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RISK/BENEFIT ANALYSIS EDMUND A.C. CROUCH RICHARD WILSON 3 The importance of perceptions of risks is illustrated by Table 1-1, which summarizes results of a public opinion survey. Most people seem to believe that life is becoming more dangerous, even rhoug!; most objective ;reu,suri,S show the contrary to be true. The expecta- tio;; of life, for example, an inverse measure of the probability of dying, has steadily increased, from perhaps twenty-eight years fifteen centuries ago, to fifty years one century ago, to about seventy-two years currently, although the rate of increase has been decreasing. The increase has been brought about by the elimination of many large risks to life, among them many infectious and contagious dis- eases, poor working conditions, and inadequate nutrition. Figure 1-1 shows the reduction in death rates in this century by age group. De- tailed examination shows that the increase since 1960 in the 15 to 24 age group is due to automobile accidents. Doll (1979) has also shown how health, as measured by most medical indicators, is improving. It is now necessary to concentrate on the many smaller risks, often poorly understood, in order to further reduce total risks. Perhaps it is Table 1-1. Public Opinion Survey Comparing Risk Today to Risk of Twenty Years Ago. BALLINGER PUBLISHING COMPANY Cambridge, Massachusetts A Subsidiary of Harper & Row, Publishers, Inc. PERSPECTIVE ON RISK Q: Thinking about the actual amount of risk facing our society, would you say that people are subject to more risk today than they were twenty years ago, less risk today, or about the same amount of risk today as twenty years ago? Q: I'd like to start by asking you a few questions about the amount of risk we face in our day-to-day living. Thinking about the actual amount of risk facing our society, would you say people are subject to more risk today than th( ~ were twenty years ago, less risk today, or about the same amount of risk today as twenty years ago? Top Corporate Investors, Federal Executives (N = 401) Lenders (N = 104) Congress (N = 47) Regulators (N = 47) Publlc (N = 7,488) More risk 38 60 (percent) 55 43 78 Less risk 36 13 26 13 6 Same amount 24 26 19 40 14 Not sure 1 1 ... 4 2 Source: Marsh & McLennan Companies (1980).

12 RISK/BENEFIT ANALYSIS THE MEANING OF RISK 13 Figure 2-1. Accidental Deaths per Million Tons of Coal Mined - . .._- ~ in the United States. _ FiW_lre 2-2. .,wwrai n_:'_._cn.. Deaths per Thoucanri Cea! ~^ --- ~... .. ~a•...., u~~ Niuyce5 in the United States. 2.50 N ~ U O ~ 2.25 c ~ 1 0-I v T O F-O . d W 2.00 a L n O v ° 1.75 ~ L h 0.5 ~ m v C ~ L n R 1.50 V Q c V a J Q 1.25 0 1950 1955 1960 1965 1970 0 00 Year . 1950 What measures of risk are appropriate for a particular risk assess- ment depend on the specific details of the question the assessment is designed to illuminate. Presumably they will be the measures corre- sponding asinearly as possible to the way in which the risks are per- ceived. In what follows we will usually be limiting consideration to risks of death (measured by probabilities of dying or expected excess numbers of deaths) resulting from various actions, although other risks will occasionally be mentioned. Although we shall not concern ourselves much with it, the dis- tinction between risks and measures of risk is not totally academic. A simple example is the American coal industry, taken as a whole, between 1950 and 1970. Figure 2-1 is a plot of one measure of risk in this industry-the number of accidental deaths per million tons of coal mined. Clearly this measure steadily declined during this period, so that, if we follow the industry through successive years, it appears to be getting safer. Looking at Figure 2-2, which shows the behavior of another measure of risk-the number of accidental deaths per 1955 1960 1965 1970 Year thousand persons employed-one might naively assert that the indus- try is getting more dangerous, not safer. Evidently the two measures illustrated might be used to support opposing views on the safety of coal mining. Neither measure taken alone is right or wrong, nor are they even contradictory even though they may be so perceived. Any risk assessment supposed to be com- plete would have to draw attention to the two aspects of the risk of coal mining gauged by the two different measures and would have to take both into account, depending exactly on the purpose of the risk assessment. From a national point of view, given that a certain amount of coal has to be obtained, deaths per million tons of coal is the more appropriate measure of risk, whereas from a labor leader's point of view, deaths per thousand persons employed may be more relevant. What steps to take to reduce the risk will depend on which of the two measures is used. Doubling the number of miners, each working

THE MEANING ®E RISK l I RISK(SENEFIT ANALYSIS 4 Figure 1-1. Death Rates at Five Year Intervals from 1900 to 1975 for Various Age Groups: United States. Date s T4s1Vsszoz Age Group ovrk 85 75 -84 65 -7 4 UNDER I 55 -64 45-54 35-44 25-34 15-24 1-4 5-14 1980 mum from some point of view. One attempt at reducing such possi- bilities is the objective analysis of risk, which is pursued throughout this book. To make any start cr; objcciive assessment it is neces;a~ °-- y to realize what is being measured. Death is one clear objective measure, The total annual risk of death at any age is just the probability of dying within one year. In the absence of any extra causes, population aver- ages for this measure are obtained from national mortality tables (see Chapter 7). But in risk assessments we are interested in additional risks of death or components of the total risk of death due to some specific actions undertaken either voluntarily or involuntarily. More often, we are interested in how much of an action to undertake, so that we wish to evaluate measures such as extra probability of death per unit of action (per cigarette smoked, or pet ton of coal mined, for example). Death is not the only measure of risk of interest, for, although it is probably the most objective one and for this reason often used, it may not capture large components of what are perceived as risks. In balanced decisions it may become vital to consider other measures. A few possible such measures are: by age Deaths by cause Injuries Illness Man-days lost by cause by type by severity index by cause by type by severity index I by cause Days of impaired health Days of pain Loss of life expectancy I Total numbers (whole task) or probabilities (for individuals) per unit operation size per event per unit dose (per cigarette, per ton produced, per unit output, etc.)

70 RISK/BENEFIT ANALYSIS This form of analysis constitutes an all-at-once technique, but one that is less useful than the preceding example (chemical hazards) be- cause it aIves no clue as to how to reduce the risks. The limitatin n ca, ~e Overcome if it is possible to analyze each event leading to risks as a sequence of well-understood events forming an event tree. A set of event trees would cover all possible cases leading to the final risky event. The most well-known use of event tree analysis is, perhaps, the analysis of nuclear reactor accidents in the so-called Rasmussen report (Nuclear Regulatory Commission 1975). The procedure will be briefly outlined here with a highly simplified example from the report. The first step is identification of all possible sequences of events that may lead to serious consequences to public health and safety, followed by the separation of these sequences into segments that are approximately independent of each other. By analyzing each event in each sequence separately, using theory or past experience or both, the overall probability of occurrence of the whole sequence can be evaluated. Thus the most probable (highly simplified) se- quence for catastrophic failure in a PWR is shown in Figure 3-6. The overall accident probability (with assumptions to be mentioned) is then equal to Probability of a pipe break (from theory and past data on other pipes) x probability of failure of emergency core cooling system (from a fault tree analysis) X probability of containment violation (more fault trees) x probability of unfavorable weather (past data on wind patterns, rain- fall, and so on) ~ PI P2 P3 Pa • The accident described by this event tree is initiated by the break of N a water pipe in the cooling system causing loss of coolant and result- ing, ing, if the emergency core cooling system subsequently fails, in the ~ meltdown of the reactor core and the release of the fission products ~ therein. This may cause a violation of the concrete containment ves- ~ sel, so that if the wind direction is right the released fission products ~ may be blown over population centers, possibly causing radiation .~ overdoses to a large segment of the population. In each case the probability of the event and also its severity must be evaluated. As ~ indicated, the probability (pl ) of a pipe break may be estimated from historical experience with pipes first in other industries, sec- 104 RISK/BENEFIT ANALYSIS cases are examined in detail major flaws ~^u wedK '- u.. ncsses can be dis- covered_ We are l:eartc;,cd, iiowever, by the realization that many of the flaws can easily be remedied and that in at least one case (saccha- rin) common sense filled in the gaps. Before beginning a detailed discussion of individual studies, it is useful to picture an idealized scheme (Figure 6-? ) of the complete decision process, and the place of risk assessment within it. Informa- tion is passed from scientist, engineer, and economist to risk assessor and to cost and benefit assessors. The results of these assessments and comparisons between them are made available to the decision- Figure 6-1. Idealised Scheme for Risk Analysis. I ASSUM PTIONS " " De Minimis Risk. STO P 10's/yr. Occupational 10'6/yr. General Total Societal Impact 10/ yr. Scientific R isk C Data Asses sment --~~ Numbers ± ~ Uncertainty 1 Economic and ~ C ost I Engineering Data I Asses sment Numbers ± ( \ Uncertainty Risk/Benefit Risk/Risk ~ ~ Risk/Cost ~ ( Numb Comparisons Ben efit Uncertaint ~ Asses 9 sment y ~ I ~ i Interested ~ Va lue Parties ludge ments 1- DECISIONS ( L --l Results of decision Questions Alternative f tw 1 P i l K or Decision . oss e b Decisions nighthoods, Insults, Anonymous letters etc.

174 RISK/BENEFIT ANALYSIS EVERYDAY LIFE: A CATALOGUE OF RISKS 175 Table 7-1. Some One in a Million Risks. Table 7-1. continued Living in the United States: Time to accumulate a on from the cause indicated. e in a million risk of death Eating and Drinking. Motor vehicle accident 1.5 days 40 diet sodas (saccharin) Falls 6 days 6 pounds of peanut butter (aflatoxin). Drowning 10 days 180 pints of milk (aflatoxin). Fires 13 days 200 gallons of drinking water from Miami or New Orleans. Firearms 36 days 90 pounds of broiled steak (cancer risk only). Electrocution 2 months Smoking Tornadoes 20 months Floods 20 months 2 cigarettes Lightning 2 years Source: Tables 7-2 to 7-5. Animal bite or sting 4 years Occupational Risks. Time to accumulate a one in a million risk of death in the occupation indicated. General Manufacturing 4.5 days Trade 7 days Service and Government 3.5 days Transport and Public Utilities 1 day Agriculture 15 hours Construction 14 hours Mining and Quarrying 9 hours Specific Coal Mining (accidents) 14 hours Police duty 1.5 days Railroad Employment 1.5 days Fire Fighting 11 hours Other Risks. Cosmic Rays. One transcontinental round trip by air. Living 1.5 months in Colorado compared to New York. Camping at 15,000 feet for 6 days compared to sea level. Other Radiation 20 days of sea level natural background radiation. 2.5 months in masonry rather than wood building. 1/7 of a chest X-ray using modern equipment. ZOUSt7sizQZ clearly into categories within which intercomparison is more easily justified and probably more accurate. Table 7-2 is a list of various commonplace risks of death, most of which would be considered involuntary. Notice that there may be some overlapping between categories (home accidents, for example, includes falls within the home). Table 7-3 shows some occupational risks, mostly risks of fatal accidents. Again, most such risks would be considered involun- tary by those exposed. Table 7-4, in contrast, shows a set of volun- tary risks of death, those incurred in sporting activities. Table 7-5 is a further set of everyday risks, but now specialized to cancer risks, selected because such risks arouse particularly strong emotions. Before discussing these risks in more detail and indicating how they are all estimated, we would like to give another example that may help place these risks in perspective. Four tablespoons of pea- nut butter per day is shown as giving a risk of liver cancer of 8 X 10-6 per year, or a lifetime risk of 6 X 10-4. But four tablespoons of peanut butter corresponds to 400 kilocalories (Kcal), so if one were to eat only peanut butter, daily energy requirements would be sup- plied by 26 tablespoons per day, giving a lifetime liver cancer risk of 4 X 10-3, or 0.004. This should be cor -oared with a lifetime proba- bility of any kind of cancer of about 0.25, even in the absence of peanut butter. r

~ Table 7-•2'. Some Commonplace Risks of Death in the United States, Based on Estimated U.S. Resident v Population (Source 1). a Risk Annual per Capita Risk a Annual Trendb Uariability, Percentc Based On z Source x Motor vehicle accident Total .4 x 10-4 .. 0 950-78 m z m 1 ~ -~ Collision wirh pedestrian 4.2 x 10-s -3.9 x 10' 10 1950-78 2 a Home accidentsd Falls 1.1 X 10-4 6.2 x 10-s -2.9 x 10 6 -3.0 x 10-6 5 6 1950-78 1963-77 2 z a 2 r -~ -s ~ Drowning 3.6 x 10 ... 7 1963-77 2 N Fires 2.8 x 10-5 -1.0 x 10-6 5 1963-77 2 Inhalation and ingestion of objects 1.5 x 10-s ... 10 1968-77 2 Firearms 1.0 x 10-s -2.4 x 10-' 8 1968-77 2 Accidental poisoning Gases and vapors 7.7 x 10-6 ... 5 1963-77 2 Solids and liquids (Not drugs or medicaments) 6.0 x 10-6 ... 10 1971-77 2 Electrocution 5.3 x 10-6 ... 5 1971-77 2 Tornadoes 6 x 10-' ... 100 1950-77 1 Floods 6 x 10' ... 100 1950-77 1 Lightning 5 x 70-' ... 18 1971-77 2 Tropical cyclones and h urricanes 3 x 10 ' ... 160 1952-77 '. Bites and stings by venomous animals and insects 2.4 x 10-' .. 13 1971-77 2 Air Pollution 2.4 x 1074 ... -see text- a. Average over indicated years, if no trend is shown. The value of trend line in last year of indicated years is used if a trend is shown. b. Average annual change of annual per capita risk during years shown. Least squares straight line fit of annual risk versus time. A trend is shown if the estimated trend was significant at the 5 percent level (two-tailed). c. Estimated standard deviation of annual per capita risk about the trend line (trend) or of the mean value (no trend). d. Home accidents inciude,s some proportion of some of the following seven risks. Sources: 1. U.S. Bureau of the Census (1975, Annual). 2. National Safety Council (Annual). ~ ~ ~

Table 7-3. Some Occupational Risks of Death. ~ ~ ~ Occupation or In,dastry Annual Riska Annua! Trendb Variability, Percent` Based On z Source ~ ~ Manufacturing 8.2 x 10-5 -1.6 x 10-6 8 1955-78 m m 1 z -5 -6 ~ Trade 5.3 x 10 -2.3 x 10 15 1955-78 1 ~ "4 -6 -~ Service and government 1.0 x 10 -2.0 x 10 8 1955-78 1 a Transport and public utilities 3.7 x 10'4 ... 16 1955-78 1 z Agricultured 0 x 10-4 6 9 1955-78 a 1 r . ... < Construction 6.1 x 10-4 -7.0 x 10 6 6 1955-78 1 ~ ~ Mining and Quarrying 9.5 x 10-4 ... 22 1955-78 1 Farminge 3.6 x 10-4 -5.0 x 10-6 7 1964-77 1, 2 Tractor fatalities per tractor 8.8 x 10-$ -1.0 x 10-5 22 1969-77 1 Metal mining and milling 9.4 x 10-4 ... 15 1959-71 3 Nonmetal mining ,and milling 7.1 x 10-4 +2.3 x 10-5 15 1959-71 3 Stone quarries and rnills 5.9 x 10-4 ... 20 1959-71 3 Coal mining (accidents) 6.3 x 10-4 -1.0 x 10-4 46f 1963-77 4 Police officers killed in line of duty Total 2.2 x 10-4 ... 19 1975-78 4 By felons 1.3 x 10 ° -2.1 x 10-5 8 1975-78 4 Railroad employees 2.4 x 10-4 -6.0 x 10 6 7 1963-77 1,4 Steel worker (accident only) 2.8 x 10 4 ... ? 1969-72 5 Fire fighter 8.0 x 10 4 ? 1971-72 5 a. Per person at risk. Average over indicated years, if no trend is shown. The value of trend line in last year of indicated years is used if a trend is shown. b. Average annual change of annual risk during indicated years. Least squares straight line fit of annual risk versus time. A trend is shown if the estimated trend was siE;nificant at the 5 percent level. Note that the error estimates for these trends are generally large. c. Estimated standard deviation of annual risk about the trend line (trend) or of the mean value (no trend). Expressed as a percentage of the risk shown in the first column. d. Not strictly compara.ble with farming category, includes transport accidents and all agriculture. e. Not strictly comparable with agriculture category, refers to nontransport deaths occurring on farms, the population at risk being assumed to be all employed workers, unpaid family members working more than fifteen hours per week and operators working more than one hour per week. f. The large variability is due to the bad choice of model (straight line fit) and the large changes occurring in the years indicated. Sources: i. National :iat'ety Council (Annual). 2. U.S. Department of Agriculture (1979). 3. U.S. Bureau of Mines (Annual). 4. U.S. Bureau of the Census (Annual). 5. Baldewicz et al. (1974).,

Table 7-4. Annual Fatality Risks in Sports a ~ 0 port Average Annual Riskb A verage Annual Deaths Estimated Population at Risk r Years of Coverage z Source ~ X d h ~ Aerial acrobatics (professional) , <2X10-3 ~ 0.22 360 1970-78 1 z Air show/air racing and acrobatics 5 x 10-3 4.9 1,050c 1971-77 1 m Flying amateur/home built aircraft 3x 10-3 25 8,000` 1970-77 1 Bicycle racing (registered) < 9 x 10-s d,e 0.33 9,800 1970-78 1 a z Boating 5 x 10 s 1,300 27 x 106 1972-78i 2, 3 a r Bobsledding < 7 X lC-4d,f 0 450 1970-78 -G 1 ~ Footbai l Sandlot 2 x 10-6 1.7 106 1970-78 V) 1 Professional and Semiprofessional <4x10-4 d, 9 ~ 0.11 1,500 1970- 78 1 High school 1 x 10-51 13 106 1970-78 1 College 3 x 10"sl 1.2 40,000 1970-78 1 Glider flying 4 x 10-4 7 18,000` 1970-77 1 Hang gliding ~8x 10-4 31 20,000-60,000 1974-78 1 Hunting 3 x 10 5 600-800 22 x 106 1972 2,3 Ice yachting < 1 x 10-4d,h ~ 0.22 4,500-6,500 1970-78 1 Lighter-than-air flying 9x 10-4 2.6 3,000c 1970-77 1 Mountaineering 6 x 10-" 34 60,000 1970-78 1 Mountaineeringk 7 x 10-4 12 19,000 1951-60 4 Power boat racing 8 X 10 4 5.2 6,500 1970-78 1 Professional stunting <_ 1 x 10'd°r 1 200 1975-78 1 Rodeo < 3 x 10-s d, e 0.33 34,000 1970-78 1 Scuba diving 4 x 10-4 126 300,000 1970=76 1 Ski racing 2 x 10-$ 2 81,000 1970-78 1 Spelunking < 1 X 10 4 d' i 0.44 10,000 1970-78 1 Sport parachuting 2 x 10 3 41 25,000 1970-78 1 Thoroughbred horseracing 1 x 10-3 2.6 1,800 1970-78 1 Swimming 3 x 10-5 2,600 82 x 106 1972-78j 2,3 a. No error estimates are: given. The reason is that, although we could give statistical sampling errors on the risks shown, the population size is so uncertain in most cases (by a factor of 2 to 3) that this uncertainty dominates. b. Per person at risk. See preceding note on error estimates. c. This population corresponds only to pilots certified by the Federal Aviation Administration. d. The value shown is statistical 95 percent confidence upper bound, assuming risk proportional to person-years of exposure and a Poisson dis- tribution of deaths. See also note a on error estimates. e. Three deaths observed in time indicated. f. No deaths observed in time indicated. g. One death observed in time indicated. h. Two deaths observed in time indicated. i. Four deaths observed in time indicated. j. Population figures from 1972, deaths from 1978. We have assumed a similar population went swimming or boating in 1978. k. Not strictly comparable with the preceding entry, also labeled Mountaineering. The figure in the population column is total man-mountain- ays, and the risk is per man-mountain-day. This agrees with the previous figure for annual risk if an average of - 0.9 days per year is spent moun- aineering, but note that the year; of coverage differ also. I. If participation has remaiined constant, as we assume, there are possibly decreasing trends in these risks. Sources: 1. Metropolitan Life Insurance Company (1979). 2. U.S. Bureau of the Census (Annual). 3. National Safety Council (Annual). 4. Fer- s(1963). (The article also discusses some of the problems of interpretation of risks such as those shown in this table). ~ tb ~

Table '7••5. Everyday Cancer Risks a Annual Average Riskc Estimated Uncertaintyd Source Current Cancer Rai`esb r All Cancers 2.8 x 10-3 Buccal cavity, pharynx, respiratory 7.2 x 10-4 Digestive organs and peritoneum 7.5 x 10-4 Bone, connective tissue, skin, breast 3.1 x 10-` ^' 20% 1 Genital organs 3.2 x 10-4 Urinary tract 1.2 x 10-a Other 2.7 x 10-4 Leukemia and other blood and lymph 2.6 x 10-4 Cosmic Ray Risks° Airline pilot (50 hours per month at 12 kilometers altitude) 4 x 10-$ 2 One transcontinental round trip by air per year 10-6 2 Frequent airline passenger (4 hours per week flying) 10-$ i 2 Living in Colorado compared to New York Camping at 15,000 feet for 4 months per year 8 x 10-6 2 x 10-s ~ Factor of 3f 3 3 Other Radiation Risks Natural background radiation (sea level) 2.0 x 10-s / 3 Average diagnostic medical X-rays in the United States Living in masonry building rather than wood 2.0 x 10-5 5.0 x 10-6 {` 4 5 Eating and Drinking One 12h ounce diet drink per day 10-$ Average saccharin consumption in the United States 2.0 x 1Q 6 Four tablespoons peanut butter per day' One pint milk per dayi Miami or New Orleans drinking water charcoal broiled steak per week 1/2 lb 8.0 X 10-6 2.0 x lv 6 10-6 Factor of order 10 See text. . (cancer risk only; heart attack and other risks additional) 3.0 x 10-' ,,Icohol, averager< over smokers and nonsmokersg 5.0 x 10-s ~ Factor of See text. Alcohol, light drinker (one beer per day) g 2.0 x 10-5 order 10 Tobaccoh Smoker, cancer only 1.2 x 10-3 Factor Smoker, all effects (including heart disease) 3.0 x 10"3 of 3 See text. Person sharing room with smoker 10-s ~ Factor of 10 Air Pollution Polycyclic organics, all effects 1.5 x 10_s See text. See text. a. These are risks of death, the difference between incidence and mortality being well within the uncertainties shown, (except for the Current Cancer Rates category. b. Included to give some perspective. The figures given correspond approximately to the lifetime risk divided by the lifetime. The lifetime risk is estimated by the fraction of those dying who die of the given cancer, average lifetime is estimated as seventy years. Since cancer rates increase rapidly with age and the population age structure is changing, these figures are only approximate. Data from Vital Statistics of the United States, 1975. c. Averaged over the whole population of the United States. d. Even the uncertainties in these estimates can be very large. The uncertainties are mostly estimated subjectively and are conditional on the models used for extrapolation being approximately correct. e. Averaged over males and females. The risk is approximately double for females only. f. We assume a linear model with a total of 1 cancer per 5,000 man-rem, corresponding to BElR"1972. More recent estimates of the BEIR committee (1980) would give >lightly lower estimates. g. Cirrhosis of the liver. N'ot a cancer, but included here since the methods used are similar. It is possible that in this case there is a threshold effect for damage. In addition there is some evidence that moderate alcohol consumption is associated with lower death rates from other diseases. h. Based on human data. Based on human data for aflatoxin carcinogenicity. Note that we assume that the measured aflatoxins are aflatoxin B, the most potent. If .e corresponds to other atlatoxins, these estimated risks should be reduced. Sources• (The following references are the sources of data used in the models. We have estimated the risks). 1. U.S. Department of Health, Education and Welfare (1975). 2. United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) (1962). 3. Oakley (1972). 4.. United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR) (1977). We have used the bone marrow dose here. 5. Moeller and Underhill (1976). ~ 00 tJ