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Cost-Effectiveness Analysis Life Years Analysis. Scott Matthews Courses: 12-706 / 19-702. Admin. HW 5 Due Wednesday Project 2 Coming soon. Due Monday Nov 24 (2 weeks). Specifics on Saving Lives. Cost-Utility Analysis Quantity and quality of lives important

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## Cost-Effectiveness AnalysisLife Years Analysis

Scott Matthews

Courses: 12-706 / 19-702

• HW 5 Due Wednesday

• Project 2 Coming soon.

• Due Monday Nov 24 (2 weeks)

### Specifics on Saving Lives

• Cost-Utility Analysis

• Quantity and quality of lives important

• Just like discounting, lives are not equal

• Back to the developing/developed example

• But also: YEARS are not equal

• Young lives “more important” than old

• Cutting short a year of life for us vs

• Cutting short a year of life for 85-year-old

• Often look at ‘life years’ rather than ‘lives’ saved.. These values also get discounted

### Cost-Effectiveness Testing

• Generally, use when:

• Considering externality effects or damages

• Could be environmental, safety, etc.

• Benefits able to be reduced to one dimension

• Alternatives give same result - e.g. ‘reduced x’

• Benefit-Cost Analysis otherwise difficult/impossible

• Instead of finding NB, find “cheapest”

• Want greatest bang for the buck

• Find cost “per unit benefit” (e.g. lives saved)

• Allows us to NOT include ‘social costs’

### The CEA ratios

• CE = C/E

• Equals cost “per unit of effectiveness”

• e.g. \$ per lives saved, tons CO2 reduced

• Want to minimize CE (cheapest is best)

• EC = E/C

• Effectiveness per unit cost

• e.g. Lives saved per dollar

• Want to maximize EC

• No practical difference between 2 ratios

### Lessons Learned

• Ratios still tend to hide results

• Do not take into account scale issues

• CBA might have shown Option B to be better (more lives saved)

• Tend to only consider budgetary costs

• CEA used with constraints?

• Minimize C s.t. E > E*

• Min. effectiveness level (prev slide)

• Find least costly way to achieve it

• Minimize CE s.t. E > E*

• Generally -> higher levels of C and E!

• Can have similar rules to constrain cost

### Sample Applications

• Cost-effectiveness of:

• New drug/medical therapies* very popular

• Pollution prevention

• Safety regulations

### Definitions

• Overall cost-effectiveness is the ratio of the annualized cost to the quantity of effectiveness benefit.

• Incremental cost-effectiveness is the difference in costs divided by the difference in effectiveness that results from comparing one option to another, or to a benchmark measure.

### Incremental CE

• To find incremental cost-effectiveness :

• Sort alternatives by ‘increasing effectiveness’

• TAC = total annualized cost of compliance

• PE = effectiveness (e.g. benefit measure)

• CE = (TACk – TACk-1) / ( PEk – PEk-1)

• CE = incremental cost-effectiveness of Option k

• Use zero values (if applicable) for base case

### Incremental CE Example

• Inc CE here only relevant within control categories (metals v. oils v. org’s)

• ** Negative CE means option has more removals at lower cost

• Source: US EPA Office of Water EPA 821-R-98-018, “Cost Effectiveness Analysis of Effluent Limitations Guidelines and Standards for the Centralized Waste Treatment Industry”

### Definitions (2)

• Marginal cost-effectiveness refers to the change in costs and benefits from a one-unit expansion or contraction of service from a particular intervention (e.g. an extra pound of emissions, an extra fatality avoided).

### Why is CEA so relevant for public policy analysis?

• Limited resources!

• Opportunity cost of public spending

• i.e. if we spend \$100 M with agency A, its \$100 M we cannot spend elsewhere

• There is no federal rule saying ‘each million dollars spent must save x lives’

### Gray Areas

• How to measure cost-effectiveness when there is a single project cost but multiple effectiveness categories

• E.g. fatalities and injuries, CO2 and SO2

• Alternatives:

• Keep same cost, divide by each benefit

• Overstates costs for each

• Keep same cost, divide by ‘sum of benefits’

• Allocate cost, divide by each benefit separately

• Weight the costs and/or benefits

• Will see this more in next lecture

### Another CEA Example

• Automated defribillators in community

• http://www.early-defib.org/03_06_09.html

• What would costs be?

• What is effectiveness?

## Value of Life Analysis

Scott Matthews

Courses: 12-706 / 73-359 / 19-702

### “Value of Life”

• Economists don’t 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”?

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### WTP versus WTA

• Economics implies that WTP should be equal to ‘willingness to accept’ loss

• Turns out people want MUCH MORE in compensation for losing something

• WTA is factor of 4-15 higher than WTP!

• Also see discrepancy shrink with experience

• WTP formats should be used in CVs

• Only can compare amongst individuals

### Economic valuations of life

• Miller (n=29) \$3 M in 1999 USD, surveyed

• 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

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### DALY/QALY measures

• 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.

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### 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

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### 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.

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### MAIS Table - Used for QALY Conversions

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### Sample QALY comparison

• A: 4 years in a health state of 0.5

• B: 2 years in a health state of 0.75

• QALYs: A=2 QALY; B=1.5 QALY

• So A would be preferred to B.

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### 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

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### 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?

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### 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..

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### 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 -> \$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.

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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

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### 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 @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 -> just need to further scale for life-years by 17.42

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### 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) => \$6.22 million in \$1993

• Cost/life-year = \$6.22 million/17.42 = \$360,000

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### Overall Results in Paper

• Some had < \$0 cost, some cost > \$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

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### Comparisons

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### 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?

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