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1© 2006 Emmett Keeler
RAND
More on Value of Life and CBA
Use of CBA in Health
Problems with Willing-to-Pay for lives
VSL vs. VSLY
Is Modern medicine worth its cost?
Slides on Other VSL topics
Cost-Effectiveness Analysis in Health Care
2© 2006 Emmett Keeler
RAND
Key Points
• We use WTP to get the Value of a statistical life (VSL), but there are problems in doing so. Contingent valuation can help.
• “Lives saved” and QALYs can lead to different decisions
• How should VSL vary with age, wealth?
• Cutler: the health gains from technical progress makes higher medical costs worthwhile.
3© 2006 Emmett Keeler
RAND
Summary Table of Costs and Effects
Options
A
DirectCost, millions
IndirectCost
Years ofLife Exp.
Restricted Satis-Activity factionDays
B
C
Measures of Effects
100
50
200
4
1
10
1000
4© 2006 Emmett Keeler
RAND
Cost Effectiveness and Cost Benefit
• Cost-Effectiveness Analysis (CEA) Focuses on a single effect
• e.g. number of kids vaccinated or aggregates all health effects into QALYs gives efficient way to allocate fixed budget
• Cost-Benefit Analysis (CBA) Aggregates all effects into dollars
• even living longer or better answers “ Is a program worth it”
5© 2006 Emmett Keeler
RAND
Willingness to Pay for a statistical life (VSL)
• So CBA needs a value for health or life-saving gains. “lost wages” was the historic measure, but
• WTP is now the economist’s favorite approach comes from observed behavior, or surveys
• VSL is an estimate of an individual’s willingness to pay to avoid a small risk of death, scaled up to 1 death.
• VSL = WTP for risk reduction/(size of risk reduction)
6© 2006 Emmett Keeler
RAND
Example of WTP for safety
• So suppose airbags reduce chances of dying in an car accident over the life of a car from 1/5,000 to 1/10,000 = .0002-.0001 = .0001
• Air bags save the life of 1 driver per 10,000 cars
• 10,000 car buyers each paying $300 for an air bag is like paying $300 x 10,000 = $3 million for each life saved if laws reflect values, then those buyers value life >= $3 million
7© 2006 Emmett Keeler
RAND
More Sophisticated Estimates
• Use change in income needed to tolerate a change in risk as a measure of WTP
• Use data on job risks and wages to estimate the compensation wage necessary to induce someone to take a risky job.
• Regress wages on risk, other characteristics but personal risk tolerance is unobserved and effects
job choice search for papers, books by Kip Viscusi on this.
8© 2006 Emmett Keeler
RAND
Summary: WTP Values for a statistical life
• $/life comes from scaling up $/fraction of life. appropriate because most life-saving programs
change risks only slightly. allows us to compare values from different risks
• Surveys, wage premia, prices of safer products
• Range VSL = $3-15 million /life 5-10 times larger than lost wages EPA now uses $6 million.
Reference. Hirth et al. Med Dec Making, 2000
9© 2006 Emmett Keeler
RAND
Problems with Willingness-to-Pay
• People find it hard to guess what to do with bad answers? caused by confusion, gaming, distaste
• List paradox: What are you WTP for cutting your chance of getting breast cancer in half? of US age-specific incidence of breast cancer
in half? of all US cancers in half?
• Each charity wants to be first in line.
10© 2006 Emmett Keeler
RAND
Contingent Valuation
• A method to get better WTP answers
• Forced choice: are you WTP $X for better school? vary X randomly from 5-100 in large survey. fit logistic regression line, find 50% value
• Say they must pay in taxes
• Mention substitutes, the full list
• Use telephone or face to face to reduce bad answers by help from interviewer
References: see Hammitt handout
11© 2006 Emmett Keeler
RAND
Logistic regression of NOs ---> WTP
1.0
Would not pay
$ for program
50%
X
12© 2006 Emmett Keeler
RAND
Problems with Willingness-to-Pay -2
• Willingness-to-Pay (WTP) higher for rich Could value outcome by % of income
• Also high for old due to “dead anyway” effect ( Pratt & Zeckhauser,1996)
• Money has fewer other good uses
13© 2006 Emmett Keeler
RAND
WTP and utility: Bill Gates’ headache
utility = f(health, w)
Good health
wealth
wtp is not aligned with utility, because MV $ lower for rich
headache
paraplegia
wtpwtp
∆ U
∆ UB
b A
a
14© 2006 Emmett Keeler
RAND
Measuring the value of life year (VSLY)
• To base decisions on LE gains using BCA, we need to estimate VSLY.
• Harder to think of hedonic measures or realistic scenarios for VSLY than for VSL.
• In practice, VSLY = VSL / E(discounted QALE) for example, all 42 studies reviewed in Hirth et
al. “Willingness to pay for a QALY” MedDecMaking 2000 had estimated a VSL from which Hirth computed a VSLY
15© 2006 Emmett Keeler
RAND
Using Lives vs QALYs in CBA
• Historically EPA, NHTSA and other government agency have used CBA and “lives” valued at $6 million in fine-tuning regulations.
• Compared to using QALYs gained, “lives” gives more weight to people who: won’t live long are already sick
• So reducing air pollution, which primarily kills people with COPD, is weighted heavily using lives compared to reducing environmental lead which affects kids.
16© 2006 Emmett Keeler
RAND
Young old lifesaving tradeoffs
age prevent. deaths
life years QALYs QALYs disc at 7%
5 1 73 65 13
35 1 44 37 12
75 1 12 9 6.1
Ratio 5/75 1 6.1 7.1 2.1
17© 2006 Emmett Keeler
RAND
Cutler: Is Technology Worth it?
• Even if medical spending is rising, social welfare is enhanced if the benefits exceed the costs
• Cutler paper estimates the RoR from 4 clinical areas that have experienced rapid technological change
• Estimating medical spending is easy See Levitt et. al. 2004
• Benefits are harder to estimate
Your money or your life, Oxford UP 2004 has more
18© 2006 Emmett Keeler
RAND
Outline of Cutler’s Approach
For each disease area,
• Measure Years of life added in QALYs
• Assume value of a current QALY = VSLY = VSL/LE = $4 million/ 40 years = $100,000*
• Compute all discounted costs and benefits 3% discount rate
* How does this VSLY compare to a value of a discounted QALY in theory?
19© 2006 Emmett Keeler
RAND
Advances in Treatment of CVD
• Roosevelt dies of hypertension Largely untreatable in 1945
• Eisenhower heart attack Bed rest recommended No treatment except anticoagulant
• Mortality from CVD has fallen by ½ since 1950
20© 2006 Emmett Keeler
RAND
Case 1: Heart Attacks
• Thrombolytic drugs to dissolve clots
• Coronary Artery Bypass Graph (CABG)
• Angioplasty
• Use of stents to open blockages
• Drugs for CHD (e.g. ACE inhibitors)
• Statins to lower cholesterol (e.g. Lipitor)
21© 2006 Emmett Keeler
RAND
Calculations for CVD
• Average 45 year old can expect to live 4.5 years longer relative to 1950 2/3rds attributable to medical treatment (2.8 years) PV of these three years is $108,000
• Cost of keeping folks alive in non-working years is $10,000 more than in 1950
• PV of costs for CVD medical care is $30,000 (zero costs in ’50)
• Net return = 260% Or $3.60 gained for every $1 invested
22© 2006 Emmett Keeler
RAND
Value of LBW Medical Care
• Low birthweight Since 1950, LBW babies live 15 more years About .04 of all infants are LBW So 0.6 years saved per infant (.04*15)
• NICU, CVD Tx have increased lives by 3.4 years
• Do the results generalize, i.e. Is it true (generally) that the benefits of medical
spending have been worth it? Cutler et al. NEJM 2006 says yes for young
people, maybe not for those over 65.
23© 2006 Emmett Keeler
RAND
Summary: Is technical progress worth its cost?
• David Cutler looked at changes in life expectancy in the US since 1960. multiplied by a value of QALY or life year Compared them to the estimated change in
medical costs. On average, benefits are bigger than costs.
• Others have done similar analyses for new drugs.
• Still, US could do much better at the margin. I.e. there is a lot of waste in the system
24© 2006 Emmett Keeler
RAND
Supplementary slides
Setting Treatment cutoffs
contains (x) contains 1- (x) of kidsX
Discounted Years saved bytreatment b(x)
Let A(x) = E(b(c) | c > x)
Let Strategy 1 be treat one moreStrategy II be screen more, treat if above x
Let (x) be cdf of X= P(c < x)
26© 2006 Emmett Keeler
RAND
Nordhaus’: fun vs. health and VSLY
• Suppose you’re offered a choice between All the consumption gains since 1950 (better
cars, computers, TV’s, veggies etc…) OR All the health improvements (9 years of life
and better health while alive).
• Difficult choice based on informal surveys
• Nordhaus estimates it’s $750,000/9 years Just under $100,000 per year
27© 2006 Emmett Keeler
RAND
Reconciling lifetime wages with willingness to pay for safety.
• Young adults will work 10-20% of their future living hours
• So if they value leisure hours like work hours,
• Value of life = 5-10 times future lifetime wages
Keeler, The value of remaining lifetime is close to estimated values of life, J Health Econ, (20) 141-3 (2001)
half of discounted 50 years
0
5
10
15
20
25
30
discount rate
0 .01 .03 .05 .07
Discounting as decreasing returns?
How many years for sure are equivalent to a SG with a 50% chance of living 50 years + a 50% chance of living 1 week?
29© 2006 Emmett Keeler
RAND
WTP for a QALY studies
• Researchers have patients rate their current HRQL, and give their WTP for a lifetime cure
• This gives low values of WTP/QALY, e.g. $12,500 - $32,000/QALY in VA patients facing
possible neurosurgery King et al MDM 2005 average HRQL ~ .7, WTP ~ $100,000
• use of average lifetime, income effects? 5 other such studies gave similarly low values.
30© 2006 Emmett Keeler
RAND
Estimating waste using CBA
• Waste is defined as resources spent unnecessarily in US health care system Inefficient production of given services In producing the wrong things
• whose value < the cost of producing them.
• Artificial heart Preventable asthma hospitalizations?
We just finished a paper on this.