Life is a risky business. We all continuously face risks of some sort or another. Sometimes we face risky monetary decisions; sometimes we face dangers to life and limb. Not only do we face these dangers, we make decisions daily about them and compare, even if only implicitly, the risk to the benefit. Each morning we decide to get up, face the world and the boss and forgo the benefit of a day in bed, but avoid the risk of being fired and the cost of lost salary. We decide when it is safe to cross the road, and when it is wiser to wait; we may choose to ride by auto rather than bicycle or walk; we may use safety glasses while home woodworking, or decide to quit smoking.

In these everyday choices that we make consciously or unconsciously, we assess the risk more or less crudely, assess the benefits of monetary gain, pleasure, or other objectives, and make our own trade off. This rapid risk-cost-benefit analysis is based on a host of factors, such as reasoning, guesswork, and past experience. In many obvious cases, the actual risks are small, and the risk assessment need be done only crudely and perfunctorily to be adequate. Individuals may reach different decisions on the timing for crossing roads since different individuals may not agree on the values they apply to different risks. In the old aphorism: "one man's meat is another man's poison." Moreover, these values may not remain constant over time in even one individual.

In this book we introduce a few of the ideas and difficulties associated with attempts to formally perform risk assessments and make risk benefit comparisons. The risks that we discuss are to health and human welfare. While it is plausible that other species are of interest, usually it is the survival and welfare of the whole population of such species that are of concern, not individuals or specific groups. Risks to such other species may be included in a risk-cost-benefit analysis, but we will assume that such effects are included in the monetary or non-monetary analysis of benefits and costs--while noting that our concern may ultimately in fact be for the indirect effects on humans of the direct effects on other species.

We will endeavor to put the analysis in commonplace terms as much as possible. We maintain that if the risk assessor cannot express the risk simply enough to be understood by others, it is likely that he does not understand the risk himself. We therefore argue that words used in risk assessment should follow common parlance rather than have a specialized meaning. That is not to downplay the role of the expert, however, nor to suggest that technicalities are not appropriate in technical documentation.

The word risk implies uncertainty. We do not discuss situations with outcomes that are definite and certain, although uncertainties can arise in many different ways. The uncertainty about involvement in auto accidents does not arise because we do not know whether cars are involved in accidents, but because we do not know whether our particular car will be involved in an accident. There are other cases where the risks are hypothetical--we do not know whether the event actually occurs--and much of our uncertainty arises from this. Trichloroethylene given repeatedly at high doses causes liver cancer in some strains of mice, but there is no strong direct evidence that it causes cancer in humans at low doses, although it is often considered prudent for regulatory policy to make the hypothetical assumption that it does. Individuals exposed to trichloroethylene are faced with an uncertainty of a different kind from that in the automobile example above. This is discussed in Chapter 3 under "Model Uncertainty." The important distinction between variability and uncertainty is also discussed in Chapter 3.

Events or actions, which may pose a risk to humans are perceived through the filter of our senses. Perceptions are further modified by experience, time of occurrence, culture, religion, and other variables that make each person unique. We cannot, a priori, expect the assignment of the same values to similar risks by different persons. The experience of attempting to cross a street in an unfamiliar city is an example--an inhabitant may clearly recognize a "safe" situation, where the visitor hesitates. The results are differences of opinions, each opinion based on perceptions of risk, but differing from all others with different perceptions. We include a discussion of risk perception in Chapter 4.

The importance of perceptions of risks is illustrated by Table 1-1 (Marsh-McLennan 1978), which summarizes results of a public opinion survey of twenty years ago. Most people seem to believe that life was becoming more dangerous, even though most objective measures show the contrary to be true. Figure 1-1 (from the Vital Statistics of the U.S.) shows how in almost every age group the risk of dying has steadily fallen in the last 100 years. This figure shows the dramatic bump in 1919 due to the worldwide influenza epidemic which killed more people than the First World War. The increases in death rate among the 25-35 year olds in 1965 to 1975 are attributable to car accidents, and from 1975 to 1990 to AIDS.

One standard inverse measure of the probability of dying is the expectation of life, or life expectancy. This has been steadily increasing in the U.S. since about 1900. This is shown in U.S. statistics in Figure 1-2. There is a difference (fortunately decreasing) in life expectancy between black and white Americans. Life expectancy has changed slowly throughout the millennia. Half the skeletons in the Beijing caves, 7,000 years ago, were young, suggesting a life expectancy of 13 years. Roman writers talked about 23 years. Life expectancy slowly rose and reached 35 years in Sweden in 1750, from which time more accurate records were kept. Figure 1-3 shows the rapid rise in life expectancy for Sweden since about 1850 reaching 80 years recently. Figure 1-3 shows that life expectancy in Japan and France has almost caught up, as it has in the United States. Until 1980, life expectancy in the USSR was about 1 year less than in the United States, France, Japan and Sweden, but fell to about 67 for Russian males in the mid 1990s, rose again in 1997, and is slowly decreasing again. As also shown in Figure 1-3, life expectancy in some developing countries is still substantially shorter than for the other countries shown in Figures 1-2 and 1-3.

This increase in life expectancy in developed countries has been brought about by the elimination of many large risks to life, such as many infectious and contagious diseases, poor working conditions, and inadequate nutrition1 (Doll 1979). Improved medical technology is now making small improvements, at high cost. This, in itself, leads to problems. The issues that these concepts address are illustrated both by a cartoon and by a quotation from H Daly in 1982:

"As far as we know, God is not impatient for our lives to be lived soon"

Western societies now concentrate on the many smaller risks, many of which are poorly understood, in order to further reduce total risks. Perhaps the fact that many more risks, even though smaller, are now being discussed has caused the apparent alarm of those whose opinions are summarized in Table 1.1. The problem may also be a question of a different understanding of the word risk. We have, for example, not found anyone who thinks that life expectancy in the U.S. is going down or is about to go down, in spite of the fact that many people believe that life is riskier! This different understanding of the word "risk" is one of the issues in perception of risks discussed in Chapter 4. The problem is very deep seated. Mankind is used to dealing with decisions in a binary manner: "yes, it is safe" or "no, it is dangerous." Yet the world rarely works that way, and chance events are inherent. We therefore suggest that it is a role of a specialist to interpret for the general public and guide them as to which risks are acceptable and which are not.

But even if a risk is acceptable (worthy of acceptance) it may not be accepted. Decisions are clearly never based on actual risks but (at best) on the decision maker's perception of them. In this book we make an assumption, most of the time, that an expert's calculation of the magnitude of a risk is likely to be more accurate than a lay person's perception, and that societal decisions are more likely to lead to a general good if the expert's calculation is used in an analysis than if a lay person's perception is used. But a failure of a decision maker to recognize the perception of a lay person can lead to a public revolt--and a negation of the decision. The effectiveness and correctness of any decision is usually judged by lay persons. This point is discussed further in Chapter 7.

It is the differing perceptions, opinions, and sometimes political agendas, of individuals and groups that control their differing actions. When an individual action has a small possible consequence--ranging from no harm to a maximum of one death at a time--and the action is repeated by large numbers of individuals, typically these differences lead to a spectrum of results, good, bad and indifferent, but typically, no single action is likely to have a catastrophic effect.2 Individuals can see not only the results of their own actions, but also the results of the ill-conceived actions of others. They can then adjust their future behavior to reduce the harmful effects. Recently we have built large technological systems, so that a single decision can now result in large harmful effects--several thousands of deaths. In such circumstances, there is much less opportunity for this feedback to limit harmful effects, since the first wrong action could be disastrous, when compared with historical precedents. We therefore often want to find out how risky an action is before anyone has performed it, and so we attempt to introduce some objectivity into the analysis of risk, instead of relying on imperfect and uninformed direct perception. We introduce objectivity in an attempt to modify a priori perceptions by the use of objective evidence. Furthermore, it is necessary always to bear in mind that any such attempt at analysis of risks only attacks one aspect of any problem--the risks of any event or action have always to be weighed against costs and benefits.

Risk is a word used in many different ways by different disciplines. Indeed, so varied is its use that some authors have avoided the word entirely. Accordingly we consider it necessary to define precisely what we mean by a risk and by its numerical measurement. There are three meanings of the noun in the Oxford English Dictionary: (1) "hazard, endanger, exposure to mischance or peril" and (2) "the chance of hazard or commercial loss," (3) "as in Risk-Money, an allowance paid to a cashier to cover accidental deficits." The quantitative meaning we use in this book is close to (2).

Although there are uses of the word risk that are more inclusive, in this book we associate risks with events or actions. It is an often overlooked fact that inaction, whether it is conscious or unconscious, can also be risky and is susceptible to analysis. For example, society has so far decided to take no action to prevent a meteor or comet from striking the earth, and society is so far taking few actions to reduce the CO2 buildup in the atmosphere. The events and actions may be small or large, from digging one shovel of dirt to creating new seas, from creating a one-way street to decisions on whole highway construction programs. For each event or action we associate some units of risk, leading to a risk per street crossing for example, or a risk per ton of copper ore mined. Thus in some way we have a visualization:

How much or how often,

per total risk

or per unit of action,

or per event

In more useful form we can write:

Risk = Probability x Severity

In a decision-making context we are concerned with a perception of a risk. This is an approximation of the risk itself so that we initially interpret the terms in this equation as being perceptions (either of the decision maker or of his expert consultant or his employer), so that the equation thus reads:

Our perception of the magnitude of risk from some event depends on some form of product of how often we think the event will occur and how serious we consider each occurrence to be in its effects.

To illustrate, consider the following cases:

(a) The risk of a broken leg is greater for an inexperienced skier than for an experienced skier.

(b) The risk of death or injury in auto accidents is greater for those not wearing restraint harnesses (seat belts) than for those who are.

in (a), the severity of injury (broken leg) is the same, but we expect the probability, per day of skiing, to be higher for the inexperienced skier. In (b), we expect the probability of accidents is approximately the same, but the severity to be markedly higher for the unrestrained auto occupants.
 

Notice that we have refrained from putting an ordinary multiplication sign (X) in the above equation, since in some practical cases risk perceptions may not be truly multiplicative (Tversky et al., 1990). Nevertheless, it appears that most risks do have some multiplicative features, and we shall use this below in our first attempt to introduce objectivity. Others have defined risk less objectively (Fischoff, 1984).
 

Thus far, the discussion has been concerned mainly with single events or actions. Of course, the definition was left open, so that such "single" events/actions could cover most cases, but in essence they consist of the most elementary actions we are to analyze with respect to their risk content. To associate a risk with more complex events or actions, it is necessary to break down the actions into individual smaller actions. Then we usually assume that summation is possible and write:

Risk = S {probability X severity X weight} (1-3)

where the S stands for whatever form of addition (unknown) is actually used by individuals. The weight factor is included separately here--it could perhaps be included in the "severity" term if the equation relates perceptions, but it is convenient for later discussion to isolate it. It is included to account for the possibility that in evaluating a problem consisting of many different parts, risks of apparently similar magnitude may be accorded very different weights in consideration of the totality. Any inappropriate assignment of weight, or erroneous perception of the risk of any section of a problem, may lead to inappropriate ("incorrect") actions or decisions. That is, such actions or decisions would result in end results different from those planned, and thus not optimal from some point of view. One attempt at reducing such non-optimal results is the objective analysis of risk, which we pursue throughout this book. A technical reader will recognize that we are describing a Bayesian approach to a discussion of probability: that is, a perceived probability is a prior probability modified by subsequent data.

It is important to realize that the concept of risk is not static in time. As events develop, the risk changes. When I start to cross a road there is a risk that I will be killed by an oncoming car. If I reach the other side the risk will have dropped to zero. If I fail to reach the other side and the car does me in, the risk reaches 100% and is no longer called a risk. This point also holds for the assessment of risks of exposure to radiation or to a chemical. Whereas there is a risk that anyone will develop cancer as a result of exposure to radiation that is not a sensible concept for a person who already has that cancer. Instead we can ask "what is the probability that his cancer was caused by radiation." This is often called "The Probability of Causation" (POC) (Mettler and Upton, 1975; NIH, 1985) and can be related quantitatively to the risk by the equation derivable from Bayes' theorem:
 
 

It is important to distinguish clearly the two concepts of Risk and Probability of Causation. For example, although the risk of developing angiosarcoma from vinyl chloride exposure is small, the incidence of angiosarcoma is itself small, so that the fraction of angiosarcomas caused by agents other than vinyl chloride can also be small, so that the Probability of Causation is high when someone even with a small exposure to vinyl chloride develops an angiosarcoma.

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