Value of Life Analysis

1
Value of Life Analysis

• Scott Matthews
• Courses 12-706 / 73-359 / 19-702

2
Administrivia

• PS 5 due next wednesday
• Project 2 - same rules as last time, etc.

3
Value of Life

• Economists dont like to say they put a value on
  life
• They say they Study peoples willingness to pay
  to prevent premature mortality
• Translation how much is your life worth?

4
Economic valuations of life

• Miller (n29) 3 M in 1999 USD, surveyed
• Wage risk premium method
• WTP for safety measures
• Behavioral decisions (e.g. seat belt use)
• Foregone future earnings
• Contingent valuation
• Note that we are not finding value of a specific
  life, but instead of a statistical life

5
DALY/QALY measures

• Disability adjusted life years or
  quality-adjusted life years
• These are measures used to normalize the
  quality-quantity tradeoff discussed last time.
• E.g., product of life expectancy (in years) and
  the quality of life available in those years.

6
Another CEA Example

• Automated defribillators in community
• http//www.early-defib.org/03_06_09.html
• What would costs be?
• What is effectiveness?

7
Risk Analysis

• Study of the interactions between decision
  making, judgment, and nature
• Evidence cost-effectiveness of risk reduction
  opportunities varied widely - orders of magnitude
• Economic efficiency problems

8
Example - MAIS scale

• Abbreviated Injury Scale (AIS) is an anatomically
  based system that classifies individual injuries
  by body region on a six point ordinal scale of
  risk to life.  
• AIS does not assess the combined effects of
  multiple injuries. 
• The maximum AIS (MAIS) is the highest single AIS
  code for an occupant with multiple injuries. 

9
MAIS Table - Used for QALY Conversions
Comprehensive Fatality / Injury Values Comprehensive Fatality / Injury Values
Injury Severity 1994 Relative Value
MAIS1 .0038
MAIS2 .0468
MAIS3 .1655
MAIS4 .4182
MAIS5 .8791
Fatality 1.0
10
Sample QALY comparison

• A 4 years in a health state of 0.5
• B 2 years in a health state of 0.75
• QALYs A2 QALY B1.5 QALY
• So A would be preferred to B.

11
Cost-Effectiveness of Life-Saving Interventions

• From 500 Life-saving Interventions and Their
  Cost-Effectiveness, Risk Analysis, Vol. 15, No.
  3, 1995.
• References (eg 1127) are all other studies
• Model
• Estimate costs of intervention vs. a baseline
• Discount all costs
• Estimate lives and life-years saved
• Discount life years saved
• CE CI-CB/EI-EB

12
Specific (Sample) Example

• From p.373 - Ref no. 1127
• Intervention Rear outboard lap/shoulder belts
  in all (100) of cars
• Baseline 95.8 of cars already in compliance
• Intervention require all cars made after 9/1/90
  to have belts
• Thus costs only apply to remaining 4.2 (65,900)
  cars
• Target population occupants over age 4
• Others would be in child safety seats
• What would costs be?

13
Example (cont)

• 1986 Costs (from study) 6 cost per seat
• Plus added fuel costs (due to increased weight)
  total 791,000 over life of all cars produced
• Effectiveness expect 23 lives saved during 8.4
  year lifetime of fleet of cars
• But 95.8 already exist, thus only 0.966 lives
  saved
• Or 0.115 lives per year (of use of car)
• But these lives saved do not occur all in year 0
  - they are spread out over 8.4 years.
• Thus discount the effectiveness of lives saved
  per year into year 0 lives..

14
Cost per life saved

• With a 5 discount rate, the present value of
  0.115 lives for 9 years 0.817 (less than 0.966)
• Discounted lives saved
• This is basically an annuity factor
• So cost/life saved 791,000/0.817
• Or 967,700 per life (in 1986/1986 lives)
• Using CPI 145.8/109.6 -gt 1,287,326 in 1993
• But this tells us only the cost per life saved
• We realistically care more about quality of life,
  which suggests using a quality index, e.g.
  life-years saved.

15
Sample Life Expectancy Table 35-year old
American expected to live 43.6 more years (newer
data than our study) Source National
Center for Health Statistics, http//www.cdc.gov/
nchs/fastats/lifexpec.htm
16
Cost per life-year saved

• Assume average age of fatality in car accident
  was 35 years
• Life expectancy tables suggested a 35 year old
  person would on average live to age 77
• Thus 42 life years saved per fatality avoided
• 1 life-year for 42 yrs _at_5 17.42 years (ann.
  factor)
• 1993 cost/life-year 1,287,326/17.42
• With 2 sig. figures 74,000 as in paper
• Note 1,287,326 is already in cost/life units -gt
  just need to further scale for life-years by 17.42

17
Example 2 - Incremental CE

• Intervention center (middle) lap/shoulder belts
• Baseline outboard only - (done above)
• Same target population, etc.
• Cost 96,771,000
• Incremental cost 96,771,000 - 791,000
• Effectiveness 3 lives/yr, 21.32 discounted
• Incremental Effectiveness 21.32 - 0.817 20.51
• Cost/life saved 95.98 million/20.51
  4.7 million (1986) gt 6.22 million in 1993
• Cost/life-year 6.22 million/17.42 360,000

18
Overall Results in Paper

• Some had lt 0 cost, some cost gt 10B
• Median 42k per life year saved
• Some policies implemented, some only studied
• Variation of 11 orders of magnitude!
• Some maximums - 20 billion for benzene emissions
  control at tire factories
• 100 billion for chloroform standards at paper
  mills

19
Comparisons
20
Agency Comparisons

• 1993 Costs per life year saved for agencies
• FAA (Aviation) 23,000
• CPSC (Consumer Products) 68,000
• NHTSA (Highways) 78,000
• OSHA (Worker Safety) 88,000
• EPA (Environment) 7,600,000!
• Are there underlying causes for range? Hint are
  we comparing apples and oranges?