Outcomes in Decision Outcomes in Decision Analysis: Utilities, Analysis: Utilities,

QALYs, and DiscountingQALYs, and Discounting

Aaron B. Caughey, MD, PhDabcmd@berkeley.edu

Associate Professor in ResidenceDirector, Center for Clinical and Policy Perinatal Research

Department of Obstetrics and GynecologyUniversity of California, San Francisco

January 14, 2010

Disclosures

No personal financial disclosures

Research Funding: NIH/NICHD AHRQ – Elective Induction of Labor Robert Wood Johnson Foundation –

Cesarean Delivery: Outcomes, Preferences, Costs Hellman Foundation

OverviewOverview

Back to the aneurysm example: Back to the aneurysm example: To Clip Or Not To Clip? To Clip Or Not To Clip?

Clinical OutcomesClinical Outcomes Utilities and utility measurementUtilities and utility measurement

Standard GambleStandard Gamble Time TradeoffTime Tradeoff

Calculating quality-adjusted life yearsCalculating quality-adjusted life years Discounting Discounting

Review—Last LectureReview—Last Lecture

• Formulated an explicit questionFormulated an explicit question

““to clip or not to clip” (incidental to clip or not to clip” (incidental aneurysm )aneurysm )

• Made a simple decision treeMade a simple decision tree• Conducted an expected value calculation to Conducted an expected value calculation to

determine which course of action would determine which course of action would likely yield the highest life expectancylikely yield the highest life expectancy

To Clip or Not To ClipTo Clip or Not To Clip

.865 vs .977

M s. B rooks

N o trea tm ent

S urgery

Surgery:yes or no?

AneurysmRupture?

Nop=0.9825 Norm al surviva l=1

Yesp=0.0175

Early Death=0

SurgicalDeath?

Nop=0.977

Yesp=0.023 Early Death=0

Death?

Nop=.55

Yesp=.45

Norm al surviva l=1

AneurysmRupture?

Nop=1.0 Norm al surviva l=1

Yesp=0

Early Death=0

Death?

Nop=.55

Yesp=.45

Norm al surviva l=1

=1.0

=.55

=.55

=.9825=.9921

=.977

Diff = -0.0151 =0

To Clip or not to Clip?To Clip or not to Clip? Has an impact on life expectancyHas an impact on life expectancy

Also actual clinical outcomes:Also actual clinical outcomes: Surgical deathSurgical death Aneurysm ruptureAneurysm rupture Death from aneurysm ruptureDeath from aneurysm rupture Neurologic InjuryNeurologic Injury

MajorMajor MinorMinor

Fear of aneurysm ruptureFear of aneurysm rupture

Quantifying Health OutcomesQuantifying Health Outcomes• Mortality • Life Years

number of expected years of life • Significant Morbidity

Paralysis, loss of sight• Quality Adjusted Life Years

Expected life years adjusted for the valuation of the possible states in each year

• Financial Valuation of these Outcomes Costs to patient, payor, or society Willingness to pay to avoid outcomes, obtain

treatment

Health Outcomes – MortalityHealth Outcomes – Mortality

• MortalityMortalityDeath from disease/accident/procedureDeath from disease/accident/procedure

e.g. If Ms. Brooks undergoes surgery, one of the e.g. If Ms. Brooks undergoes surgery, one of the possible outcomes is mortalitypossible outcomes is mortality

• Life Years Life Years Calculate an expected value of life years using a Calculate an expected value of life years using a

probabilistically weighted average of expected life probabilistically weighted average of expected life

e.g. If Ms. Brooks does not undergo surgery, her life e.g. If Ms. Brooks does not undergo surgery, her life expectancy is less than if she did not have expectancy is less than if she did not have aneurysm, these outcomes are measured in aneurysm, these outcomes are measured in expected life yearsexpected life years

Health Outcomes – MorbidityHealth Outcomes – Morbidity

• MorbidityMorbiditySome health state that is less than perfectSome health state that is less than perfecte.g. disability from stroke, chronic paine.g. disability from stroke, chronic pain

• Comparison of morbidities Comparison of morbidities Difficult – apples and oranges problem Difficult – apples and oranges problem e.g. which is worse:e.g. which is worse:Blind v. DeafBlind v. DeafDeaf v. ParaplegiaDeaf v. ParaplegiaParaplegia v. BlindParaplegia v. Blind

To Clip or not to Clip?To Clip or not to Clip? Clinical outcomes for clinician readersClinical outcomes for clinician readers

Outcomes may affect health-related Outcomes may affect health-related quality of life: how do we compare?quality of life: how do we compare?

Neurologic injury can cause Neurologic injury can cause mild/moderate disabilitymild/moderate disability

Not clipping can cause anxiety associated Not clipping can cause anxiety associated with being at risk of aneurysm rupturewith being at risk of aneurysm rupture

Outcomes may occur at different timesOutcomes may occur at different times

How do we incorporate quality-of-life How do we incorporate quality-of-life effects into DA?effects into DA?

Measure/estimate and apply Measure/estimate and apply utilitiesutilities Use utilities to quality-adjust life expectancy Use utilities to quality-adjust life expectancy

for decision and cost-effectiveness analysis for decision and cost-effectiveness analysis

Preview—Where We Are Preview—Where We Are Going with this Analysis?Going with this Analysis?

Recall Ms. Brooks and her incidental aneurysm -- to Recall Ms. Brooks and her incidental aneurysm -- to clip or not to clip?clip or not to clip?

We want to: We want to: • Determine her utilities Determine her utilities • Use them to generate QALYs Use them to generate QALYs • Evaluate incremental QALYs and cost (CEA/CUA)Evaluate incremental QALYs and cost (CEA/CUA)• Compare incremental cost effectiveness ratios Compare incremental cost effectiveness ratios

(ICER) to other currently accepted medical (ICER) to other currently accepted medical interventionsinterventions

What is a Utility?What is a Utility?Utility - Quantitative measure of the strength of Utility - Quantitative measure of the strength of an individual’s preference for a particular an individual’s preference for a particular health state or outcome. health state or outcome.

Utilities can be obtained for:Utilities can be obtained for:* Disease states (diabetes, depression)* Disease states (diabetes, depression)* Treatment effects (cure, symptom * Treatment effects (cure, symptom management)management)* Side effects (impotence, dry mouth)* Side effects (impotence, dry mouth)* Process (undergoing surgery, prenatal * Process (undergoing surgery, prenatal diagnostic procedure) diagnostic procedure)

UtilitiesUtilities

Utilities are the currency we use to assign values to outcomes

Scaled from 0 to 1

1 = perfect or ideal health or health in the absence of the condition being studied

0 = death

How are utilities measured?How are utilities measured?

• Utilities are commonly estimated using comparisons to the 0 and 1 anchors

• Visual Analog ScaleVisual Analog Scale• Standard GambleStandard Gamble• Time Trade-offTime Trade-off

BKA vs. AKA ExampleBKA vs. AKA ExamplePatient in the hospital has infection of the leg Patient in the hospital has infection of the leg

Two options: Two options:

1) BKA1) BKA

BKA –1% mortality riskBKA –1% mortality risk

2)2) Medical management – 20% chance of Medical management – 20% chance of infection worsening and needing AKAinfection worsening and needing AKA

AKA – above the knee amputation AKA – above the knee amputation

10% mortality risk 10% mortality risk

Let’s draw a decision tree Let’s draw a decision tree

For which outcomes do we need For which outcomes do we need to measure utilities?to measure utilities?

Death?Death? Risk of worsening?Risk of worsening? Living with part of a leg (below the Living with part of a leg (below the

knee) missing?knee) missing? Living with a bigger part of a leg Living with a bigger part of a leg

(above the knee) missing?(above the knee) missing? Others?Others?

Visual Analog ScalingVisual Analog Scaling

100 98

2

0

99

65

55

1

Full health: intact leg

Dead

BKA

Outcomes rated on a 0-to-100 “feeling thermometer.”Outcomes rated on a 0-to-100 “feeling thermometer.”

AKA

Standard GambleStandard Gamble

What chance of immediate death would you What chance of immediate death would you be willing to incur to avoid living with the be willing to incur to avoid living with the outcome being assessed?outcome being assessed?

Method relies on respondents choosing Method relies on respondents choosing between:between:

1) a certain outcome (BKA)1) a certain outcome (BKA)

2) a gamble between an ideal outcome 2) a gamble between an ideal outcome (intact leg) and the worst outcome (dead)(intact leg) and the worst outcome (dead)

Standard Gamble QuestionStandard Gamble Question

Choose BKA?

Yes

No

BKA (intermediate outcome)

Perfect health

Death

Live?

p %

(100-p) %

Death

Perfect Health

Standard Gamble Exercisexercise

Spend the rest of your life with BKA

[p]]% chance of immediate deathimmediate death

1-[p]% chance of 1-[p]% chance of spending the rest of your spending the rest of your

life with an intact leglife with an intact leg

Which do you prefer?

Choice A Choice B

Standard GambleStandard Gamble

• Standard gamble measurement involves questioning patients to determine the p at which the two outcomes are equivalent

• Using expected utilities, the value of p gives the utility

Utility (BKA) x Prob (BKA) = Utility(cure) x (p) + Utility(death) x (1-p)

The utility of BKA = p: note P(BKA) = 1

Utility (BKA) = [Utility(cure) x (p) + Utility(death) x (1-p)] = [1.0 x p + 0 x (1-p)] = p

Time TradeoffTime Tradeoff

How many years of your life would you be How many years of your life would you be willing to give up to spend your remaining willing to give up to spend your remaining life without the condition/health state being life without the condition/health state being assessed? assessed?

Method relies on respondents Method relies on respondents choosing between:choosing between:

1) Full life expectancy with the 1) Full life expectancy with the condition/outcome being assessed (BKA)condition/outcome being assessed (BKA)

2) A reduced life expectancy with the 2) A reduced life expectancy with the ideal outcome (intact leg)ideal outcome (intact leg)

Time Tradeoff Preference Elicitation

Spend the remaining 40 years of your life

with BKA

Live 40 more years of life with an intact leg (give

up 0 years of life)

Which do you prefer?

Choice A Choice B

Time Tradeoff Preference Elicitation

Spend the remaining 40 years of your life

with BKA

Live 30 more years of life with an intact leg (give

up 10 years of life)

Which do you prefer?

Choice A Choice B

Utility Measurement – Time Utility Measurement – Time Trade-offTrade-off

Time Trade-off involves patients choosing between: quality of life v. length of time alive

When patients are equivocal between choice:Time A * Utility A = Time B * Utility B

e.g. If you have a life expectancy of 30 years with a BKA; how much time would you give-up to live in your current state?

Would you give up 5 years? 3 years? 1 year?30 years * Utility (BKA) = (30-x) years * 1.0

If you’re willing to give up 3 years, that means: Utility of BKA = [(30-3)*1/ 30] = 27/30 = 0.9

Pros and Cons - VASPros and Cons - VAS

Advantage: Advantage: Easy to understandEasy to understand

Disadvantages: Disadvantages:

Doesn’t require the respondent to: Doesn’t require the respondent to:

Think about what they’d be willing to give upThink about what they’d be willing to give up

Explore risk preferenceExplore risk preference

Values spread over the rangeValues spread over the range

Pros and Cons – SGPros and Cons – SG

Advantages: Advantages: Requires assessor to give Requires assessor to give something up, incorporates risk attitudesomething up, incorporates risk attitude

Disadvantages: Disadvantages:

Choices may be difficult to make Choices may be difficult to make

Most confusion-prone methodMost confusion-prone method

Lack of engagement or willingness to participate Lack of engagement or willingness to participate in exercisein exercise

Values tend to cluster near 1Values tend to cluster near 1

Pros and Cons – TTOPros and Cons – TTOAdvantages: Still asking assessor to give something up Easier choices than SG. Values not so clustered near 1

Disadvantages: Fails to incorporate riskLack of clarity of when time traded occurs Isn’t something that one can choose to give up. (One can take on a risk of death, but not “pay with life years.”)

Utilities in decision Utilities in decision analysisanalysis

• Utilities can adjust life expectancy in DA Utilities can adjust life expectancy in DA where outcomes include morbidity/quality-where outcomes include morbidity/quality-of-life effects.of-life effects.

• Quality Adjusted Life-Years (QALYs)Quality Adjusted Life-Years (QALYs)

QALYsQALYs• QALYs are generally considered the standard QALYs are generally considered the standard unit of comparison for outcomes unit of comparison for outcomes

• QALYs = time (years) x quality (utility)QALYs = time (years) x quality (utility)

• e.g. 40 years life expectancy after AKA, e.g. 40 years life expectancy after AKA, • utility (AKA) = 0.9utility (AKA) = 0.9

= 40 x 0.9 = 36 QALYs= 40 x 0.9 = 36 QALYs

Back to aneurysmBack to aneurysm

M s. B rooks

No treatm ent

Surgery

Surgery:yes or no?

AneurysmR upture?

N op=0.9825 N orm al survival=1

Yesp=0.0175

Early Death=0

SurgicalDeath?

N op=0.977

Yesp=0.023 Early Death=0

Death?

N op=.55

Yesp=.45

N orm al survival=1

AneurysmR upture?

N op=1.0 N orm al survival=1

Yesp=0

Early Death=0

Death?

N op=.55

Yesp=.45

N orm al survival=1

.865 vs .977

M s. B rooks

N o trea tm ent

S urgery

Surgery:yes or no?

AneurysmRupture?

Nop=0.9825 Norm al surviva l=1

Yesp=0.0175

Early Death=0

SurgicalDeath?

Nop=0.977

Yesp=0.023 Early Death=0

Death?

Nop=.55

Yesp=.45

Norm al surviva l=1

AneurysmRupture?

Nop=1.0 Norm al surviva l=1

Yesp=0

Early Death=0

Death?

Nop=.55

Yesp=.45

Norm al surviva l=1

=1.0

=.55

=.55

=.9825

=0

=.9921

=.977

Diff = -0.0151

Now we want to add utilities Now we want to add utilities for intermediate outcomesfor intermediate outcomes

Normal survivalNormal survival 1.01.0

Worry about possibility of Worry about possibility of aneurysm ruptureaneurysm rupture

0.950.95

Stroke (clipping complication Stroke (clipping complication or aneurysm rupture) or aneurysm rupture)

(0.76+.25)/2=0.5 (0.76+.25)/2=0.5

Early deathEarly death 0.50.5

Immediate deathImmediate death 0.00.0

QALYsNo aneurysm rupture0.9825

No surgery34.86 Die

Aneurysm rupture 0.450.0175 Survive

0.55

No aneurysm ruptureDifference 1

_ QALYs -2.85 Survive surgery0.902 Die

Aneurysm rupture 0.45Clipping 0 Survive

32.01 0.55Key Inputs Surgery-induced disabilityRupture risk/yr 0.0005 0.075Expected life span 35RR rupture w/ surgery 0 Surgical deathSurgical mortality 0.023 0.023Surg morb (disability) 0.075

0.0

Ms. Brooks

17.5

35.0Normal survival

Disability, shorter survival

5.8

Immediate death

Normal survival 35.0

Normal survival

Normal survival

Early death

Early death

35.0

17.5

35.0

Including utility for early death Including utility for early death and stroke=0.5and stroke=0.5

Adding utility for worry =.95Adding utility for worry =.95

QALYsNo aneurysm rupture0.9825

No surgery34.78 Die

Aneurysm rupture 0.45

0.0175 Survive0.55

No aneurysm ruptureDifference 1

Δ QALYs -2.77 Survive surgery0.902 Die

Aneurysm rupture 0.45

Clipping 0 Survive32.01 0.55

Key Inputs Surgery-induced disabilityRupture risk/yr 0.0005 0.075

Expected life span 35RR rupture w/ surgery 0 Surgical deathSurgical mortality 0.023 0.023

Surg morb (disability) 0.075

Normal survival,worry

34.91

Normal survival

Normal survival

Early death,worry

Early death

35.0

17.5

35.0

0.0

Ms. Brooks

17.46

34.91Normal survival,

worry

Disability, shorter survival

5.8

Immediate death

““Men often, from infirmity Men often, from infirmity of character, make their of character, make their election for the nearer election for the nearer

good, though they know it good, though they know it to be the less valuable”*to be the less valuable”*

*Mill JS. Utilitarianism. London: Routledge, 1871

Outcomes - Outcomes - DiscountingDiscounting

Outcomes - DiscountingOutcomes - Discounting• Aneurysm ExampleAneurysm Example• We said since life expectancy is reduced by We said since life expectancy is reduced by 2/3, so instead of 35, it is = 35 * .333 = 11.672/3, so instead of 35, it is = 35 * .333 = 11.67

• However, are all years considered equal?However, are all years considered equal?• Consider: Consider: Favorite MealFavorite Meal

Extreme PainExtreme Pain

Lifetime IncomeLifetime Income

Outcomes - DiscountingOutcomes - Discounting• Generally, present > futureGenerally, present > future• One common way to value the different times One common way to value the different times is discounting is discounting • Essentially this year is worth Essentially this year is worth δδ more than more than next yearnext year• δδ is commonly set at 0.03 or 3% is commonly set at 0.03 or 3%• In order to compare values of all future times, In order to compare values of all future times, a calculation, net present value, is often useda calculation, net present value, is often used• NPV = 1 / (1 + NPV = 1 / (1 + δδ))t t Where t is number of years Where t is number of years in the futurein the future

Outcomes - DiscountingOutcomes - Discounting• Aneurysm ExampleAneurysm Example• If utility is 0.6 and life expectancy is If utility is 0.6 and life expectancy is 3 years3 years• NPV would be: NPV would be: Utility / (1 + Utility / (1 + δδ))t t

• However, when is year 1? However, when is year 1? Often, since events in year one occur on Often, since events in year one occur on average half way through, we use 0.5 for average half way through, we use 0.5 for

year 1year 1

• NPV = 0.6 / (1.03)NPV = 0.6 / (1.03)0.50.5 + 0.6 / (1.03) + 0.6 / (1.03)1.51.5 + + 0.6 / (1.03)0.6 / (1.03)2.52.5

• NPV = 0.6 * {(1.03)NPV = 0.6 * {(1.03)-0.5 -0.5 + (1.03) + (1.03) -1.5-1.5 + + (1.03) (1.03) -2.5-2.5}}

Outcomes - DiscountingOutcomes - DiscountingQALYs

discNo aneurysm rupture0.9825

No surgery21.37 Die

Aneurysm rupture 0.45

0.0175 Survive0.55

No aneurysm ruptureDifference 1

Δ QALYs -1.63 Survive surgery0.902 Die

Aneurysm rupture 0.45

Clipping 0 Survive19.74 0.55

Key Inputs Surgery-induced disabilityRupture risk/yr 0.0005 0.075

Expected life span 35RR rupture w/ surgery 0 Surgical deathSurgical mortality 0.023 0.023

Surg morb (disability) 0.075

0.0

Ms. Brooks

13.3

21.4Normal survival,

worry

Disability, shorter survival

4.8

Immediate death

Normal survival,worry

21.4

Normal survival

Normal survival

Early death,worry

Early death

21.5

13.4

21.5

Exponential DiscountingExponential Discounting

Exponential discounting first described in 1937* Mathematically easy to manipulate

Assumed discounting in “simple regular fashion”

Does not differentiate difference between: Today vs. tomorrow Ten years vs. ten years plus one day

*Samuelson PA. A Note on Measurement of Utility. Rev Econ Stud 1937;4:155-61

Discounting – Special TopicDiscounting – Special Topic

• Think about your favorite dessert.Think about your favorite dessert.

• How much would you pay to have now?How much would you pay to have now?

• How much would pay to have tonight?How much would pay to have tonight?

• How much would you pay to have in 1 yr?How much would you pay to have in 1 yr?

•How much would you pay in 1 yr and 1 day?How much would you pay in 1 yr and 1 day?

Exponential DiscountingExponential DiscountingProblems with the ModelProblems with the Model

Discounting unlikely to be constant Anticipal effect is not demonstrated

Difference in valuations appears greater when closer

Discount reversal effects not incorporated Far future, prefer A to B Near future, prefer B to A

Discounting – Special Discounting – Special TopicTopic

• Solutions:• Measure discount rates through life• Could model with present-biased preferences • Essentially, “today” versus all other time periods is valued higher for many outcomes• Difference in future outcomes is likely similar

Present-Biased PreferencesPresent-Biased Preferences Described by:

Phelps and Pollack in 1968* O’Donoghue and Rabin in 1999**

Two parameter model***: β – the difference between today and “tomorrow” δ – the difference between all future time intervals

Model accounts for Discount reversal effects Component of anticipal effects

*Phelps ES, Pollack RA. On Second-Best National Saving and Game-Equilibrium Growth. Rev Econ Studies 1968;35:185-99**O’Donoghue T, Rabin M. Doing it Now or Later. Amer Econ Rev 1999;89:103-124*** Laibson D. Golden Eggs and Hyperbolic Discounting. QJE 1997;112:443-77

Exponential vs. PBPExponential vs. PBP

• Exponential: • UT = UP(outcome) + Σn δn UP(outcome)• Present-biased preferences:• UT = UP (outcome) + β[Σn δn UP (outcome)]• UT is the total NPV utility• UP is the moment to moment utility • β gives difference between immediate and all other time periods, while δ is difference in the future

Discounting: Discounting: Prescriptive vs. DescriptivePrescriptive vs. Descriptive

We discountWe discount

But, should weBut, should we

Example - perceived timeExample - perceived time

Overall ReviewOverall Review• OutcomesOutcomes

MortalityMortalityMorbidityMorbidity

• Measuring UtilitiesMeasuring UtilitiesVisual AnalogVisual AnalogStandard GambleStandard GambleTime Trade-offTime Trade-off

• Quality Adjusted Life Years (QALYs)Quality Adjusted Life Years (QALYs) QALYs = time (years) x quality (utils)QALYs = time (years) x quality (utils)• Discounting Discounting

NPV = NPV = Utility / (1 + Utility / (1 + δδ))t t