Application of Longevity Measures to Transportation Risk
Application of Longevity Measures to Transportation Risk C. Craig Morris, Ph.D. Office of Advanced Studies Bureau of Transportation Statistics Research and Innovative Technology Administration U.S. Department of Transportation 26 July 2010
Background •
Risk measurement, analysis, and communication in terms of life expectancy is standard practice in public health fields: ¾ ¾ ¾ ¾ ¾ ¾ ¾
Fine-Particulate Air Pollution and Life Expectancy in the United States, Pope et al. (2009) Life Expectancy in Relation to Cardiovascular Risk Factors, Clarke et al. (2009) Estimating Health-Adjusted Life Expectancy Conditional on Risk Factors: Results for Smoking and Obesity, van Baal et al. (2006) Ten Years of Life: Is It a Matter of Choice? Fraser et al. (2001) Smoking, Physical Activity, and Active Life Expectancy, Ferrucci et al. (1999) Low Risk-Factor Profile and Long-Term Cardiovascular and Noncardiovascular Mortality and Life Expectancy, Stamler et al. (1999) Life Expectancy Following Dietary Modification or Smoking Cessation: Estimating the Benefits of a Prudent Lifestyle, Grover et al. (1994)
U.S. Department of Transportation Research and Innovative Technology Administration
2
Risk •
Transportation-related fatality risk: varies across age, gender, other demographic groups, and with choices (e.g., wearing seatbelts) ¾ is cumulative (increasing with exposure) ¾ causes premature deaths far beyond those counted shortly after trauma (e.g., delayed deaths due to traumatic brain injury) ¾ is part of a portfolio of health risks managed at individual and societal levels ¾
•
Life-table methods quantify all these essential elements of risk
U.S. Department of Transportation Research and Innovative Technology Administration
3
Life Table Concepts •
Population – a defined set of individuals, e.g., total U.S. population, males or females, belted or unbelted motor vehicle occupants, etc
•
Age (X) – individual’s time since birth rounded down to nearest year
•
Age-specific probability of death (qx) – proportion of individuals of age X who die each year in a specified period (e.g., 2005)
•
Life expectancy (ex) – average years of life remaining at age X for each individual in the population
•
Current life table – method to estimate longevity from mortality rates across all ages of the population, assuming age-specific mortality rates remain stable over time U.S. Department of Transportation Research and Innovative Technology Administration
4
Total Mortality Life Table Total Probablity
Age
Number
Person-years
of dying
Number
dying
lived
between
surviving to
between
between
ages x to x+1 qx
age x lx
number of person-years Expectation
ages x to x+1 ages x to x+1 dx Lx
lived above
of life
age x Tx
at age x ex
0
0.0068785
100,000
688
99,398
7,744,259
77.4
1
0.0004634
99,312
46
99,289
7,644,861
77.0
2
0.0003069
99,266
30
99,251
7,545,572
76.0
3
0.0002197
99,236
22
99,225
7,446,321
75.0
4
0.0001840
99,214
18
99,205
7,347,096
74.1
………………………………………………………………………………………………………………………….. 99 100+ Formulas:
0.3122311
2,209
690
1,864
5,193
2.4
1.0000000
1,519
1,519
3,329
3,329
2.2
qx = Dx / Nx
lx+1 = lx−dx
dx = qx lx
Lx = lx−dx + bxdx
Tx = Σ Lx
ex = Tx / lx
Notes: 1. l0 = 100,000 is an arbitrary initial life table population called the radix. 2. bx = proportion of age X year lived by individuals who died at age X (bx = .5 after age 4). Source: Life table for the total population: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
5
How Do Males and Females Compare on Probability of Death and Life Expectancy?
U.S. Department of Transportation Research and Innovative Technology Administration
6
Probability of Death, 2005
Sources: Life table for males: United States, 2005; Life table for females: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
7
Life Expectancy, 2005 Expectation of life at age x Difference ex Age
Male
Female
Δ ex
0
74.9
79.9
-5.1
15
60.6
65.6
-5.0
20
55.9
60.7
-4.8
25
51.3
55.9
-4.6
35
42.0
46.2
-4.2
45
32.8
36.8
-3.9
55
24.4
27.8
-3.4
65
16.8
19.5
-2.7
99
2.1
2.4
-0.3
100+
2.0
2.2
-0.2
Sources: Life table for males: United States, 2005; Life table for females: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
8
How Does Wearing a Seat Belt Affect Life Expectancy? Approach: adjust age-specific probability of death for wearing vs. not wearing seat belts, then compute and compare life expectancies (using total deaths, total population, proportion of population wearing or not wearing seatbelts, and fatalities wearing or not wearing seatbelts)
U.S. Department of Transportation Research and Innovative Technology Administration
9
Male Occupants, 2005 Life Expectancy Age
Δ ex
Restrained Unrestrained Years Months
0
75.1
74.1
0.94
11.3
15
60.8
59.9
0.92
11.0
20
56.1
55.3
0.75
9.0
25
51.4
50.9
0.52
6.2
35
42.0
41.8
0.28
3.4
45
32.9
32.7
0.16
1.9
55
24.4
24.4
0.08
1.0
65
16.8
16.7
0.04
0.4
97+
3.0
3.0
0.01
0.1
Source: Bureau of Transportation Statistics, Research and Innovative Technology Administration, U.S. Department of Transportation, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
10
Female Occupants, 2005 Life Expectancy Age
Δ ex
Restrained Unrestrained Years Months
0
80.1
79.6
0.50
6.0
15
65.7
65.3
0.46
5.6
20
60.8
60.5
0.34
4.1
25
56.0
55.7
0.25
3.1
35
46.3
46.1
0.15
1.8
45
36.8
36.8
0.08
1.0
55
27.9
27.8
0.04
0.5
65
19.5
19.5
0.02
0.2
97+
3.7
3.7
0.00
0.0
Source: Bureau of Transportation Statistics, Research and Innovative Technology Administration, U.S. Department of Transportation, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
11
What is Meant by Years of Potential Life Lost?
U.S. Department of Transportation Research and Innovative Technology Administration
12
Years of Potential Life Lost (YPLL) •
YPLL for an individual is his or her life expectancy at time of death due to a given cause
•
YPLL for a population is the sum of YPLL across all individuals who died due to a given cause
•
Eliminating a given cause of death decreases age-specific probability of death and increases life expectancy, so YPLL is estimated from life expectancies with that cause eliminated in the population1
1Trends
in Mortality Analysis.
U.S. Department of Transportation Research and Innovative Technology Administration
13
Motor Vehicle Occupant Fatalities, 2005 Age 0-4 5-9 10-14 15-19 20-24 25-29 30-39 40-49 50-59 60-69 70-79 80-89 90+ Subtotal Total
Occupant Deaths per Years of Potential Life Occupant Deaths 100,000 Population Lost Male Female Male Female Male Female 236 221 2.3 2.2 17,411 17,358 207 194 2.1 2.0 14,234 14,308 252 234 2.4 2.3 15,958 15,996 2,705 1,500 25.1 14.6 158,025 95,190 3,501 1,227 32.2 12.1 190,330 72,442 2,184 771 21.3 7.9 108,573 41,785 3,152 1,376 15.2 6.8 134,599 64,382 3,025 1,473 13.5 6.4 101,295 55,082 2,317 1,209 12.7 6.3 58,296 34,465 1,498 984 13.7 8.1 26,155 19,738 1,246 945 18.0 10.5 13,229 11,808 921 721 28.3 12.9 5,612 5,330 120 103 28.7 9.7 436 449 21,364 10,958 14.6 7.3 844,152 448,335 32,322 10.9 1,292,487
Sources: Fatality Analysis Reporting System, National Highway Traffic Safety Administration, 2005; U.S. Population Estimates, July 2005, US Census Bureau; Research and Innovative Technology Administration, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
14
Improving Validity of Longevity Measures •
Some serious injuries reduce life expectancy by increasing probability of death at later ages (e.g., traumatic brain injuries)
•
Estimates of life expectancy or years of potential life lost based only on deaths shortly after trauma underestimate the true quantities, because they ignore delayed premature deaths
•
Accounting for delayed effects of traumatic injuries on longevity, as done in court and actuarial1 contexts, would improve the validity of longevity measures
Source: 1. Life Expectancy in Court: A Text book for Doctors and Lawyers, Anderson TW, Vancouver, Canada: Teviot Press, 2004. U.S. Department of Transportation Research and Innovative Technology Administration
15
Conclusion •
Transportation-related fatality risk: varies across demographic groups and with individual choices ¾ is cumulative ¾ involves premature deaths ¾ is part of a portfolio of health risks managed at individual and societal levels ¾
•
Life table methods quantify all these important aspects of risk
•
Research is needed to estimate the full impact of transportationrelated trauma on age-specific probability of death and longevity
•
Data are needed to apply longevity measures of transportation risk, e.g., on motorcycle riding with and without wearing helmets U.S. Department of Transportation Research and Innovative Technology Administration
16
Background •
Risk measurement, analysis, and communication in terms of life expectancy is standard practice in public health fields: ¾ ¾ ¾ ¾ ¾ ¾ ¾
Fine-Particulate Air Pollution and Life Expectancy in the United States, Pope et al. (2009) Life Expectancy in Relation to Cardiovascular Risk Factors, Clarke et al. (2009) Estimating Health-Adjusted Life Expectancy Conditional on Risk Factors: Results for Smoking and Obesity, van Baal et al. (2006) Ten Years of Life: Is It a Matter of Choice? Fraser et al. (2001) Smoking, Physical Activity, and Active Life Expectancy, Ferrucci et al. (1999) Low Risk-Factor Profile and Long-Term Cardiovascular and Noncardiovascular Mortality and Life Expectancy, Stamler et al. (1999) Life Expectancy Following Dietary Modification or Smoking Cessation: Estimating the Benefits of a Prudent Lifestyle, Grover et al. (1994)
U.S. Department of Transportation Research and Innovative Technology Administration
2
Risk •
Transportation-related fatality risk: varies across age, gender, other demographic groups, and with choices (e.g., wearing seatbelts) ¾ is cumulative (increasing with exposure) ¾ causes premature deaths far beyond those counted shortly after trauma (e.g., delayed deaths due to traumatic brain injury) ¾ is part of a portfolio of health risks managed at individual and societal levels ¾
•
Life-table methods quantify all these essential elements of risk
U.S. Department of Transportation Research and Innovative Technology Administration
3
Life Table Concepts •
Population – a defined set of individuals, e.g., total U.S. population, males or females, belted or unbelted motor vehicle occupants, etc
•
Age (X) – individual’s time since birth rounded down to nearest year
•
Age-specific probability of death (qx) – proportion of individuals of age X who die each year in a specified period (e.g., 2005)
•
Life expectancy (ex) – average years of life remaining at age X for each individual in the population
•
Current life table – method to estimate longevity from mortality rates across all ages of the population, assuming age-specific mortality rates remain stable over time U.S. Department of Transportation Research and Innovative Technology Administration
4
Total Mortality Life Table Total Probablity
Age
Number
Person-years
of dying
Number
dying
lived
between
surviving to
between
between
ages x to x+1 qx
age x lx
number of person-years Expectation
ages x to x+1 ages x to x+1 dx Lx
lived above
of life
age x Tx
at age x ex
0
0.0068785
100,000
688
99,398
7,744,259
77.4
1
0.0004634
99,312
46
99,289
7,644,861
77.0
2
0.0003069
99,266
30
99,251
7,545,572
76.0
3
0.0002197
99,236
22
99,225
7,446,321
75.0
4
0.0001840
99,214
18
99,205
7,347,096
74.1
………………………………………………………………………………………………………………………….. 99 100+ Formulas:
0.3122311
2,209
690
1,864
5,193
2.4
1.0000000
1,519
1,519
3,329
3,329
2.2
qx = Dx / Nx
lx+1 = lx−dx
dx = qx lx
Lx = lx−dx + bxdx
Tx = Σ Lx
ex = Tx / lx
Notes: 1. l0 = 100,000 is an arbitrary initial life table population called the radix. 2. bx = proportion of age X year lived by individuals who died at age X (bx = .5 after age 4). Source: Life table for the total population: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
5
How Do Males and Females Compare on Probability of Death and Life Expectancy?
U.S. Department of Transportation Research and Innovative Technology Administration
6
Probability of Death, 2005
Sources: Life table for males: United States, 2005; Life table for females: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
7
Life Expectancy, 2005 Expectation of life at age x Difference ex Age
Male
Female
Δ ex
0
74.9
79.9
-5.1
15
60.6
65.6
-5.0
20
55.9
60.7
-4.8
25
51.3
55.9
-4.6
35
42.0
46.2
-4.2
45
32.8
36.8
-3.9
55
24.4
27.8
-3.4
65
16.8
19.5
-2.7
99
2.1
2.4
-0.3
100+
2.0
2.2
-0.2
Sources: Life table for males: United States, 2005; Life table for females: United States, 2005. National Center for Health Statistics. U.S. Department of Transportation Research and Innovative Technology Administration
8
How Does Wearing a Seat Belt Affect Life Expectancy? Approach: adjust age-specific probability of death for wearing vs. not wearing seat belts, then compute and compare life expectancies (using total deaths, total population, proportion of population wearing or not wearing seatbelts, and fatalities wearing or not wearing seatbelts)
U.S. Department of Transportation Research and Innovative Technology Administration
9
Male Occupants, 2005 Life Expectancy Age
Δ ex
Restrained Unrestrained Years Months
0
75.1
74.1
0.94
11.3
15
60.8
59.9
0.92
11.0
20
56.1
55.3
0.75
9.0
25
51.4
50.9
0.52
6.2
35
42.0
41.8
0.28
3.4
45
32.9
32.7
0.16
1.9
55
24.4
24.4
0.08
1.0
65
16.8
16.7
0.04
0.4
97+
3.0
3.0
0.01
0.1
Source: Bureau of Transportation Statistics, Research and Innovative Technology Administration, U.S. Department of Transportation, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
10
Female Occupants, 2005 Life Expectancy Age
Δ ex
Restrained Unrestrained Years Months
0
80.1
79.6
0.50
6.0
15
65.7
65.3
0.46
5.6
20
60.8
60.5
0.34
4.1
25
56.0
55.7
0.25
3.1
35
46.3
46.1
0.15
1.8
45
36.8
36.8
0.08
1.0
55
27.9
27.8
0.04
0.5
65
19.5
19.5
0.02
0.2
97+
3.7
3.7
0.00
0.0
Source: Bureau of Transportation Statistics, Research and Innovative Technology Administration, U.S. Department of Transportation, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
11
What is Meant by Years of Potential Life Lost?
U.S. Department of Transportation Research and Innovative Technology Administration
12
Years of Potential Life Lost (YPLL) •
YPLL for an individual is his or her life expectancy at time of death due to a given cause
•
YPLL for a population is the sum of YPLL across all individuals who died due to a given cause
•
Eliminating a given cause of death decreases age-specific probability of death and increases life expectancy, so YPLL is estimated from life expectancies with that cause eliminated in the population1
1Trends
in Mortality Analysis.
U.S. Department of Transportation Research and Innovative Technology Administration
13
Motor Vehicle Occupant Fatalities, 2005 Age 0-4 5-9 10-14 15-19 20-24 25-29 30-39 40-49 50-59 60-69 70-79 80-89 90+ Subtotal Total
Occupant Deaths per Years of Potential Life Occupant Deaths 100,000 Population Lost Male Female Male Female Male Female 236 221 2.3 2.2 17,411 17,358 207 194 2.1 2.0 14,234 14,308 252 234 2.4 2.3 15,958 15,996 2,705 1,500 25.1 14.6 158,025 95,190 3,501 1,227 32.2 12.1 190,330 72,442 2,184 771 21.3 7.9 108,573 41,785 3,152 1,376 15.2 6.8 134,599 64,382 3,025 1,473 13.5 6.4 101,295 55,082 2,317 1,209 12.7 6.3 58,296 34,465 1,498 984 13.7 8.1 26,155 19,738 1,246 945 18.0 10.5 13,229 11,808 921 721 28.3 12.9 5,612 5,330 120 103 28.7 9.7 436 449 21,364 10,958 14.6 7.3 844,152 448,335 32,322 10.9 1,292,487
Sources: Fatality Analysis Reporting System, National Highway Traffic Safety Administration, 2005; U.S. Population Estimates, July 2005, US Census Bureau; Research and Innovative Technology Administration, 2010. U.S. Department of Transportation Research and Innovative Technology Administration
14
Improving Validity of Longevity Measures •
Some serious injuries reduce life expectancy by increasing probability of death at later ages (e.g., traumatic brain injuries)
•
Estimates of life expectancy or years of potential life lost based only on deaths shortly after trauma underestimate the true quantities, because they ignore delayed premature deaths
•
Accounting for delayed effects of traumatic injuries on longevity, as done in court and actuarial1 contexts, would improve the validity of longevity measures
Source: 1. Life Expectancy in Court: A Text book for Doctors and Lawyers, Anderson TW, Vancouver, Canada: Teviot Press, 2004. U.S. Department of Transportation Research and Innovative Technology Administration
15
Conclusion •
Transportation-related fatality risk: varies across demographic groups and with individual choices ¾ is cumulative ¾ involves premature deaths ¾ is part of a portfolio of health risks managed at individual and societal levels ¾
•
Life table methods quantify all these important aspects of risk
•
Research is needed to estimate the full impact of transportationrelated trauma on age-specific probability of death and longevity
•
Data are needed to apply longevity measures of transportation risk, e.g., on motorcycle riding with and without wearing helmets U.S. Department of Transportation Research and Innovative Technology Administration
16
