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RISK BENEFIT ANALYSIS
Special Lectures
University of Kuwait
Richard Wilson
Mallinckrodt Professor of Physics
Harvard University
January 13th, 14th and 15th 2002
January 13th 9 am to 2 pm
What do we mean by Risk?
Measures of Risk
How do we Calculate Risk?
(a) History
(b) Animal analogy
(c) Event Tree
Day 2. January 14th 2002
Uncertainties and Perception
Types of Uncertainties
Role of Perception.
Kahneman’s 2002 economics Nobel prize
We will try to show his effect in class
List of interesting attributes
Major differences between Public and Expert
perceptions
Day 3 January 15th 2003
Formal Risk-benefit comparisons.
Net Present Value
Decision Tree
Value of Information
Probability of Causation
Cases:
Chernobyl, TMI
Bhopal
ALAR as a pesticide
Research on particulates
Sabotage and Terrorism
The Biggest Risk to Life is Birth.
Birth always leads to death!
We talk about premature death.
Table 1-1. Public Opinion Survey Comparing Risk Today to Risk of Twenty
Years Ago
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?
More risk
Less risk
Same amount
Not sure
Top
Coroprate
Executives
(N=401)
38
36
24
1
Investors, Congress
Federal
Public
Lenders
(N=47) Regulators (N=1,488)
(N=104)
(N=47)
60
13
26
1
55
26
19
0
43
13
40
4
78
6
14
2
MEASURES of Risk
Simple risk of Death (assuming no other causes)
by age
by cause
Risk of Injury
by cause
by type
by severity
Per
year
lifetime
unit operation
event
ton
unit output
RISK MEASURES (continued)
Loss of Life Expectancy (LOLE)
Years of Life Lost (YOLL)
Man Days Lost (MDL)
Working Days Lost (WDL)
Public Days Lost (PDL)
Quality Adjusted Life Years (QALY)
Disability Adjusted Life Years (DALY)
Different decisions may demand different measures
LOLE from cigarette smoking
In USA 600 billion cigarettes made (presumably smoked)
400,000 people have premature death
(lung cancer, other cancers, heart)
1,500,000 cigarettes per death
Each death takes about 17 years (8,935,200 minutes) off life
or
6 minutes per cigarette
ABOUT THE TIME IT TAKES TO SMOKE ONE
(easy to remember)
Expectation of Life at Birth in the United States
(1900-1928: Death Registration States only)
80
Expectation of Life at Birth
70
60
50
40
30
20
10
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
Expectation of Life at Birth in the United States
(1900-1928: Death Registration States only)
80
Expectation of Life at Birth
70
60
50
40
30
20
10
0
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Year
WHAT IS LIFE EXPECTANCY?
An artificial construct assuming
that the probability of dying as
one ages is the same as the
fraction of people dying at the
same age at the date of one’s
birth.
Both the specific death rate and
the life expectancy at birth have a
dip at 1919
world wide influenza epidemic.
BUT anyone born in 1919 will
not actually see this dip.
Peculiarity of definition of life
expectancy
Life Expectancy in the USA
80
75
70
65
60
All Races
55
White
50
Black
45
40
35
1996
1988
1980
1972
1964
1956
1948
1940
1932
1924
1916
1908
1900
30
Figure 1-3a
Life Expectancy
100
90
80
70
France
60
Japan
Sweden
50
Russia
Papua (54)
Gambia (37)
40
Palasra (52)
30
20
10
0
1750
1800
1850
1900
1950
2000
Half the “Beijing men’ were
teenagers.
This puts life expectancy about 15
Roman writings imply a life
expectancy of 25.
Sweden started life expectancy
statistics early.
Russia has been going down
since 1980
Risk is Calculated in Different
Ways and that influences
perception and decisions.
(1) Historical data
(2) Historical data where
Causality is difficult
(3) Analogy with Animals
(4) Event tree if no Data exist
Accidental Death Rate
Figure 1-4 Occupational Risk in Coal Mining, US
4.00
3.00
Per Million Man
Hours
2.00
1.00
Per Million Tons of
Coal Mined
0.00
1931 1941 1951 1961 1971 1981 1991
Per Thousand
Employees
Year
Risk is different for different
measures of risk.
Different decision makers will
use different measures depending
on their constituency
Accidental Deaths
per million man
hours worked
Figure 1-5 Accidental Death Rates by Type of Coal Mine,
U.S.
2.00
1.50
1.00
0.50
0.00
1931 1941 1951 1961 1971 1981 1991
Year
Underground Mines
Surface Mines
Annual Death Rate
Figure 2-1 Death Rates for Motor Vehicle Accidents in
the United States
35
30
25
20
15
10
5
0
per 100,000 population
per 10,000 vehicles
per 1 million vehicle
miles
1925 1935 1945 1955 1965 1975 1985 1995
Year
Accidental Deaths per
million tons of coal
produced
Accidental Death Rates by Type of Coal Mine, U.S.
4
3
Underground M ines
2
Surface M ines
1
0
1931 1941 1951 1961 1971 1981 1991
Year
1.50
Underg rou nd Mines
1.00
Surface Mines
0.50
0.00
1931 1941 1951 1961 1971 1981 1991
Year
4
3
Undergroun d Mines
2
Surface Mines
1
0
1931 1941 1951 1961 1971 1981 1991
Year
4.00
3.00
2.00
1.00
0.00
1931 1941 1951 1961 1971 1981 1991
Year
Accide nt al De ath Rates by Type of Coal Mine, U.S.
Accidental Deaths per
mi ll ion tons of coal
produced
Three Diffe re nt Metrics of Occupational Risk in Coal
Mining, Unite d States
2.00
Acci dental Death
Rate
Accidental Deaths per
mill ion man hou rs
work ed
Accide nt al De ath Rates by Type of Coal Mine, U.S.
Per M illion M an
Hours
Per Million To ns of
Coal Mined
Per Thous and
Employ ees
1800
1850
1900
1950
2000
50
Agriculture, Forestry,
Fishing
45
Mining
40
Construction
35
30
Manufacturing
25
20
Private Industry
15
Transportation and
Public Utilities
10
5
(Year)
1990
1988
1986
1984
1982
1980
0
1978
Deaths per 100,000
employed
Annual Occupation Fatality Rates
(US)
Wholesale & Retail
Trade
Finance, Insurance,
Real Estate
Services
Epidemiology
Associate Death (or other Measure)
to Postulated Cause
Is it statistically significant?
Are there alternative causes (confounders)?
THINK.
No case where cause is accepted unless there is a
group where death rate has doubled.
Risk Ratio (RR) > 2
Correlation of
Number of
Brooding sSorks
with Newborn
Babies
A contribution to epidemiology....
Associations vs. Cause-Effect
Sies, H. (1988) Nature 332, 495
Figure 2-7
Alternative Dose-Response Models That Fit the Data
Datum
Response
Super Linear
Linear
Datum
Hockey Stick
Hormesis
Threshold
Dose
Death Rate (Per 100,000)
Annual Death Rate By Daily Alcohol
Consumption
1600
1400
1200
1000
800
600
400
200
0
Alcohol-augmented
conditions
Cardiovascular
disease
All causes
0
0.5
1
2
3
4
5
Average Number of Drinks Per Day
6
We contrast two types of medical
response to pollutants.
ACUTE TOXIC EFECT
A dose within a day causes death within a few days
(causality easy to establish)
CHRONIC EFFECT
lower doses repeated give chronic effects
(cancer, heart) within a lifetime.
(Causality hard to establish)
Characteristics
• One dose or dose accumulated
in a short time KILLS
• 1/10 the dose repeated 10
times DOES NOT KILL
Typically an accumulated
Chronic Dose equal to the Acute LD50
gives CANCER to 10% of the population.
Assumed to be proportional to dose
E.g. LD50 for radiation is about 350 Rems.
At an accumulated exposure of 350 Rems
about 10% of exposed get cancer.
What does that say for Chernobyl?
(more or less depending on rate of exposure)
CRITICAL ISSUES FOR
LINEARITY at low doses
• THE POLLUTANT ACTS IN THE SAME WAY AS
WHATEVER ELSE INFLUCENCES THE CHRONIC
OUTCOME (CANCER) RATE
• CHRONIC OUTCOMES (CANCERS) CAUSED BY
POLLUTANTS ARE INDISTINGUISHABLE FROM
OTHER OUTCOMES
• implicit in Armitage and Doll (1954)
• explicit in Crump et al. (1976)
• extended to any outcome Crawford and Wilson (1996)
Early Optimism Based on
Poisons
There is a threshold below which nothing
happens
__________
J.G. Crowther 1924
Probability of Ionizing a Cell
is Linear with Dose
Note that the incremental Risk
can actually be greater than the
simple linearity assumption of a
non-linear biological doseresponse is assumed
ANALOGY of animals and
humans
Start with Acute toxic effects
data from paper of
Rhomberg and Wolf
Assumptions for animal analogy
with cancer:
A man eating daily a fraction F of
his body weight is as likely to get
cancer (in his lifetime) as an
animal eating daily the fraction f
of his body weight.
Transparency from Crouch
Transparency of Allen et al.
Risks of New Technologies
Old fashioned approach. Try it.
If it gives trouble, fix it.
E.g. 1833
The first passenger railroad
(Liverpool to Manchester) killed
(a member of parliament) on the
first day!
Risks of New technologies
We now want more safety
New technologies can kill more
people at once.
We do not want to have ANY
history of accidents.
Design the system so that if a failure
occurs there is a technology to fix it.
(called DEFENSE IN DEPTH or
Factorize the technology.)
Draw an EVENT TREE following with
time the possible consequences of an
initiating event.
Calculate the probability
First done for Nuclear Power
(Rasmussen et al. 1975)
Schematic of a nuclear power
plant
Simple event tree
Final Probability for an accident
with serious consequencies
P = P1 X P2 X P3 X P4
which can with care be
1/10,000,000
but without care can be
1/1,000
Simple Fault tree
ASSUMPTIONS
(1) We have drawn all possible trees
with consequencies
(2) The probabilities are independent
(design to make them so; look very
carefully about correlations
(3) Consider carefully - with some
confidentiality - actions that can
artificially correlate the separate
probabilities
The event tree analysis SHOULD
have been used by NASA in the
1980s and it would have avoided
the Challenger disaster
Example: Risk of a Space Probe
major risk:
Probe (powered by Plutonium)
reenters the earth’s atmosphere
burns up
spreads its plutonium widely over
everyone
Causes an increase in lung cancer
2 Steps
(1) What is the probability of reentry
(2) What is the distribution of
Plutonium
Compare with what we know