is ecological fallacy a fallacy

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This article was downloaded by: [swasti mishra] On: 10 July 2014, At: 08:59 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Human and Ecological Risk Assessment: An International Journal Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/bher20 Is the “Ecological Fallacy” a Fallacy? Fritz A. Seiler & Joseph L. Alvarez Published online: 03 Jun 2010. To cite this article: Fritz A. Seiler & Joseph L. Alvarez (2000) Is the “Ecological Fallacy” a Fallacy?, Human and Ecological Risk Assessment: An International Journal, 6:6, 921-941, DOI: 10.1080/10807030091124365 To link to this article: http://dx.doi.org/10.1080/10807030091124365 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Ecological studies of health effects due to agent exposure are generally consideredto be a blunt instrument of scientific investigation, unfit to determine the“true” exposure-effect relationship for an agent. Based on this widely acceptedtenet, ecological studies of the correlation between the local air concentration ofradon and the local lung cancer mortality as measured by Cohen have been criticizedas being subject to the “Ecological Fallacy” and thus producing invalid riskdata. Here we discuss the data that a risk assessment needs as a minimum requirementfor making a valid risk estimate. The examination of these data and a “thoughtexperiment” show that it is Cohen’s raw ecological data, uncorrected for populationcharacteristic factors, which are the proper data for a risk assessment. Consequently,the “true” exposure-effect relationship is less and less important the more populationcharacteristic factors are identified and the larger they are. This reversal of theusual argument is due to our approach: Here, the prediction of the health effectsin an exposed population is of primary importance, not the shape of the “true”exposure-effect relationship. The results derived in this paper hold for ecologicalstudies of any agent causing any health or other effect.

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This article was downloaded by: [swasti mishra]On: 10 July 2014, At: 08:59Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Human and Ecological Risk Assessment: AnInternational JournalPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/bher20

Is the “Ecological Fallacy” a Fallacy?Fritz A. Seiler & Joseph L. AlvarezPublished online: 03 Jun 2010.

To cite this article: Fritz A. Seiler & Joseph L. Alvarez (2000) Is the “Ecological Fallacy” a Fallacy?, Human and Ecological RiskAssessment: An International Journal, 6:6, 921-941, DOI: 10.1080/10807030091124365

To link to this article: http://dx.doi.org/10.1080/10807030091124365

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Human and Ecological Risk Assessment: Vol. 6, No. 6, pp. 921-941(2000)

1080-7039/00/$.50© 2000 by ASP

Is the “Ecological Fallacy” a Fallacy?

Fritz A. Seiler1 and Joseph L. Alvarez2

ABSTRACT

Ecological studies of health effects due to agent exposure are generally consid-ered to be a blunt instrument of scientific investigation, unfit to determine the“true” exposure-effect relationship for an agent. Based on this widely acceptedtenet, ecological studies of the correlation between the local air concentration ofradon and the local lung cancer mortality as measured by Cohen have been criti-cized as being subject to the “Ecological Fallacy” and thus producing invalid riskdata. Here we discuss the data that a risk assessment needs as a minimum require-ment for making a valid risk estimate. The examination of these data and a “thoughtexperiment” show that it is Cohen’s raw ecological data, uncorrected for populationcharacteristic factors, which are the proper data for a risk assessment. Consequently,the “true” exposure-effect relationship is less and less important the more popula-tion characteristic factors are identified and the larger they are. This reversal of theusual argument is due to our approach: Here, the prediction of the health effectsin an exposed population is of primary importance, not the shape of the “true”exposure-effect relationship. The results derived in this paper hold for ecologicalstudies of any agent causing any health or other effect.

Key Words: radon, lung cancer, risk assessment, epidemiological studies, ecological fallacy.

INTRODUCTION

In 1995, Cohen published his data on the negative correlation between theaverage local air concentrations of radon and the average local lung cancer mortal-ity rates in U.S. counties (Cohen, 1995; and references therein). Ever since then, hisdata have been attacked as being distorted by confounding factors and thus beingsubject to the “Ecological Fallacy.” Following the majority of epidemiologists, manyhealth physicists and risk assessors seem to agree that ecological studies are notrepresentative of the “true” dependence of the lung cancer mortality on the concen-trations of radon. Consequently, Cohen’s data have been dismissed from use in risk

1 Sigma Five Consulting, P.O. Box 1709, Los Lunas, NM, 87031-1709, USA. Tel: 505-866-5193;Fax: 505-866-5197; e-mail: [email protected], to whom all correspondence should be sent

2 Auxier & Associates, 9821 Cogdill Rd., Suite 1, Knoxville, TN, 37932, USA. Tel: 865-675-3669; Fax: 865-675-3677; e-mail: [email protected] Mar. 3, 1999; revised manuscript accepted Sept. 18, 2000

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assessments; and in countless presentations and papers, these well-measured andprecise data have been ignored.

Recent examples are the report of the BEIR VI committee (NRC, 1999) and twopapers in the journal Health Physics with accompanying discussions (Lubin, 1998 a,b;Smith et al., 1998; Field et al., 1998; Cohen, 1998 a,b). The reason their authors giveis that an ecological study does not constitute a proper database for the “true”exposure-effect function and does not allow the determination of an individual risk.A matched cohort study is deemed to be the only way to get reliable data for thedetermination of the undistorted and thus “true” exposure-effect function.

It is remarkable that Cohen’s measurements themselves are not in dispute, onlytheir use in risk assessment. In fact, these data are the only copious source ofinformation on the actual incidence of lung cancer fatalities correlated with the airconcentrations of radon. They cover almost the entire population in the contiguousUnited States; and in this context we shall call it the test population. These data pointshave quite small random errors and show a consistently negative trend with increas-ing exposure. The important question now is the meaning of these data for riskassessment.

Another set of available data consists of the same correlation determined foruranium miners. They were exposed underground to much higher radon levels,and their exposures were not determined at the time, but much later. These minerdata, with their large errors and doubtful exposures, have been used consistently inrisk evaluations for radon exposures.

It is the purpose of this paper to carefully investigate this situation and todetermine the minimum information needed to make a valid prediction of the risksfor a population exposed to radon and its progeny. In our approach we shall relyheavily on the Scientific Method, and therefore will give a short discussion of it,particularly with regard to its application to the problem of the “Ecological Fallacy.”It will also be shown that these arguments hold for ecological studies of exposuresto any kind of radioactive or chemical agent, resulting in any kind of a health effect.

THE SCIENTIFIC METHOD AND EXPERIMENTAL RADON DATA

It is not straightforward to summarize our knowledge on the health effects ofinhaling radon and its progeny, because the BEIR IV and BEIR VI Committees haveignored the Cohen data set. This act is fraught with problems, as we shall discuss inthis section (NRC, 1988, 1999). Also, a strong pro-linear bias is evident in manypublications, represented by the question: “Are our data compatible with the linearmodel?” or by the statement “A linear model only was fitted to the data.” We willproceed here by using the Scientific Method (Popper, 1968; Kuhn, 1970; Bunge,1979; Lett, 1990; Seiler and Alvarez, 1994a). This approach allows us to evaluate thedata without prejudice by asking: “What can we learn from the data?”

The Scientific Method

The Scientific Method was first formulated by René Descartes in 1637 (Descartes,1968) and lies at the root of the tremendous progress made in science and technol-ogy since then. It has been adapted to remain current with the development ofmathematics and its application to science, but its essence has remained the same:

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We use experimental observations to formulate a hypothesis, a theory, or a model,and then subject these ideas to the test with new experimental observations. If thenew data consistently confirm the predictions, we declare a new paradigm and thenlook for ways to test it until we discover something new again and have to modify themodel or its theory. If the data consistently contradict the prediction, we have todrop the paradigm or modify it. This process of changing the paradigm has beenwidely discussed in the literature (for instance, Popper, 1968; Kuhn, 1970; Bunge,1979). The results vary in their approaches, interpretations, and conclusions, butthey all agree on one point: Experimental data are used to either confirm or reject thepredictions of models and theories.

It has been shown that, in order to make this method feasible, the experimentaltests have to be preceded by a modeling effort fulfilling of a number of precondi-tions (Bunge, 1979; Lett, 1990; Seiler and Alvarez, 1994a). These conditions arecomponents of what is usually called “Doing Good Science.” Lett (1990) has puttogether a set of five preconditions and one test condition that summarize recentapproaches to this problem. In short, they are:

1. Sufficiency of Observations: Sufficient data have to be available and serve as thebasis to formulate a new hypothesis or model. A lack of sufficient data is oftenovercome by making an additional hypothesis but that can lead to wrongconclusions if the model consists of more assumptions than data. A classicalexample of initially insufficient data is the orbit calculation for the Near EarthAsteroid 1997XF11 made two years ago, based on a number of data pointsclosely spaced in time right after the discovery. This led to the prediction ofa close encounter or even a possible collision with earth early in the 21st

century (Scotti, 1998). The discovery of the same asteroid on some stellarplates taken eight years before then led to a combined data set which covereda much larger time interval. It improved the precision of the orbit calculation,and the probability of a close encounter was found to be smaller but still notnegligible. It finally disappeared for all practical purposes after a more carefulconsideration of the uncertainties by three groups of researchers with thesame result.

2. Replicability of Observations: The same and other scientists must be able toreproduce the original experimental data. Irreproducible results are often thecause of false models and predictions. As an example, the original “ColdFusion” data could not be reproduced by the authors or any other scientists(Taubes, 1993), and interest in the effect died away.

3. Comprehensiveness of Data Evaluation: All data in the modeling range must becompared to the model, not only those which agree with it. Ignoring any setof experimental data is a highly restrictive act that demands a high level ofjustification. We shall see in the following discussions whether dismissing theCohen data set from use in radon risk assessment can really be justified.Another example of ignoring this requirement with severe consequences isthe way Soviet scientist Trofim Lysenko suppressed all data that could andwould have contradicted his Lamarckian theory on the inheritance of ac-

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quired characteristics by grain. His selectivity led to catastrophic consequencesfor Soviet agriculture and its grain harvests for many decades (Friedlander,1995).

4. Logical Consistency of Model Approach: The set of assumptions and properties ofa theory or model must be free of internal inconsistencies. An example offailing this requirement are the linear and nonlinear models used in the BEIRIII and BEIR V reports on radiation carcinogenesis in man (NRC, 1980, 1990).There, the use of event doses instead of total accumulated doses for thesurvivors of the nuclear attacks on Japan, leads to logical inconsistencies.Whereas event doses can be used for the linear model, their use in anynonlinear model is a mistake. For those models, total accumulated doses mustbe used (Seiler and Alvarez, 1994b). This mistake removes the logical founda-tion for all statements about nonlinear models in both BEIR reports.

5. Scientific Honesty: This is a difficult requirement. We all know that scientiststend to be faithful to their brainchildren, sometimes beyond all reasonabledoubt (Popper, 1968; Kuhn, 1970). A scientist should admit when his modelhas failed and should go on from there. An example is the famous writtenwager between Stephen Hawking and Kip Thorne on whether the X-ray sourceCygnus-X1 contains a black hole at its center (Thorne, 1994). When theexperimental evidence became overwhelming, Hawking conceded in goodhumor and in writing that Cygnus-X1 does indeed contain a black hole.

Unfortunately, there is another aspect of scientific honesty that has to bementioned here. It concerns the integrity of the data presented or evaluatedby a researcher. Recently, we have all become aware of yet another case ofalleged scientific fraud by an investigator (Medical Tribune News Service,1999). Similar to Lysenko, this investigator is accused of having discarded 93%of the data in one case because they did not agree with his hypothesis. In thiscontext, honesty or the lack of it is an integral part of a scientist’s reputation.

6. Verification of Model: After these five preconditions are met, verification is theessence of the Scientific Method: Success or failure in predicting the outcomeof an experiment. If the five pre-conditions are not met, however, the outcomeof such an experiment means little, if anything. It must also be noted that allphysical measurements are subject to uncertainties stemming from varioussources. Uncertainties can be classified into two categories: random and sys-tematic errors.* Therefore, success or failure of a model prediction can onlybe established statistically within the experimental errors for a given confi-dence level. Therefore, one experiment alone leads often only to an increaseor decrease of confidence in the model. What is usually required for a com-

* The term uncertainty is used here as a general expression, covering both random andsystematic errors. This definition runs counter some recent usage in risk assessment, butit has now been adopted as U.S. National (ANSI) and international (ISO) standardterminology (Taylor and Kuyatt, 1993, 1994; Seiler and Alvarez, 1998b).

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plete loss of confidence in the model and an eventual change of paradigm isa set of results of the same experiment and, even better, failures in one ormore other types of experiment.

This time-proven framework is the basis on which we will judge the data and thetheories for the correlation between the radon concentrations and lung cancermortality in U.S. counties.

Information Derived from the Radon Data Available

In the controversy regarding the applicability of Cohen’s data to risk assessment,six aspects stand out as important cornerstones for our discussion:

1. Cohen’s data are derived from a large, statistically robust study. They are sodetailed in radon concentrations that they form a smooth curve of data points,well within the quite small experimental uncertainties, and withoutdiscontinuities or outliers. All other data (Lubin and Boice, 1997; Lubin,1998b) are not of comparable quantity and quality, as they are taken at onlya few broadly averaged exposure levels, and have random and systematicstandard errors which are dramatically larger than those of Cohen’s data

The plot in Figure 1 shows all of the other data together with Cohen’smeasurements which are given as the diamond symbols with the small errorsbetween radon concentrations of 20 to 230 Bq m- 3. They range from a relativerisk of 1.2 down to about 0.8 near 200 Bq m- 3 and are clearly nonlinear. It isalso obvious that, within their standard errors, there is no disagreementbetween Cohen’s data and all others, taking into account that standard errorsinclude a total probability of 68%. The dashed straight line is the linear modelof the BEIR VI Committee, essentially based on an extrapolation of theuranium miner data at higher exposures. Here, there is a dramatic disagree-ment of up to twenty standard errors between the BEIR VI Model predictionsand Cohen’s data (Cohen, 1995, 1998a,b, 1999).

2. Cohen has given a comprehensive evaluation of all potential confoundingfactors (Cohen, 1995) to counter various allegations involving confoundingfactors. Yet, up to now, his detailed discussions have not been given theattention they deserve, although the authors of two papers have attempted todo so (Lubin, 1998a; Smith et al., 1998).

3. In these papers, Lubin and Smith et al. try to show that correlated smokingcorrections of an unspecified magnitude would be needed to make Cohen’sdata acceptable (Lubin, 1998 a,b; Smith et al., 1998; Field et al., 1998). Cohen’scomments on these papers, however, show that these correlations would haveto have implausible magnitudes to bring about differences of twenty standarderrors and more (Cohen, 1998 a,b).

Here we shall approach this problem from a completely different point ofview and make a simple argument in the framework of the Scientific Method.Non-numerical arguments that show what effects could possibly occur and

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might somehow lead to a modification of the exposure dependence are notacceptable as valid evidence (Bunge, 1979; Lett, 1990; Seiler and Alvarez,1994a). Even worse, this approach is the exact opposite of the basic intent ofthe scientific method that is based on the numerical verification of theoreticalor modeling predictions by measurements. The arguments of the proponentsof the linear no-threshold theory criticize Cohen’s data for not agreeing withthe predictions of their model. They are thus putting the cart before the horse,and that is scientifically indefensible. It is their job to calculate their predic-tions in such a manner that they can be compared directly with the experimen-tal data.

4. Up to the present, nobody has successfully questioned the validity and integ-rity of Cohen’s measurements, only their applicability to a risk assessment hasbeen denied. What is required for a refutation of experimental data is a set ofbona fide contradictory data of roughly equal or better quality. Thus, the onlyway to obtain such data is by making new measurements in the same region ofexposures that would contradict Cohen’s data. No such measurements areavailable.

5. Logic dictates that Cohen’s data set should be used as the null hypothesis whenmeasurements are made to confirm or contradict it. It is a common butdeplorable practice to exercise all kinds of options when selecting a nullhypothesis. The null hypothesis is at a strong advantage when statistical deci-sions are made. Instead of even odds of 50:50, the odds are 1:10 and 1:20 infavor of the null hypothesis for confidence levels of 90% and 95%, respectively.This is a strong bias in favor of the null hypothesis, and a risk managementdecision can be influenced merely by the selection of a favorable null hypoth-esis.

The Scientific Method offers guidance for such tests in clear and unambigu-ous terms: We start with our best knowledge and thus with the current para-digm as the null hypothesis. After all, the model works to a certain extent,otherwise it would not be the current paradigm. Now we check for deviationsfrom the paradigm, and it is here that we require rather high standards of thecontradictory data, such as 90% or 95% confidence levels. Only then do weaccept these data as evidence to the contrary and, upon sufficient confirma-tion, abandon or modify the paradigm.

Thus it becomes clear that the Scientific Method is the only justification forthe use of such highly biased procedures as making decisions based on 90%or 95% confidence levels. Unfortunately, standard statistics texts do not stresssufficiently the fact that a cogent reason must be given to justify the selectionof the null hypothesis with its strong biases inherent in high confidence limits.

6. Both Cohen’s data set and the uranium miner data have serious dosimetryproblems that focus mainly on the time average of the radon concentrationsin air:

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a. Both sets of data are based on measured exposure concentrations of radon,which are given in Bq m-3 or rely on the corresponding total exposures inBq s m-3, although exposures are often still given in working level months(WLM). What is actually measured is the concentration of radon in the air.This concentration is equivalent to an infinite set of different mixtures ofradon and its progeny outside the detector. Also, for the health effects dueto radon and progeny, it is not the radon that matters but its alpha-emittingprogeny, and their concentrations are not measured. The relations be-tween the measured radon concentrations and the mixture of radon and itsprogeny outside the detector are thus multi-valued and undefined. In thispaper, as in most other work, we will discuss the lung cancer mortality interms of time-averaged exposures to ambient radon concentrations that arethe only measured quantities. Here, the assumption is made implicitly thatthe average isotope mixture is the same everywhere, and that thetime-averaged radon concentrations are a reasonable measure of theexposures relevant to lung cancer.

b. The miner data involve exposures given in units of WLMs, inferred frommeasurements of the exposure concentrations in mines that were mademuch later. These data were then used to calculate the concentration •time product of accumulated occupational exposures over years ordecades. Also, for the fit of the linear model to the data, Model I regressionsare used, as if the exposure values had no uncertainties (Sokal and Rohlf,1981). As we have just shown, they have considerable errors, and it is easyto demonstrate that, because exposures are difference measurements, theirrelative errors are bound to increase as the exposures decrease (Alvarezand Seiler, 1996; Seiler and Alvarez, 1998a). Clearly, Model II regressionsare required here which treat both mortality rates and exposures as thestochastic quantities they are (Sokal and Rohlf, 1981; Seiler andAlvarez, 1994b). When Model I regressions are used despite these facts,considerable systematic errors may be incurred.

c. For Cohen’s data, exposures to radon were measured, primarily in theliving areas of residential dwellings. By assuming a more or less constantaverage rate of exposure up to the age of the receptors, an averagepopulation exposure could be estimated for every exposure interval. Thisargument needs the additional assumption that there is a common set offactors between the average exposure concentrations in the houses and theactual time-integrated exposure concentrations of the receptors. Theseassumptions could lead to considerable uncertainties in the values foreffective exposures. However, these conversion factors and theiruncertainties are irrelevant, at least in first order, as long as subsequentprediction calculations are made using the same experimental method andthe same assumptions to determine the exposure data.

For the case considered in this paper, we will show that the ExposureConversion Factors (ECF) involved in the conversion from the radon

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measurements to exposures or doses and their errors cancel. No suchcancellation of conversion factors and their uncertainties is possible for theextrapolations of the uranium miner data way down to the low exposuresof the general population. The exposures of miners and of the generalpopulation involve different assumptions and conversion factors that donot cancel.

This discussion shows that there are significant differences between the informa-tion derived from the miner data and those from Cohen’s measurements. It isimportant to see that there is no a priori need for a cause-effect model in applyingCohen’s data. The data can be used either directly from a data table, or it can beused indirectly by calculating an interpolating polynomial for convenience. A visualinspection of Figure 1 shows that a good fit is possible. The miner data, on the otherhand, require the use of a model to extrapolate their information down to muchlower levels of exposure, a much more complex procedure.

As we shall show in the following, only the first, fourth and fifth of these sixarguments are relevant to the problem of predicting health effects. The second,third and sixth arguments, regardless of their merits, will be shown to have nobearing on the use of Cohen’s data for the assessment of risks due to exposures ofhumans to radon and its progeny.

MINIMUM REQUIREMENTS FOR A POPULATION RISK ASSESSMENT

Here, we will determine the minimum information required for a prediction ofthe number of health effects in an exposed population. To this purpose, we will firststate what a risk assessment does, and what kind of information it needs. Thus, weseek the most direct connection between exposure and effects data, and will usetime-averaged radon concentrations as measures of exposure. As a next step, we willthen conduct a thought experiment (“Gedankenexperiment”) in order to clarifysome of the issues mentioned above. Thought experiments are a valuable theoreti-cal tool, based on a careful step by step evaluation of an experimental procedurewithout numbers. Thus it is essentially a dry run of the whole evaluation, carried outto isolate salient facts.

Minimum Information for a Risk Assessment

The purpose of a risk assessment for the exposure of humans to radon and itsprogeny is to estimate the number and type of health effects in a population whoseexposure to radon is known or has been projected. We will call this population theprediction population. The minimum of information that this risk assessment requiresis thus an effective cause-effect relationship for the prediction population which willconvert the known set of radon exposures of that population directly into a set ofhealth effects in that population. This is all that is needed, no more.

This minimum requirement has another consequence: The initial goal of themodeling effort is to predict the number and kinds of health effects in the testpopulation. The Scientific Method requires a comparison of the experimental datato the corresponding predictions made by the model. This then leads to a judgmentabout the power of the model to predict effects. This is the way that science operates

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and not the other way around. The ball is thus clearly in the court of the modelers,and they have to show a successful modeling of the measured risk data for the testpopulation.

An additional requirement is that both cause-effect relationship and pre-dicted health effects must be applicable to the prediction population. Note thatall other sets of derived exposure information for the test population, such asradiation doses to the lung epithelium and so on, may be scientifically interest-ing and quite useful, but they are not needed to make a valid risk prediction. Adose-effect relationship for the risk assessment is determined only when it isconvenient and meaningful to do so. Then, the error calculations have to bedone carefully to avoid inserting some errors twice, once when calculating thecause-effect relationship and again when applying it for a prediction. It isextremely important to keep these basic facts in mind during the followingdiscussion.

Preliminary Remarks for the Thought Experiment

From reactions to an earlier version of this paper by some of our friends, andfrom the comments of the reviewers of this journal, we have learned that it may bequite difficult for some readers to let go of some ingrained concepts and “wellknown” facts. In addition, any theoretical thought experiment, such as the one usedhere, needs a lot of care in reading and interpretation. However, this is preciselywhat we must ask the reader to do.

Also, not being epidemiologists but risk assessors, we will approach these prob-lems using scientific but not necessarily epidemiological terminology and patternsof thinking. As an example, ecological studies are not treated as a mere screeningtool, preparatory to a “real” analysis. These studies furnish data just like any otherdata source. We will address the properties of these data, confounding factors andall, later in this section.

In addition, the idea that the sole purpose of ecological data, and indeed of allepidemiological data, should be to find the “true” cause-effect relationship for theagent, is in our opinion short-sighted and only partly correct. The purpose of anyepidemiological study should be to help make risk predictions for future exposuresof people. A cause-effect relationship is merely a tool often used by risk assessors, butit is of purely academic interest if it is not needed. We will also show here, that inthis case we do not need this tool at all, not as long as we have good and plentifuldata.

Some readers may have problems with some of the basic and often implicitassumptions made in risk assessment. Essentially, data from past experience areused to project risks into the near or far future. Obviously, this cannot be donewithout making some assumptions about the transfer of this knowledge from thepast to the future. We will aggregate all needed assumptions into one, anassumption which is made implicitly or explicitly in every science-based riskassessment, and that we shall call the Assumption of Equivalent Populations. We willshow that the details of this assumption should not be questioned without reallygood numerical evidence, because without this assumption, no risk assessment ispossible.

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Assumptions for the Thought Experiment

For the thought experiment, we will now make — and for the sake of this thoughtexperiment only — four assumptions that cover the situation of health effects dueto radon exposure as it is proposed implicitly by the proponents of the linear theory:

1. The linear model is correct at low exposures and represents the “true” expo-sure-effect relationship;

2. The measurements by Cohen accurately report the observable dependence ofthe local lung cancer mortality on the local air concentrations of radon in thepopulations of U.S. counties;

3. The underlying linear exposure-effect relationship is modified by some factorscharacteristic for the test population to such an extent that the result is theexposure-dependence found in Cohen’s data; and, finally,

4. The influence of each one of these population characteristic factors is knownexactly.

The implications of the first and the last assumptions for our thought experimentare obvious, but the second and third need some comment. The second assumptioncovers the actually observed health effects in the exposed test population and,because nobody has been able to invalidate Cohen’s primary data, these measure-ments are used here.

The first and second assumptions are of course contradictory, and the thirdassumption is needed in order to reconcile them. Actually, the third assumption isthe claim made by the proponents of the linear model in order to save their model.It states that the total of the confounding factors leads from the “true” model to the“modified” data measured.

To test the logic of this claim, we introduce two factors for every radonconcentration. The first is the Exposure Conversion Factor, ECF, as the usualstraightforward factor converting the radon concentrations Cr to concentra-tion • time products or some other measures of exposure or dose; and thesecond is a new factor which we will call the Factor of Population Characteristics,FPC (Cr ). It comprises all the population-derived confounding factors, includ-ing any population influence on the conversion factors such as average resi-dence time and so on. This FPC (Cr ) leads, as required, from the “true” cause-effect relationship to the data found by Cohen. Note that the FPC (Cr ) containsin particular the entire correlation between smoking and the radon level. Evenmore important, it contains the influence of all confounding factors, bothknown and unknown, which are introduced by the characteristics of the testpopulation. In the absence of confounding factors, the FPC (Cr ) is equal tounity. In the presence of confounding factors, the FPC (C r ) is representativeof the collective numerical influence of all the confounding factors contribut-ing to the “Ecological Fallacy” and more. Therefore, the FPC (C r ) factorincludes the numerical influence of all the objections to Cohen’s data voicedby the proponents of the linear model.

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It must be stated here that there is, of course, the far more likely explanation thatthe discrepancy between the first and second assumptions represents a classical caseof measurements contradicting theoretical or calculated model values. In this case,the latter are obtained by the questionable extrapolation of a straight line fitted touncertain risk values at higher exposures, using a maximum likelihood fittingprocedure that does not take into account the uncertainties of the exposures.

Therefore, Cohen’s data of the second assumption of our thought experimentsuccessfully contradict the BEIR VI model values of the first assumption. An excep-tion would be possible only if the proponents of the linear theory were to showconclusively that their FPC (Cr ) quantities lead to risks that are numerically compat-ible with Cohen’s data (Cohen, 1995). However, it is equally important to realizethat the scientific method puts the responsibility for making a correct prediction ofthe data squarely in the lap of the modelers and not in the lap of the experimenters.

However, for the sake of this thought experiment, we will proceed and maintainthat all four assumptions made above are valid.

Results of the Thought Experiment

Now we consider the logical situation created by the four assumptions. Thenationwide measurements of the average local lung cancer mortality and the aver-age local radon concentrations result in the exposure-mortality correlation mt e s t

(Cr ) for a radon concentration Cr in the test population as found by Cohen. In a firststep, we now correct these nonlinear mortality data for the influence of all knownand unknown confounding factors of the test population by multiplying with theinverse of the population characteristics factor FPCt e s t ( Cr ) and of the conversionfactor ECF, and, by our assumptions, the result is the underlying “true” linearexposure-effect relationship Rt e s t ( Cr ) for the test population,

(1)

It should be noted here that there is really nothing that requires Rt e s t (Cr) to belinear, so that this equation holds for any algebraic form of the “true” exposure-effect relationship.

In a second step, we will now assume that it becomes necessary to make aprediction for the change in lung cancer mortality for an exposed predictionpopulation, such as the population of an area in and around Denver, CO. Theassumed reason is that this population is suddenly subjected to three times thenormal radon concentration, C′ r = 3 Cr , a situation which is likely to continue far intothe future. In order to make a prediction for the long-term change in the numberof lung cancer fatalities expected, we now use the “true” linear model for theprediction population and apply the population characteristics factor FPCp r e d (C′ r)and the conversion factor ECF, but this time as direct factors. In this manner, weobtain the appropriately modified expectation values of the lung cancer risk, andthe appropriate cause-effect relationship for the prediction population is,

R C m CFPC C ECFtest r test r

test r( ) = ( ) ( ) ⋅1

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(2)

It is thus obvious that the two ECFs cancel as previously predicted in item 6.c. of thispaper and that the result therefore is independent of the exposure quantity usedand its uncertainty.

The Assumption of Equivalent Populations

What is usually done implicitly, and what we will here do explicitly, is the transferof the information on the test population to the prediction population, a processsometimes called, a bit imprecisely, the generalization of the data. To this purposewe make an assumption that is always made, but usually just by implication: theAssumption of Equivalent Populations. It states that the test population is representativefor the prediction population in all aspects important to the adverse effect. Withoutthis assumption, no risk predictions can be made for the prediction population.

This assumption is nothing new. In fact, implicitly or explicitly, it has been madein every science-based numerical risk assessment ever made. The risk of the expo-sure to any agent that causes an effect is derived from the number of those effectsin an exposed test population and results in an exposure-effect function for thatpopulation. If that function is then to be used to calculate the number of expectedhealth effects in a prediction population, the assumption is needed that these twopopulations react to the agent in exactly the same way. Thus, if we want to use thedata obtained from the test population for a risk projection in the predictionpopulation the FPCs for the two populations have to be identical,

FPCpred(C′r) = FPCtest (C′r) . (3)

This equality, together with Eq. (2), then leads to the final equation,

Rpred(C′r) = Mtest (C′r) . (4)

This means that the risk for the prediction population is given directly by Cohen’srisk of lung cancer mortality for the test population. These equations prove thestatement made earlier, and they are also the reason why the “Ecological Fallacy”does not matter in going from the test population to the prediction population: thetwo identical FPCs cancel, and thus all population characteristic factors, known orunknown, cancel also.

Actually, we quite often make the assumption of equivalent populations, evenwhen we know that it is likely to be only partly valid. As an example, we use thesituation of the cancer risk coefficient determined in the BEIR V report (NRC,1990). The use of this risk coefficient assumes implicitly that the FPC t e s t of theJapanese test population, first at the exposure after 8 years of war deprivations, thensuffering through the post-war chaos, and living only later in times of peace, isnumerically the same as the FPC p r e d for the American prediction population 50

R C R C FPC C ECF

m CFPC C

FPC C

pred r test r pred r

test rpred r

test r

' '

''

( ) = ( ) ( )

= ( ) ( )( ) ⋅

'

'

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years later in times of prolonged peace. Then, and only then, can the Japanesebomb survivor data be used in risk predictions for members of the U.S. population.

In our thought experiment, making the assumption of equivalent populationsmeans that the predicted values for the Denver population will be numerically equalto the values of the Cohen data, except for some increase in the systematic un-certainties due to making this assumption. Thus, as a direct consequence of thispartial equality,* the Cohen data can be used directly for the risk assessment. Notethat the assumption of equivalent populations, and thus the equality of the two FPCs,means that making the smoking correction or any other correction is not necessary,and that Cohen’s raw, uncorrected mortality data is the proper data set to be used.

This fact is important with regard to some of the criticisms of the smokingcorrection in Cohen’s evaluation (see, for instance, Field et al., 1998; Archer, 1998;Cohen, 1998c,d). These criticisms have now become irrelevant for a risk assessmentbecause these corrections are part of the two identical FPCs, and their influencecancels.

We are aware that, at first, these conclusions seem counterintuitive. However, itbecomes clear on further consideration that they are a logical consequence of theminimum data needs for a risk assessment, which is to use the evaluation of actualeffects in the test population to project as directly as possible the actual healtheffects in the prediction population. Therefore, the data must include all theconfounding effects, known and unknown, in both populations.

Validity of the Assumption of Equivalent Populations

The radon exposures of the uranium miners and those of the general populationcontain a series of substantially different dosimetry factors and lifestyle parameters.They can give rise to considerable confounding factors, the most important beingthe doses derived from measurements made ten years later in a different miningenvironment. Here, the validity of the assumption of equivalent populations needsto be discussed in far more detail than it has been in the past. In the BEIR reportsIV and VI (NCRP, 1988, 1999), the assumption is made a bit more explicitly thanusual but still not in sufficient detail to be convincing.

All the issues raised in discussions about the cause-effect relationships for radonand other radioisotopes, as well as for whole body irradiation with gamma-radiationsand neutrons, make the conditions for the validity of the assumption of equivalentpopulations a bit more complicated. The BEIR and the ICRP reports (ICRP, 1991)as well as similar reports consider, in varying levels of detail, the different effects ofpopulation characteristics which could affect the assumption of equivalent popula-tions. Then, however, they do not make the correction, but go on and implicitlymake the assumption of equivalent populations anyway (NCRP, 1980, 1988, 1990,1999; ICRP, 1991).

When testing for the equality of the factors of population characteristics, weshould remember that the null hypothesis must involve the assumption of equiva-lent populations because that is the current paradigm in risk assessment. Thus,according to the Scientific Method, it is the obligation of the proponents of nonzero

* The term partial equality is used here for two numbers that haveequal values but unequal errors.

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differences between the two FPCs for the test and prediction population to demon-strate numerically that a difference between the two FPCs exists and is indeedsignificantly different from zero. This would then invalidate Eq. 3 and show that thecalculated corrections to the FPCs need to be made according to Eq. 2, otherwise,no risk projection is again possible.

Generalization to Other Agents and Health Effects

It is easy to verify, by going again through our thought experiment, that its resultcan be generalized, so that it applies regardless of the agent, the health effect, or theshape of the underlying true exposure-effect relationship. All that matters is theassumption that the exposure-effect relationship has been modified by the factorsFPCs and ECFs for the test population, resulting in a particular shape. It is thismodified shape that will then predict the actually occurring health effects and whichtherefore is relevant for the corresponding risk assessment.

The generalization of the procedure also encompasses its application to inani-mate objects such as high-pressure steam valves in nuclear or fossil fuel power plants,for instance. Time to failure data determined for one set of valves can only beapplied to a newer set of the same or similar valves by making the analogue to theassumption of equivalent populations. Particularly in the case of similar valves, butalso for the same but newer valves, this assumption needs proper justification, or aprediction of the time-to-failure cannot be made.

This is the main result of our generalized thought experiment: The proper cause-effect function for predictions is the experimentally found correlation between exposure andeffects (or time and effects), and not the shape of the underlying “true” exposure-effect function.

It is important to understand here that, for sizeable factors of population char-acteristics, no underlying “true” cause-effect function can correctly predict theactual effects occurring in the prediction population. For correct predictions, theFPCs specific for the test and prediction populations are needed.

Consequently, the arguments using the concept of “Ecological Fallacy” may berelevant to finding the “true” exposure-effect relationship, but they are completelyirrelevant for a risk assessment. The use of the term “Ecological Fallacy” thereforeis inappropriate. It is the search for the “true” exposure-effect relationship which isproblematic and which requires that the confounding factors be quantitatively wellknown in order to make valid predictions of the health effects expected in aprediction population. Unfortunately, and contrary to the fourth assumption in ourthought experiment, most of the confounding factors contributing to the FPCs areactually not well known numerically, if at all.

POPULATION RISKS AND INDIVIDUAL RISKS

All of Cohen’s evaluations deal with large numbers of people, not individuals.That is why the assumption of equivalent populations can be made, and why the“true” shape of the cause-effect relationship is of little or no consequence in thepresence of large confounding factors and thus FPCs which are considerably differ-ent from one. Generally, it is maintained that individual risks cannot be predictedfrom epidemiological data unless the study uses matched cohorts, and the “true”

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cause-effect relationship can be determined. We will show that this statement is notcorrect, and that a statement about the risk for an individual can indeed be made.

Properties of a Fit to the Experimental Data

As we have demonstrated, the risks for a prediction population, given the differ-ent exposure strata of all subpopulations selected, can be estimated using theinformation from the test population. The basis for this estimate is the assumptionof equivalent populations. This means that both the test and the prediction popu-lation must be large and diverse enough so we are able to rely on the validity of theassumption. A function of exposure, such as a linear, a linear plus quadratic, or aU-shaped curve, can then be fitted to the data of the test population by using, forinstance, an inverse-variance-weighted fitting procedure (Brandt, 1976; Lancasterand Salkauskas, 1986; Bevington and Robinson, 1992). The errors of such a predic-tion can then be calculated by using the covariance matrix of the fit and either ananalytical approximation of the error propagation equation (Seiler, 1987) or acorresponding Monte Carlo simulation (Cox and Baybutt, 1981; Kalos and Whitlock,1986).

A U-shaped curve should be chosen, at least as one option (Luckey, 1991), notonly because Cohen’s data have that shape but also because a realistic cytodynamiccancer model of the Moolgavkar type can be fitted to Cohen’s data (Bogen, 1997).Also, if Bogen’s model is fitted to other, independent radon/lung cancer data, itpredicts the U-shaped curve measured by Cohen (Bogen, 1998).

Risk Evaluation for the Prediction Population

For our further discussions, we shall, without loss of generality, limit ourselves tothe properties of linear cause-effect functions. Good examples for linear maximumlikelihood fits are given in standard statistical texts (see, for instance, Walpole andMyers, 1985). A successful fit to the data results in a set of fitted parameters, and onthat basis two statements can be made. The first is the calculation of the meanresponse of the test population for a given exposure (Walpole and Myers, 1985, p.332). The second is the calculation of the response to the same exposure by anyindividual in the test population (Walpole and Myers, 1985, p. 334). For the linearcause-effect functions assumed here, the correlation matrix is a symmetrical 2 × 2matrix. For nonlinear cause-effect functions, such as U-shaped curves, analogousexpressions can be found which involve covariance matrices of the same or higherdimensions (Brandt, 1976; Lancaster and Salkauskas, 1986; Bevington and Robertson,1992).

The standard error of the average response in the prediction population is givenby the standard error of the fit value, which decreases roughly as s√(1/n) withincreasing sample size n, using the symbol s for the standard deviation of the fit. Thisasymptotic behavior is analogous to that of the standard error of a mean as it goesto very small values for large values of n (Walpole and Myers, 1985, p. 332).

Risk Prediction for an Individual

Using the data of the same fit to the test population, the prediction for the responseof an individual can be made. The procedure yields the same numerical value as the

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predicted mean response (Walpole and Myers, 1985, p. 334), but it has a much largerstandard error that decreases roughly as s√ (1+1/n) only. This error decreases asymptoti-cally with increasing sample size n, not toward very small values, but toward the value ofthe standard deviation s of the fit. A similar expression can be obtained for nonlinearcause-effect functions. Thus, for a member of the test population, the same risk and thislarger error are the correct evaluation of the individual response. If we now apply theassumption of equivalent populations, we can find in the prediction population acounterpart for each individual in the test population. For an arbitrary individual in theprediction population, therefore, the value of the risk and the large standard errordiscussed above are the correct estimate of the predicted individual risk.

In other words, the mean risk for the prediction population and the individualmean risk in that population are partially equal, differing only in the size of theirstandard errors. This conclusion can be supported by an inspection of the errors foreach point shown in Figure 1 of Cohen’s 1995 paper, reproduced also in his recentpapers (Cohen, 1998a, 1999). Note that these are point by point errors and not theerrors of a fit to the data. However, still, the small errors are the standard errors ofthe mean and the large ones are the probable errors of the sample (including 50%probability), given as quartiles.

The large errors of the individual risks can be understood intuitively by analogy:When we consider a sample of n receptors and ask the question: If we add yetanother receptor and label it n + 1, what will be the mean and the distribution ofour expectation for this measurement? The answer is clearly: It is the sample mean,and a distribution given, not by the standard error of the mean, but by the standarddeviation of the sample (Seiler and Alvarez, 1995). Therefore, the appropriate errorfor an individual risk is much larger than the error of the average risk in thepopulation, and its variability will include those of all subpopulations and thus fromall members of the prediction population. It is this risk and this error value whichshould be used in calculations which involve an individual.

It is important here to be aware that the only condition for the viability of a riskto an individual is that the individual has to be a bona fide member of the predictionpopulation. Thus, the individual has all the corresponding probabilities to be acontributor to the various confounding factors, such as smoking. In other words, theindividual chosen must in all respects be an indistinguishable member of theprediction population, selected at random.

Risk Prediction for a Particular Individual

A frequently asked question concerns the cancer risk for a particular person X,taking into account all of the characteristics of the individual, such as age, sex,smoking status, and other lifestyle parameters. The only way to make such a riskprediction possible would be to make a successful risk determination for the particu-lar subgroup of the population that has the same characteristics as individual X. Thissubgroup would have to be large enough to produce enough cancer cases so thata risk determination is possible, and also be large enough to allow making theassumption of equivalent populations. Thus risks can only be determined for allmembers of a meaningful subgroup. For the individual X, however, no personal riskcan be determined.

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DISCUSSION

In this paper we have demonstrated that, far from being unfit for a risk assess-ment, Cohen’s uncorrected measurements of the correlation between the localexposure concentrations of radon and the local lung cancer mortality are the onlydata available which can be used for a risk assessment at low exposures. An explicitadditional condition is that the exposure concentrations of the prediction popula-tion have to be measured in exactly the same way as the exposure concentrations ofthe test population. As we have also shown in our thought experiment, the “true”cause-effect function is of use only as long as there are no significant confoundingfactors and thus no total FPCs significantly different from one, because these factorsare not known well at all.

The important fact here is that, theoretically, the actual risks can be calculatedwithout knowing anything about the “true” cause-effect relationship. Conversely,the evaluation of the “true” cause-effect relationship from the data is possible anduseful only if the confounding factors are small and the FPC values lie close to one.Then, the corrections to be made are small and relatively well known. The evalua-tions made by Cohen (1995, 1998a,b,d) have shown that for his data, this conditionholds.

It is important to realize at this point that we only use Cohen’s raw data and nothis corrected data. Clearly, if these corrections were made, the inverse correctionswould have to be made in predicting a risk. As the ECFs and the FPCs, thesecorrections also would cancel in a risk assessment.

In their entirety, our statements are a complete reversal of the usual arguments.This reversal is due to our approach. Our evaluations are based on the minimumneeds of a risk assessment which has one, and one purpose only, and that is to makea prediction for the actual occurrences of health effects in a prediction population,based on data for the test population. The “true” cause-effect function is but a toolthat may or may not be needed. If the FPCs are large, as the proponents of the lineartheory claim, then the “true” cause-effect function is a practically useless tool.

Considerable progress has been made in the last few years in making plausiblenonlinear models on the basis of the Moolgavkar-Venzon-Knudson two-stage mecha-nism of carcinogenesis. For the case of radon, and based on new independent radonexposure data, Bogen’s CD2-model (Bogen, 1998) was able to predict magnitudeand shape of both Cohen’s ecological data as well as the lung cancer data forunderground uranium miners. What makes the CD2-model a truly extraordinarybiological model is that, in addition, it independently and correctly predicts aninverse dose rate effect in non-smoking uranium miners (Bogen, 1998). This isclearly the way models are tested according to the Scientific Method, particularlywhen the predictive power of Bogen’s CD2-model begins to approach the power ofmodels used in physics, chemistry, and engineering.

Contrary to the usual statement regarding the impossibility of deriving individualrisks from any kind of ecological studies, it was demonstrated here that such riskscan indeed be estimated from any epidemiological study under properly restrictiveconditions for the individual concerned. The value of the risk is the same as theaverage risk for a member of the test population, but the uncertainty is considerablylarger because it must represent the variability of the risk over all members in the

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prediction population. This means that for a particular individual, the risk can onlybe calculated as long as the individual can be regarded as an indistinguishablemember of the test population. For a specific individual X, however, no personalrisk prediction is possible.

What was introduced here as an explicit concept, is the Assumption of Equiva-lent Populations which holds that the test population is representative for theprediction population in all aspects which are important for the adverse effect.In the presence of confounding effects, this means that the FPC for the testpopulation is identical to the FPC for the prediction population. This propertyleads to the prediction of risk values that are equal to the experimental data butmay have slightly larger systematic errors. It also means that the predicted riskis practically independent of the “true” cause-effect function. Thus, for a predic-tion of health effects, the only data needed are a set of carefully made measure-ments of the effects in the test population, based on a sound experimentalprocedure.

For each future application, an explicit set of reasons should be given, stating whythe assumption of equivalent populations should be applicable for this case. If it canbe applied, a valid prediction of health effects is possible; if it cannot be made, noprediction is possible.

In this paper, we have also shown that the effects of the “Ecological Fallacy” mayor may not be sizeable, but they are relevant only if the goal is to find the “true”cause-effect function. They are, however, irrelevant as long as the goal is theprediction of health effects in a risk assessment, and the conditions for the assump-tion of equivalent populations are sufficiently fulfilled. Thus an important result ofthis paper is that, when applied to a risk assessment, the “Ecological Fallacy” isirrelevant.

What Cohen’s data did tell us is that the relative risk is at first larger than 1 atvery low concentrations, then it decreases with larger radon exposures until therelative risk drops significantly below 1. This means that, in that region of airconcentrations, the exposure decreases the risk of lung cancer below the back-ground level and thus results in a hormetic or beneficial effect. At somewhathigher exposure concentrations, the risk levels off, begins to rise again, and finallybecomes larger than background above the so-called zero-effects point (Luckey,1991). Obviously, the structure of all these well-determined nonlinear effects arenicely hidden in the large uncertainties of the other data, which up to now werethe only ones deemed acceptable by the proponents of the linear model. Noteagain that the two data sets are in statistical agreement, but only the Cohen datawith their small errors are able to reveal the finer details of the dependence onaverage concentrations. Thus this example is a clear experimental demonstrationof one of the basic tenets of the Scientific Method: “If you cannot measure it, youdo not know anything about it!”

ACKNOWLEDGMENTS

The authors express their gratitude to Drs. John Auxier, Kenneth Bogen, andBernhard Cohen, as well as Mr. James Muckerheide, for a critical reading of themanuscript and for providing valuable suggestions.

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Seiler and Alvarez

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