of cancer of about 0.2 (20 percent, or 200,000 x 10-6), estimates you can obtain simply by dividing one figure by another. Of course, simply dividing one by another is not a particularly accurate way of computing such estimates -- one should do the correct thing and take the age structure of the population into account, and the var:Cation of risks with age, and so on. But even when you do precisely that, the average lifetime risk of cancer comes out to be about 20 to 25 percent. We can expect this figure to get higher as the expectation of life increases, and as other causes of death are eliminated (assuming -- pessimistically --that most cancers cannot be eliminated). It is mainly the increase in expectation of life which has made cancer such a prominent cause of death in the (historically) recent past, because cancers tend to be diseases of old age. For many cancers it is found that the death rate varies as a power of age:- rate - agen where the exponent n is in the range 4 to 11. For such cancers, this pattern seems to hold over the age range from about 30 to 65. At lower ages the rates tend to,be very small but almost independent of age (and the cancers may be completely different diseases in youngsters), while at higher ages the reported death rates are lower than would be predicted by this sort of formula - and in some cases the reported death rates are actually lower for old enough groups. It is unclear whether these reductions in death rates in the elderly are real, or are simply due to a difference in the accuracy of diagnosis and reporting. It is also possible that the reduction in reported death rates is real, but is due to the winnowing out of the population of those who are susceptible to these particular cancers, leaving a core of more resistant individuals. The major exceptions to the power law variation of death rate with age are the cancers which are known to be hormonally dependent ( e.g. breast: cancer), or are highly curable ( skin cancers ), or in which the natural progression is altered by interventicn ( e.g. a high proportion of women have had hysterectomies by age 65, so that they cannot be at

risk of uterine cancers thereafter). With this age variation of risk of cancer understood, we can now oversimplify again and quote a lifetime average annual risk for cancer, obtained simply by dividing the lifetime risk by an average lifetime of about 70 years. This give an average annual risk of about 2 - 3 x 10-3. Notice that we are here averaging over a lifetime -- the figure is not meant to imply that the risk is the same in each year of life -- we have just seen that it varies drastically with age. When discussing the risks of carcinogens, the same caveats have to be borne in mind. We usually attempt to estimate a lifetime risk, but may express this, for comparison purposes, as an annual average risk. For an individual exposed continuously to a carcinogen, we would expect that: the risk of cancer increases with age in a fashion similar to the risl: of other (naturally occurring) cancers. There is another reason also for quoting an annual average risk obtained by averaging over a lifetime. When estimating risks of carcinogens, one is often interested in the response of a population to exposure to the carcinogen. In this case, one should strictly (if it weree possible) estimate what the effects at all future times would be on individuals of different ages at the times of exposure. The effects at all. future times on the whole population would then be an average over the effects on all the.individuals in the population (who were of different ages at the times of exposure. Thus, to obtain an estimate of the effects on a population, one implicitly performs an average over the age groups present in the population. If the population were stationary (and if certain other conditions were fulfilled) this average would be the same as an average over a lifetime. This explains the usefulness of a lifetime average, since one may argue that the differences between population and lifetime averages are small compared with other uncertainties inherent in all the procedures we will describe later. The preceding discussion must be considered only a heuristic argument for accepting a lifetime average as being useful. In practice, people will be exposed at different ages, and for varying periods, to different amounts of carcinogens. All these differences (and many more besides) will affect the probability of carcinogenesis for each of them. 2. Knokm Htuman Carcinogens There is now good evidence that human exposure to certain materials can„ under certain conditions, increase the rate of human cancer. The evidence comes from various types of epidemiological investigation (discussed in other talks in this course). In all cases, exposures to these materials has been high, compared with population exposures, and the population exposed has been small compared with the total U.S. population. The resultant risks to those exposed has been substantial. The following table indicates a few of these materials, and the types of cancer which have been caused in humans by exposure to them. -2-

Also shown are the "natural" rates for such cancers, expressed in terms of lifetime risk and annual average risk. Material/Action Site Lifetime Annual or Risk Average Type Risk (In absence of exposures) ------------------------------------------------------------------------ 4-Ajninobiphenyl Auramine manufacture Benzidine Chlornaphazine Cyclophosphamide 2-Naphthylamine Bladder 5 x 10-3 7 x 10-5 Arsenic (compounds) Asbea tos BCME CCME ung x 10-2 x 10-4 Chromium (VI compounds) (Pop'. ave.) Mustard gas Nic:kel refining Arsenic PUVA Skin 3 x 10-3 4 x 10-5 Socts, Tars, (Deaths!) Mineral oils Vinyl chloride Liver 1 x 10-3 2 x 10-5 DES (In Utero) Vagina 7 x 10-3 9 x 10-5 Benzene Myleran Chlo:rambucil Leukemia 8 x 10-3 1 x 10-4 Melphalan Typically, in epidemiological studies, a relative risk of >2 is required in order to detect any effect. Thus the (epidemiologically) discoverable population average human risks are > 10-5 per year, or 10-•3 per lifetime, and probably much larger. For the small subgroups of the population usually available for study, the observable risks are generally much larger. 3. Target Risks. The Necessity of Extrapolation. When considering the size of acceptable risks to the public at large, the usual targets are much smaller than the discoverable risks discussed above. Typically they will be of order < 10-6 per year. Note that the EPA and the FDA set targets of order 10-6 per lifetime, that is, of order 10-8 per year. It must also be borne in mind that there are a large number of materials which are of potential interest. The Chemical Abstracts -3-

Service (CAS) has now given names to well over six million distinct chemicals which have been mentioned in scientific literature, and there have been various estimates of the number (around 50,000) of chemicals in general commercial use. With such numbers, it should be immediately apparent that there are jusi: too many time, money and logistical constraints to directly detecting any adverse effects from such a plethora of materials to which humans may be exposed. Notice that a risk of 10-6'per lifetime corresponds to a rate of about 3 per year in the whole U.S. population. Thus, even if the whole U.S. population were exposed to some material causing a risk of death of 10-6 per lifetime, the resulting deaths would be statistically indistinguishable in the usual two million deaths per year (unless there were something extremely unusual about the deaths). Extrapolation is therefore essential in order to estimate the sizes of risks, and hence be in a position to demand that risks be reduced to the levels mentioned. The fundamental observation on which such extrapolation is based is that: HUMAN CARCINOGEN -->implies--> ANIMAL CARCINOGEN In other words, every known material which has been shown to be a human carcinogen is also known to cause tumors in animals under suitable conditions. The only current possible exception to this is arsenic, but it is quite plausible that this is simply because it has not been tested adequately. This observation is not very useful in itself, but what is done in order to allow risk assessments is to assume its converse: ANIMAL CARCINOGEN -->implies--> HUMAN CARCINOGEN and to work from here. This assumption is not unreasonable, in view of what is known about carcinogenesis - although it is something which can be argued about in specific cases. 4. The Nature of Carcinogenesis. In what follows, it is useful to keep in mind some information about the process of carcinogenesis. This information has been derived from studies of humans and animals, and from experiments performed in vivo or in vitro. It is based partly on experimental studies, and partly on theoretical ideas suggested by those studies. (a.) Cancers arise from one (or more) individual cell(s) which have gone "out of control" in some way - the cell becomes immortal, with no limit on the number of cell divisions, and the usual constraints on cell division no longer apply. A cell may pass through several stages before reaching this state. (b.) The underlying cause of such behavior is probably some effect(s) on the genetic material of the cell, but the exact mechanism(s) is (are) unknown. -4-

(c.) The occurrence of such events appears to be a random process at some level. One cannot tell which individual cell or animal or person will be affected. Hence we talk about the PROBABILITIES of cancer - the chance that some event will occur. (d.) When we feed materials to experimental animals, these prob<<bilities depend on various factors which can be manipulated. For example, they vary with: The total AMOUNT of material (the total dose) The AGE at which dosing takes place The RATE OF APPLICATION, or the time over which dosing continues OTHER FACTORS (some known -- stress, dietary factors, others unknown) We therefore expect, and in practice observe, DOSE-RESPONSE curves. Such dose-response curves are fundamental in extrapolating risks to humans. I like to draw an analogy to the similar problem of extrapolation which arises for acute toxicity -- in both cases, we have measurement difficulties at low doses, and in both cases there is some sort of dose-response relationship (which I deliberately leave vague for now): i LIFE'T-IME PlZo g r OF Ti4w1oR cffACIrtcSt;-~rtEC iTy PRoe oF pEATN 0 (e,) Evidently there will be some AGE STRUCTURE to the probabilities of cancer. As mentioned, for many cancers in humans the death rate from cancers increases with a power of age. In experimental studies involving long term feeding of rodents, the same sort of age structure is found for the incidence of tumors. A "LIFETIME" probability thus depends on how youe measure it - the usual practice is to assume a "standard" lifeti.me of -70 years for humans and -2 years for rodents. (f.) At high enough doses ( i.e.. at high RESPONSES one sees interactions between different materials in both animal experiments and in human data ( e.g. smoking and alcohol consumption, smoking and radon exposure, smoking and asbestos exposure). The effect of such interactions is to make the effect of two or more materials different from the sum of the effects of the materials individually (at the same -5-

dosEs). (g.) It is not possible to make direct measurements of what happens at :Low doses ( i.e. at LOW RESPONSES ). In this context, low dose means a dose at which the response probability is < 0.1 usually, and 0.071 certainly. Any attempt at studying lower doses runs up against problems of logistics, cost and the background cancer rate. (h.) The shape of dose-response curves assumed for the low dose regions are thus based on: Theoretical ideas Prejudice Guesswork For performing risk assessments for human safety purposes, naturally a prejudice to be conservative. there is < It is generally agreed that assuming LINEARITY between dose and response (for our discussion, this means the lifetime probability of a cance:_) at low enough doses is CONSERVATIVE. This assumption is made in a theoretical way -- it is assumed that the true relationship between dose and response lies, at low enough doses, entirely below (or at worst on) a linear curve joining the response at zero dose (background) with the response at some higher (but still low) dose. VCTiME P2oBy ~ ~ -r n ~ i hc~~rcun ~ ; '~'t,Lm o l' I (c~~ 0 0 G~. Typically, the background rate is of order 10"4 to 10-1, and we are interested in excesses over the background of order 10-6 to 10-4, so this df.agram is not to scale. It is useful to define the POTENCY of a carcinogen as the ratio of excess lifetime probability of cancer to the dose causing that excess (at low enough doses). On the diagram, this is the rat:io i/d. The potency is thus the slope of the dose-response curve at low enough dose, and we have the basic equation: EXCESS RISK - POTENCY x DOSE There is reasonable evidence that some mechanisms of carcinogenesis result: in a THRESHOLD -- i.e. that there is some (threshold) dose below which the excess incidence of cancer is much lower than would be -6-

predicted by a linear extrapolation from doses above the threshold, and possibly that the excess incidence of cancer is literally zero below such a threshold ( excess, here, means excess over the background occurrence of cancer). Some of the evidence for such mechanisms comes from observation of the dose-response curves in experimental situations -- the experiments on saccharin provide a good example. However, there is still the possibility that a linear mechanism may still oper-4te at low enough doses, and so any human risk assessment has to take that possibility into account. 5. The Standard Animal Test. The requirements for a "standard" animal test are quite severe. The animals involved have to be as similar to humans as possible -- in metabolism, in being omnivorous, in their sensitivity to chemicals, for example -- yet as different as possible in their life span and cost of upkeap (so that we can get results in a reasonable time at a reasonable cost). In practice, there is little option but to use standard laboratory animals. The usual choices are rodents -- rats and mice; with occasional tests being performed on golden hamsters or guinea pigs. Other animals (e.g. gerbils) have been proposed, but for now the experience built up in handling laboratory rodents is a strong incentive for continuing their use despite certain known disadvantages. Any change would now have to be done gradually, and with much cross checking with previous results. ^:t is now standard to require tests to be performed in at least two specLes (practically always rats and mice) and on both sexes, in case one or the other species or sex is peculiarly resistant to the material under test. A compromise has to be made over the number of animals to test:. It would be desirable to have as many as logistically possible, to increase the statistical sensitivity of the experiment; but as few as possible to minimize the costs of testing (since there is always another material to test). The current recommendation is for at least 50 per group, of similarly treated animals. There is a similar trade-off between costs and the number of dose levels to test in a given experiment. The current recommendation is to havee at least three dose groups -- an undosed group (the control group), a group tested at the maximum tolerated dose (MTD) of the material under test, and the third group tested at some intermediate dose (usually 1/4 to 1/2 of the MTD). The MTD of a material is roughly defined to be as much as possible, but not enough to kill off the animals early or to cause too large other overt effects (like loss of weight). The reason for using it in these exper:iments is to increase the sensitivity, on the basis that giving more of something is more likely to produce a response if any response if going to happen at all. The sensitivity has to be as high as possible, since the observable responses are of the order 10-1 (10%) while the risks of interest are of order 10-6 (100,000 times smaller). The alternative way of increasing sensitivity is to increase the number of animals tested (within reason), but this only increases sensitivity in proportion to the square root of the numbers tested, while increasing -7-

the dose gives an increase in sensitivity roughly proportional to the dose. Clearly the latter is most cost effective. Even with such a minimum design, there are: 3 dose groups x 2 sexes x 2 species x 50 animals per group ' giving a minimum of 600 animals per experiment. All the animals have to be carefully housed (under standard conditions), cared for, and in(E _vidually tracked throughout their two year lifetime. They are then sacrificed and a large number of their tissues examined individually. None~ of this comes cheap -- the cost of such an experiment is unlikely to be less than $200,000, and may run above $1,000,000. It should be noted that the type of experiment detailed here is the minimum considered necessary to answer a YES/NO question: Is this material carcinogenic under the conditions of this standard bioassay? The. experimental design and analyses performed are designed to be unlikely to answer YES if there is no carcinogenic action present (so tha.t the experiments have low alpha error), but they can easily answer NO even in the presenci--,,of carcinogenic action. This sort of test is exactly what is required, of course, if one is interested in identifying materials which are surely carcinogens; in order to study their mechanism of action for example -- one doesn't want to accidentally end up with a material with no carcinogenic action. I would submit, however, that for the purposes of protection of public health, the questions asked of the tests are entirely the wrong way round. For protecting public health, one should surely ask not whether this material is almost surely a carcinogen, but how strong a carcl!nogen it could be, given the results of the experiment. The fact that the same sort of analysis is applied now as in the past is perhaps a combination of accident and inertia, but one has to admit that, for the most part, the methodology has been largely successful so far. 6. Raw Results - and what to do with them. Having spent 2 years performing the experiment described above, what output do we get? When the animals are sacrificed, they are dissected and a whole list of tissues examined, both macroscopically and microscopically. All lesions, whether related to cancer or not, are noted down and usually (nowadays) recorded in some sort of computer database. The pathologists performing the examinations usually use some sort of standardized nomenclature for what they observe -- for example, the National Toxicology Program uses a modified version of the Systematized Nomenclature for Pathology (SNOP). Other information about individual animals is also recorded -- such information as where they came from, which cages,they were kept in, when they died ( e.g. if they died naturally, or were sacrificed at the end of the experiment, or sacrificed earlier because they clearly would not survive), and so fortli„ The outcome is that for each animal, we have a list of the lesions affect:ing them when they died. An example of a condensed listing of just -8-

the. cancer-related lesions is appended. From such listings, we can perform various analyses and statistical tests to see whether the rate of cancer was increased at any site or for any type of cancer. The simplest sort of analysis can be performed if all the animals survived for the whole length of the experiment -- and in practice the same sort of analysis is performed provided a reasonable fraction survived that long and provided there were not too many early deaths. In that case, we can simply list the dose groups and the numbers of animals with tumors compared with the total number of animals examined; Dose Number Number with Examined Tumor 0 (control) 10 50 0.5 MTD 25 50 for example MTD 30 50 However, things are not this simple. Similar results are available for o Many different sites ( See below ) o Many different tumor types ( for examples ) o Combinations of these To dletermine whether the rate of cancer has been increased involves comparing the proportion with tumor in the control group with the proportion with tumor in the dosed groups, and deciding whether there is a significant increase in any dosed group(s). The choice of which sites and/or types of tumors to combine before performing such statistical tests can be difficult. Generally, various grades of tumors (nodules, adenomas, carcinomas) may be combined for any given site. Table 2 gives an example of the sort of combination and testing which is performed. In addition to the simple numbers of animals with tumor, there is additional information available which may be used in more complicated cases. The date of death of each animal is recorded, and may be taken into account in time-adjusted analyses of tumor incidence and in the life-table tests mentioned on the appended material. For risk assessment purposes, it is necessary to make various assi.unptions about the behavior of animals in experiments like these. For example, it is assumed that: o Animals are affected independently (a tumor in one animal has no effect on any other animal). o Animals are equally likely to be affected a Each animal receives the same dose .................. It is assumed that cage effects, littermate effects, the effects of heating, lighting, stress etc. are either not present, or are randomized among all the animals in such a way that there will be no effect on the final analysis. With such assumptions, the probability of an animal having a tumor is related to the dose'by some sort of dose-response relationship, so that at any given dose this probability can be computed. The observed results, a number of animals with tumor out of a larger number examined, -9-

is then a binomial sample with this probability. In practice, we don't know what the dose-response relationship is - we wish to estimate it from the results. But we assume that we know the SHAPE of the dose-response relationship (specified by a mathematical formula), so that all that is required is to estimate some PARAMETERS in the mathematical formula. For example, the E.P.A. uses a dose-response relationship of the fo.rrx : p == 1 - exp( - (q0 + q1.d + q2.d2 + .... + qk-1•dk-1)) when there are k doses in an experiment, where p is the lifetime probability of tumor at dose d. It is usual to use a maximum likelihood tec:h.nique to estimate the various parameters q0, ql, q2, ••• qk-1> given the observed numbers of animals with tumors and the numbers of animals examined at each dose. In cases where there is appreciable early mortality in the experiment, so that the observed numbers of animals with tumors are likely to be underestimates of what would have been observed at the end of a perfect experiment, one can make modifications to the dose response relationship, just as one can make life-table adjustments to standard statistical tests. One'technique used is to modify the dose response curve to explicitly include length of life, using the idea that probability of tumor is likely to increase with a power of age (see page 1) . p = 1 - exp{ - (q0 + q1.d + q2.d2 + .... + qk-1•dk-1) (t/j,)n} where t is the age at death, and L is a standard lifetime. The parameter n can either be fixed at some reasonable value (in the range 2 to 11), or estimated from the experimental results. This technique suffers from the same limitations as the usual modifications to the standard statistical tests -- one has to introduce additional assumptions in order to apply it. In this case, one has to decide whether the tumors were a cause of death, or simply incidental. An alternative technique used when there is early mortality is to estimate the age dependence directly from the data, using a (so-called) non-parametric technique. This approach has been used to assemble a large database of comparable analyses of animal bioassays. T',7is methodology has taken the raw results of the animal experiment, and summarized them in the form of a dose-response curve with known parameters. It is also possible to estimate how uncertain one is about a given parameter, using the same maximum likelihood techniques used to obtain point estimates of them - indeed, one can plot the uncertainty distri'_bution for any of the parameters. For example, for the parameter ql (which will turn out to be the one of interest), we can plot the probability that ql lies below any given value: