Underestimating effects: Why causation probabilities need to be replaced in regulation,policy,and the law

Abstract

Causation probabilities are often a component of decisions on awarding compensation for radiation exposure and descriptions of the number of cancers caused by radiation releases. In many instances, the use of epidemiologic data to calculate such probabilities may seriously underestimate the number of people harmed and the percentage of cancers induced or accelerated by the radiation exposure. Epidemiologic studies can more reliably underpin systems that award compensation using years of healthy life lost due to the exposure. Such a system has its own imprecisions but is more scientifically supportable than using causation probabilities to award compensation.

Editor’s note

The atomic age has been punctuated by inadvertent and intentional releases of radiation that have harmed humans. From the hibakusha who survived the Nagasaki and Hiroshima bombings to the Techa River denizens contaminated by radiation released from a Soviet-era plutonium production facility, from the people around Chernobyl to those who live downwind of the Fukushima Daiichi Nuclear Power Station, scientists have studied populations affected by radiation and tried to quantify the impact of exposure.

Epidemiologic studies that compare exposed and non-exposed groups of people loom large in the legal, legislative, and regulatory landscapes of the United States and countries around the world. As a professor of epidemiology and statistics, Dr. Greenland is regularly asked by government bodies and affected parties to comment on the relevance of epidemiologic studies, particularly for legal proceedings. The estimates derived from such studies are presented to the public as indicators of risks from future and past accidents, as part of a rationale for determining damages in lawsuits, and to legislators and regulators who must decide, in the wake of radiation release, whether nuclear facilities and procedures need improvements.

Epidemiologic data play a central role in assessing harm caused by coal burning, groundwater pollutants, and a host of other environmental contaminants. But epidemiology has also been misused, particularly in the courts and in risk communication, where it has often been stretched beyond its current estimating and predictive capabilities. For example, a statement such as “the risk of cancer from a particular exposure to radiation is 1 chance in 10,000” cannot be derived from population data alone—but such statements are often given in the wake of nuclear accidents and other large-scale exposure sources by government officials, industry leaders, and even some scientists. A better form of risk communication is needed when interpreting epidemiologic studies for the public, courts, legislators, and regulators, particularly when deciding who has been harmed by radiation releases.

Simply put, without precise knowledge about the biologic processes by which radiation causes cancer, epidemiologic data alone cannot do more than provide a lower bound on causation probabilities. This limitation is important because estimates of those probabilities are often used in compensation decisions for radiation exposure and for describing the number of cancers “caused” by radiation releases. Unfortunately, the lower probability bounds estimated from epidemiologic data are routinely treated as estimates of the actual probability, which can result in serious underestimation of harm caused by radiation.

Fortunately, there is a better way to talk about risk and harm estimates: Epidemiologic studies can be used to estimate the average (expected) years of life lost due to radiation exposures. Systems that award compensation based on years of healthy life lost due to exposure to radiation are more scientifically supportable by epidemiologic data than systems that award compensation based on causation probabilities.

Problems of definition

To understand the problems just outlined, it is necessary to distinguish two percentages that are routinely confused with one another and that apply when dealing with cancers caused by a radiation release. The first is the percentage reduction in the number of cancer cases that would have occurred if there had been no radiation release—sometimes called “attributable fraction” or “excess fraction” (Greenland and Robins, 1988; Robins and Greenland, 1989a). The second is the percentage of cancer cases in which radiation from the release was a contributory cause of the cancer—sometimes called the “etiologic fraction,” “causal fraction,” or “probability of causation” (Robins and Greenland, 1989a, 1989b). The phrases “attributed to” and “caused by” may sound like synonyms. But the excess fraction and the causal fraction are actually quite different in their technical meanings. Conflating them can lead to results— from awards in major lawsuits to regulations on nuclear power plants—that are scientifically unsound. That is to say, those results, seemingly based on painstaking scientific research, are likely wrong.

An example may help clarify this important definitional difference: An estimate that atomic-bomb survivors would have suffered only 3 percent fewer cancers if they had not been exposed to bomb radiation will often be misinterpreted as the percentage of cases caused by exposure. This misinterpretation stems from a false assumption that radiation either causes a person to develop cancer, or it does not. This implicit, “all-or-none” biologic model of how radiation causes cancer may be very wrong. Instead it may be that many cancers were accelerated—that is, they occurred earlier in life than they otherwise would have—by radiation exposure at Hiroshima and Nagasaki. At the least, the inference that only 3 percent of the survivors’ cancers were caused by radiation is not logically derivable from the epidemiology, no matter how well it is or was done.

Here is why: Ordinary interpretation of language and common sense tell us that the exposure contributes causally to a person’s disease occurrence if, but for exposure, the disease either (1) would have occurred at a later time or (2) would not have occurred at all (which is, of course, just the extreme case of a later time). A case of disease can be labeled an “accelerated occurrence” if exposure causally contributed to the disease in the first sense (i.e., without exposure, the disease would have occurred at a later time). Another case would be labeled an “all-or-none occurrence” if exposure causally contributed to disease in the second sense (i.e., without exposure, the disease would not have occurred at all). Finally, a case is considered an “unaffected occurrence” if exposure made no difference in the timing of the disease, meaning the person would have contracted cancer at the same time, regardless of the exposure, and so exposure was not a contributory cause.

For both accelerated and all-or-none occurrences, exposure harmed the individual; it reduced the amount of time that the individual was able to live without the disease. Understanding of the precise biologic processes by which various types of radiation cause various types of cancer is far from complete. But radiation can accelerate the onset of at least some cancers, causing them to develop earlier than they otherwise would have (Nguyen et al., 2011). Unfortunately, such accelerated occurrences are often ignored in risk statements, in regulations, and sometimes in the courts. Failure to recognize them has resulted in unsound radiogenic cancer legislation and unfair court decisions, because for diseases like cancer, occurrence time is crucial.

Consider, for example, a person who, in the absence of a particular exposure to radiation, would have developed clinically apparent leukemia at age 70, but instead develops it at age 66 due to acceleration by a radiation exposure. This person loses four years of leukemia-free life due to the exposure, even though this loss has no discernible impact on the rate of the disease in the population as a whole.

The logical limitations of population data for distinguishing among individual effects can be seen even in very simple studies: In a hypothetical population of just four persons followed from age 50 to age 80, for example, suppose that two are subject to a particular radiation exposure and die at ages 60 and 70, and two are not exposed and die at ages 70 and 80. Suppose the exposure was the only factor creating any difference in the age of death; that is, suppose the exposed population would have exhibited deaths at age 70 and 80 (as in the unexposed population) if the exposure had been absent.

Even in such a simple, ideal study, it would not be possible to determine individual effects from the epidemiologic data: The observed pattern of deaths could be due to the first exposed person suffering a 20-year loss of life due to exposure (from age 80 to age 60), so that only half the exposed were harmed. But the same death pattern could also reflect that both exposed persons suffered a 10-year loss, so that both those exposed were harmed. Yet, under both scenarios, the average age at death is the same: 65 years for the exposed pair versus 75 years for the unexposed pair, reflecting an average of 10 years of life lost per exposed person (10 being the average of 20 years lost and zero years lost, but also the average of 10 years lost and 10 years lost). Thus, all we can say based on these data is that at least one exposed person was affected; but it may be that all (both) were affected. In other words, the very same data are perfectly compatible with both a causal fraction of ½ (50 percent of deaths had exposure as a contributory cause) and a causal fraction of 1 (100 percent of deaths had exposure as a contributory cause).

The example illustrates a fact that is often lost in legal and policy-making venues: Even if epidemiologic studies are randomized and free of all problems often found in such studies, they can identify only population distributions, not individual risks or losses. This limitation only intensifies as the population size increases. In particular, when an excess risk due to an exposure is established, even ideal population data cannot tell us whether the effect that produced the excess is concentrated among some minimum number of affected cases, or is instead distributed widely among all cases, or is instead somewhere in the range between these extremes (Robins and Greenland, 1989a, 1989b).

As a consequence, epidemiologic studies cannot determine the division of cancer cases into the accelerated, all-or-none, and unaffected categories. But in legal and policy-making venues, because of the failure to distinguish excess and causal fractions, there is an implicit assumption that the harm from exposure is concentrated in the smallest number of possible victims. Such assumptions can result in potentially huge underestimates of the number of persons harmed (Greenland, 1999; Robins and Greenland, 2000).

How risks and their ratios provide only the minimum affected

As with much science, the study of populations exposed to environmental contaminants involves a certain amount of mathematical analysis. Because it is not essential to understanding the central points made by this article, I will place most of the formulas and notation in the endnotes. (The quantitatively inclined can find more detailed treatments of statistics and epidemiologic data in the references.)

But a small amount of computation will help clarify how epidemiologic data have been misused in the legal and policy arenas. To mathematically describe the minimum harm of, for example, a radiation release, it is useful to start with what is called the risk ratio or “relative risk” (RR), a measure of effect over a specific time span among those exposed to a possible danger, as compared with the risk among the unexposed over the same time span. ¹ If there is no source of error or bias in the observation and comparison, the RR can be translated into the minimum fraction of people affected by radiation release via the formula (RR–1)/RR. This formula expresses the amount by which RR exceeds 1 as a fraction of the total RR, and thus (RR − 1)/RR is commonly known as the attributable fraction or the “attributable risk” (Rothman et al., 2008). ²

This attributable fraction is the fraction of the exposed caseload produced by exposure over the given time span; it was 3 percent in the atomic bomb example mentioned above. It is often confused with—but is not the same as—the etiologic fraction (the fraction of exposed cases that had exposure contribute to their occurrence) or the probability of causation (the probability that a given cancer had exposure as a contributory cause). In the four-person example described earlier, the risk of dying over the age span from 50 through 80 is 100 percent for both the exposed and the unexposed, leading to a risk ratio of RR = 100 percent/100 percent = 1 and thus an attributable fraction of (1 − 1)/1 = 0. Yet, as the example clearly shows, radiation exposure played a role in at least 50 percent, and perhaps 100 percent, of the deaths. ³

In an attempt to remedy the extreme insensitivity of the attributable fraction to actual causation, most analyses will also include time as a factor. These more sensitive analyses compute disease rates in terms of cases per total observation time, or survival time, or over short time spans within the total time span of interest. They then take the ratio of these time-based rates as the relative risk and use this rate ratio in the attributable-fraction formula (RR − 1)/RR.

In the four-person example, one of the simplest methods of computing time-based rates leads to an estimated rate ratio of 1.67 and an attributable fraction of (1.67 − 1)/1.67 = 40 percent. ⁴ This estimate is an improvement over the estimate of zero from using the risk ratio, indicating as it should that the radiation exposure did cause harm. But again, this fraction is far below the actual probability of causation, for in reality exposure harmed at least half and possibly all of the exposed cases. More sophisticated methods can give us better estimates of minimum probability of causation (Robins and Greenland, 1989b), but this simple example shows that equating an attributable fraction with the probability of causation can lead to serious underestimates of harm from radiation releases, even when the fraction is estimated from rates instead of risks.

Logically, any radiation exposure may have contributed to all observed radiogenic cancers, or only to some minimal fraction. Again, however, only the minimum fraction affected by the exposure can be estimated from population data alone (Robins and Greenland, 1989a, 1989b). Unfortunately, in the absence of a biologic model that explains how radiation induces cancer, there is no way to estimate the relative proportion of accelerated and unaffected occurrences in the wake of exposure and thus no way to estimate the probability of causation (Beyea and Greenland, 1999). This inability to produce an accurate estimate of causation probabilities is an absolute limitation of epidemiology, yet it is rarely recognized by experts, regulators, legislators, and the courts in assessing harms. It is thus only to be expected that the journalists who inform the general public about such matters also miss this problem.

Time lost: A better scale for thinking about effects and compensation

Many compensation schemes and legal proceedings employ the probability of causation for estimating harm from radiation exposure. Usually the estimates of causation probabilities are based on an all-or-nothing biologic model that equates the probability radiation has caused a cancer to an attributable fraction, which in a number of court districts must be shown to exceed 50 percent before a plaintiff is eligible for compensation. But, as just illustrated, the attributable fraction will underestimate the probability of causation by failing to count accelerated cases.

Despite the limitations of epidemiologic studies, there is a way for regulations to be set and litigation managed that takes into account the possibility of accelerated cases of disease. This method of looking at risk shifts its focus from causation probabilities to population averages, including the average years of life lost from exposure. Compensation schemes based on such averages do not have to rely entirely on hidden or controversial biologic assumptions that accompany efforts to use causation probabilities (Greenland and Robins, 2000; Robins and Greenland, 1991).

This is not to say that estimating the population-average effects of radiation exposure is easy. Even without entering into the minefield of detailed biologic models for the causation of cancer, statistical modeling of exposure effects involves several challenging components. Because of random errors (noise) and the many potential causes of cancer subtypes, those wishing to estimate population-average effects of radiation exposure will need many events in fine-enough outcome categories (e.g., acute leukemia, or at least all leukemias) to obtain estimates that have a useful degree of precision. To minimize bias as well as obtain age, sex, and dose-specific estimates, researchers will need to include measured disease-risk factors in the statistical-modeling process, which will inevitably require introduction of statistical (smoothing) as well as biologic (structural) assumptions. Because of potential systematic errors (i.e., bias) that affect population data, one will need a bias model to assess sensitivity of results to such error. But through these and other methods, a statistical model of population-average radiation effects can be constructed, and it will not be based on false assumptions about what epidemiologic studies are capable of estimating.

As with other compensation schemes, those based on estimated years of life lost (Berry 2007; Boshuizen and Greenland, 1997; Robins and Greenland, 1991) will suffer from inaccuracies if only because they must provide the same compensation to observationally indistinguishable individuals, some who suffered great loss and others who suffered little or none. But schemes based on average years lost spread over-compensation and under-compensation in a more balanced fashion (and, arguably, more equitably) across exposed cases than do causation-probability estimates. In particular, compensation schemes based on average years of life lost help ensure that all cases suffering loss from exposure receive some compensation, while limiting the defendants’ liability to the total years of life lost due to exposure in the whole population.

Even if the causation probabilities of a particular radiation release could be correctly estimated, the insensitivity of those probabilities to actual damage (to years of life lost, for example) argues against compensation based solely on those probabilities. To see why, suppose the cancer causation probability for a radiation release were known to be 50 percent. Quite different compensation would be warranted if the cases affected by the exposure suffered loss of one week of life, rather than loss of 10 years of life. But compensation schemes based only on causation probabilities fail to take such differences in damage into account, to the detriment of both plaintiffs and defendants.

Any rational scheme for setting compensation in radiation exposure cases has to bring in notions of actual loss. From there, it is a small step to use these losses directly for compensation, bypassing altogether the vexing problem of trying to estimate probability of causation. By using the available data to estimate losses rather than probabilities, we may reduce the impact on stakeholders of the uncertainty and controversy over the biologic mechanisms by which radiation induces cancer.

Scientists should acknowledge the limits of epidemiology

In summary, health scientists and regulators should recognize and acknowledge the limitations of epidemiologic data for determining causation probabilities. These limitations are logical and thus need to be distinguished from the less subtle (but equally important) problems of reliably identifying small relative risks. Acknowledgment means in particular that health scientists should cease to offer estimates of causation probabilities that teeter on hidden and unsupported assumptions, such as the assumption that there is no acceleration of disease from exposure. In the place of causation probabilities, it is possible to develop direct estimates of average harm and losses from exposure, such as expected years of life lost, and thus provide more rational and fair compensation schemes and judicial decisions (Greenland and Robins, 2000; Robins and Greenland, 1991).