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-1- Threshold levels Some thoughts Author : P N Lee Date : 25.3.91 Introduction For many, if not all, diseases the direct epidemiological evidence of harm to passive smokers as a result of their exposure is unconvincing. Nevertheless some have concluded harm based on an inferential argument as follows: (i) Smoking results in an increased risk of the disease, (ii) Smokers and passive smokers are exposed to essentially similar smoke constituents, (iii) There is no evidence that there is a "threshold", i.e, a level of exposure below which no effects occur. In this note, I will not concern myself with (i) or (ii) but restrict attention to points relevant to (iii). Some mechanisms uroduce a threshold, some don't Suppose I cross a road with my eyes shut (and my ears closed) and that cars, when they come by, go at 60 m.p.h. It is clear that my probability of death or serious injury decreases as the frequency cars come by decreases, but exceeds zero as long as the frequency exceeds zero. There is no threshold - however infrequently the cars come by, there is risk. Suppose now the frequency is constant, but the speed varies. Again the probability decreases with decreasing speed, but here clearly there

will be a threshold. No-one gets killed by cars that go at 1/1000th of a mile per hour (at least assuming one walks across the road carefully enough to avoid killing oneself walking into an effectively stationery car, and ignoring minor possibilities like falling over, having an epileptic fit, lying stationary and then being run over very slowly!). Clearly these examples may not be very close to the real life situation but the message is clear enough. Some mechanisms produce a threshold, some don't. One needs to know the mechanism to know whether a threshold exists. Proving or disnrovin¢ a threshold Suppose, at a given dose level, one observes a frequency of response of zero. Does this mean the dose is at or below the threshold? Of course not. The possibility of a true small risk existing, but the data set being too small to observe any responders, is not excluded. However large the data set, a zero response only allows one to make a statement such as "I am 99.9% certain risk is less than 1 in 109". The data may be consistent with zero risk, but they are also consistent with some risk. On the other side of the coin, observation of a dose-response relationship over any dose range does not exclude the possibility of a threshold existing below the lowest dose studied. Even where the dose-response relationship appears linear through the origin, it is always possible to fit a straight line which intersects the zero response point at a dose slightly greater than zero, or to fit a somewhat curved line that does the same. It has been claimed that no threshold exists for smoking/passive smoking and lung cancer because the data on active smoking show an increased risk at the lowest exposure level tested. So they do (if one combines evidence from the lowest cigarettes/day

-3- groupings from the major studies, an increase is very clearly seen) but the argument is illogical. In any case the lowest grouping tested is usually something like 1-5, 1-9 or 1-10 cigarettes a day, which is not that low. :. D_i£ference between toxicolop:ists and cancer researchers Toxicologists are brought up on Paracelsus who believed "the dose makes the poison", i.e. everything is harmful above a given dose. Their training is to believe in thresholds. When testing a compound for toxicity, the procedure is to test at very high dose levels to determine what the toxic effects are and then test at decreasing dose levels to determine at which dose level no effect can be seen under standard test conditions. Formerly termed the "No-effect level" it has more recently been referred to as the no observed effect level (NOEL) in recognition of the fact that one can observe, but not prove zero. Although toxicologists may recognize that there may actually be some true effect at the NOEL for some compounds, they will generally believe in the existence of a true threshold. - The data for acute nicotine poisoning tend to support the toxicologist's view. One knows that 100-150 mg of nicotine is very often fatal to humans. However 1-3 mg, as from smoking, has never as far as I know been reported to cause death by acute nicotine poisoning, despite the fact that this is the dose of nicotine from a single cigarette and the number of cigarettes smoked by the human race comfortably exceeds IO1z. Cancer researchers who believe that cancer results from damage to the DNA of a single cell (which then multiplies) tend not to believe in thresholds. If one molecule of the compound can damage DNA and start off

-4- the whole cancer process, how can a threshold exist, they argue. As evidence in favour of the no-threshold argument, cancer researchers might cite the BIBRA nitrosamine data. In this huge rat study, exposed rats received 15 doses ranging from 0.033 ppm to 16.896 ppm. There was a very clear dose-response relationship for liver tumours and NDMA/NDEA. At high dose levels, where essentially all animals got tumours, mean time to onset reduced with reducing dose. At lower dose levels, frequency of tumours reduced with increasing dose and there was no real evidence of a threshold (although at the very lowest dose levels the increase in tumour incidence was not significant). Aside from the fact that there might still actually have been a threshold for liver tumours in relation to nitrosamine exposure had much lower doses been tested, it must be realised that there are compounds which show dose-response relationships which seem much more consistent with a threshold. A well-known example is formaldehyde and nasal cancer in Fischer rats, where the frequency of squamous cell carcinoma was 0/232 at 0 ppm, 0/236 at 2.0 ppm, 2/235 at 5.6 ppm and 103/232 at 14.3 ppm. In this case, it is believed that the carcinomas arise from other changes in the nose (degeneration, necrosis, inflammation) not evident at the lowest dose tested. There has also been an increasing tendency in recent years to classify carcinogens as genotoxic and non-genotoxic, it being evident that some compounds which cause cancer do not have any apparent effect on DNA. It is believed by many that thresholds are much more plausible for N non-genotoxic than for genotoxic carcinogens. ~ O N When it comes down to it, however, for a great many diseases 'i P Q! (including lung cancer and probably all the major smoking associated N CO diseases) not enough is actually known about mechanisms to tell to

-5- whether thresholds exist or not. "No-threshold" toxicologists and "one molecule causes cancer" researchers are both probably putting over a view that is over-simple and wrong in a number of cases. Before leaving this section, some further comments on the one molecule causes cancer hypothesis are worth making. Firstly, I do not find it convincing to say that if a dose is low enough cell repair mechanisms will cope with damage so that a threshold can occur even for a genotoxic agent. This relies on cell repair being absolutely 100% perfect. So long as some errors in repair can occur, the more damage the more the risk. Secondly, on the other side of the coin, I do not regard it as proven that there are no thresholds for genotoxic carcinogens. One could easily imagine that a concentration has to be above a given amount to reach the target cell or to do damage when it gets there. Some mathematical/statistica7l considerations Because a statistical model fits a set of data, it does not mean that the model is necessarily correct. This particularly applies to predictions of the model outside the observed range of the data. Thus, height of men may be well described by a normal (Gaussian) distribution in the sense that it predicts quite accurately the relative frequency of different heights in the 5 foot to 7 foot range, There is no particular reason why its predicted frequency of 7 foot 6 inch men will be very accurate, however. Although a normal distribution (and other statistical distributions) can be predicted under certain assumptions, the assumptions are usually simplistic and unlikely to hold exactly. Remember, many statistical models are merely convenient, and mathematically tractable, ways of summarizing data approximately. Dose-response relationships used for mathematical model-fitting typically

-6- do not assume thresholds. This is not actually because statisticians are too blinkered to realize there might be thresholds. Rather this is because models involving thresholds tend to be mathematically rather messy to fit. One point that has emerged very clearly from many mathematical/ statistical attempts to try to determine either thresholds or virtually safe doses (doses for which response is less than some pre-defined very small amount) is that the result depends much much more on the model used than on the data to which it is fitted. In the late 1960's and early 1970's I was involved in fitting multistage models to animal and human cancer data. Under certain simple assumptions, the principal one of which was that a cell had to undergo a certain fixed number of changes before cancer could develop, one could predict that the incidence rate of cancer (i.e. the probability a cancer-free individual gets cancer in the next unit of time) should be proportional to dose raised to one power multiplied by duration of exposure fitted to another. I fitted the model to a large experiment in which the skins of the backs of the mice were regularly painted with a standard carcinogen, benzpyrene, at 4 dose levels. Incidence rate (I) after t weeks of exposure in all four groups was beautifully described by the formula I - d2t3 where d is dose. Armed with these data I attended a US conference on low dose extrapolation. Could one assume that if one reduced dose further, by a factor f, then incidence would be reduced by f2? It soon became clear that this was not the case. The valid counter-argument ran as follows. Suppose that risk was in fact not proportional to d2 but to (b+d)2 where b is a small "background" dose representing risk from sources other than benzpyrene exposure. Here the incidence due to benzpyrene is (b+d)2 - b2 - d2 + 2bd.

-7- At high doses, where b is small compared to d, the term in d2 would dominate so that the dose-response relationship would look quadratic - and clearly the data would not distinguish the predictions from b- 0 and b - a very small value. At low doses, where d is small compared to b, the term in bd dominates, so that the dose-response relationship becomes linear. For a very low dose, the predicted response of the two models is wildly different. The problem is the appropriate model can only be selected if the mechanism is known. We cannot mathematically estimate thresholds or virtually safe doses unless the mechanism is known. In the above, we have considered risk relative to a background. The mathematical formulation assumed there in fact implied the mechanism by which the agent acted and by which the background acted is the same; - d was an additional dose. This leads to an important point. If the population is exposed to an agent in which risk is clearly dose-related and if one's concern is with another agent which acts by the same mechanism, then it is difficult to see how one can have a threshold (at least once the agent of interestt has reached the site where the known agent acts). Given smoking 20 cigarettes a day causes lung cancer and that risk increases with increasing amount smoked, it is difficult to see how ETS exposure - if it acts by the same mechanism as smoking - can fail to increase risk of lung cancer in a smoker. Smoking 20.01 cigarettes a day is more hazardous than smoking 20 cigarettes a day. Is ETS exposure below the threshold for lung cancer risk? While one cannot demonstrate that there is no threshold for the effect of exposure to tobacco smoke constituents, and my personal belief is that there probably is a threshold, I am far from convinced that all N ~ O N ~ A 01 N ~ N

passive smokers have an exposure to ETS that renders them at no risk whatsoever for lung cancer. There are two reasons for this belief. One is that, although we do not know which smoke constituents cause lung cancer, it seems reasonably clear that the exposure of the most heavily ETS exposed non-smokers is not greatly less than that of the lighter active smokers. The other is that humans are not identical and may vary materially in their susceptibility to the effects of smoke constituents for a number of reasons, genetic or environmental. For reasons I have given at length elsewhere, I believe the epidemiologically-based estimates of lung cancer from ETS exposure are far to high, but I actually see no reason to believe risk should be zero. Where next? Many of the arguments regarding thresholds are rather unproductive - trying to prove "absolutely safely" is absolutely silly, it could be argued. It is probably more useful to try to come up with estimates of average risk that are more sensible than the epidemiologically based ones and to try to argue that these are "de minimis". Levels of exposure to individual smoke constituents for passive smokers could usefully be compared with levels of exposure from other sources and to permitted levels in varying regulatory scenarios.