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Outcomes in Decision Analysis: Utilities, QALYs, and Discounting. Aaron B. Caughey, MD, PhD abcmd@berkeley.edu Associate Professor in Residence Director, Center for Clinical and Policy Perinatal Research Department of Obstetrics and Gynecology University of California, San Francisco

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outcomes in decision analysis utilities qalys and discounting

Outcomes in Decision Analysis: Utilities, QALYs, and Discounting

Aaron B. Caughey, MD, PhD


Associate Professor in Residence

Director, Center for Clinical and Policy Perinatal Research

Department of Obstetrics and Gynecology

University of California, San Francisco

January 14, 2010



  • No personal financial disclosures
  • Research Funding:
    • AHRQ – Elective Induction of Labor
    • Robert Wood Johnson Foundation –
      • Cesarean Delivery: Outcomes, Preferences, Costs
    • Hellman Foundation


Back to the aneurysm example:

To Clip Or Not To Clip?

Clinical Outcomes

Utilities and utility measurement

Standard Gamble

Time Tradeoff

Calculating quality-adjusted life years


review last lecture

Review—Last Lecture

Formulated an explicit question

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

Made a simple decision tree

Conducted an expected value calculation to determine which course of action would likely yield the highest life expectancy


To Clip or Not To Clip







Diff = -0.0151


.865 vs .977

to clip or not to clip
To Clip or not to Clip?
  • Has an impact on life expectancy
  • Also actual clinical outcomes:
    • Surgical death
    • Aneurysm rupture
    • Death from aneurysm rupture
    • Neurologic Injury
      • Major
      • Minor
    • Fear of aneurysm rupture

Quantifying 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 – Mortality

  • Mortality

Death from disease/accident/procedure

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

  • Life Years

Calculate an expected value of life years using a probabilistically weighted average of expected life

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


Health Outcomes – Morbidity

  • Morbidity

Some health state that is less than perfect

e.g. disability from stroke, chronic pain

  • Comparison of morbidities

Difficult – apples and oranges problem

e.g. which is worse:

Blind v. Deaf

Deaf v. Paraplegia

Paraplegia v. Blind

to clip or not to clip10
To Clip or not to Clip?
  • Clinical outcomes for clinician readers
  • Outcomes may affect health-related quality of life: how do we compare?
    • Neurologic injury can cause mild/moderate disability
    • Not clipping can cause anxiety associated with being at risk of aneurysm rupture
  • Outcomes may occur at different times
how do we incorporate quality of life effects into da
How do we incorporate quality-of-life effects into DA?
  • Measure/estimate and apply utilities
  • Use utilities to quality-adjust life expectancy for decision and cost-effectiveness analysis
preview where we are going with this analysis

Preview—Where We Are Going with this Analysis?

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

We want to:

Determine her utilities

Use them to generate QALYs

Evaluate incremental QALYs and cost (CEA/CUA)

Compare incremental cost effectiveness ratios (ICER) to other currently accepted medical interventions

what is a utility

What is a Utility?

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

Utilities can be obtained for:

* Disease states (diabetes, depression)

* Treatment effects (cure, symptom management)

* Side effects (impotence, dry mouth)

* Process (undergoing surgery, prenatal diagnostic procedure)



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 Scale

Standard Gamble

Time Trade-off

bka vs aka example

BKA vs. AKA Example

Patient in the hospital has infection of the leg

Two options:

1) BKA

BKA –1% mortality risk

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

AKA – above the knee amputation

10% mortality risk

Let’s draw a decision tree

for which outcomes do we need to measure utilities
For which outcomes do we need to measure utilities?
  • Death?
  • Risk of worsening?
  • Living with part of a leg (below the knee) missing?
  • Living with a bigger part of a leg (above the knee) missing?
  • Others?

Visual Analog Scaling

Full health: intact leg












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

standard gamble

Standard Gamble

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

Method relies on respondents choosing between:

1) a certain outcome (BKA)

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

standard gamble question

Standard Gamble Question


Perfect Health


Standard Gamble Exercise

Which do you prefer?

Choice A

Choice B

Spend the rest of your life with BKA

[p]% chance of immediate death

1-[p]% chance of spending the rest of your life with an intact leg


Standard 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 tradeoff

Time Tradeoff

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

Method relies on respondents choosing between:

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

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


Time Tradeoff Preference Elicitation

Which do you prefer?

Choice A

Choice B

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)


Time Tradeoff Preference Elicitation

Which do you prefer?

Choice A

Choice B

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)


Utility Measurement – Time Trade-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 vas

Pros and Cons - VAS

Advantage: Easy to understand


Doesn’t require the respondent to:

Think about what they’d be willing to give up

Explore risk preference

Values spread over the range

pros and cons sg

Pros and Cons – SG

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


Choices may be difficult to make

Most confusion-prone method

Lack of engagement or willingness to participate in exercise

Values tend to cluster near 1

pros and cons tto

Pros and Cons – TTO


Still asking assessor to give something up Easier choices than SG.

Values not so clustered near 1


Fails to incorporate risk

Lack 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 analysis

Utilities in decision analysis

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

Quality Adjusted Life-Years (QALYs)



QALYs are generally considered the standard unit of comparison for outcomes

QALYs = time (years) x quality (utility)

e.g. 40 years life expectancy after AKA,

utility (AKA) = 0.9

= 40 x 0.9 = 36 QALYs








Diff = -0.0151


.865 vs .977

outcomes discounting

Outcomes - Discounting

  • “Men often, from infirmity of character, make their election for the nearer good, though they know it to be the less valuable”*

*Mill JS. Utilitarianism. London: Routledge, 1871

outcomes discounting38

Outcomes - Discounting

Aneurysm Example

We said since life expectancy is reduced by 2/3, so instead of 35, it is = 35 * .333 = 11.67

However, are all years considered equal?

Consider: Favorite Meal

Extreme Pain

Lifetime Income

outcomes discounting39

Outcomes - Discounting

Generally, present > future

One common way to value the different times is discounting

Essentially this year is worth δ more than next year

δ is commonly set at 0.03 or 3%

In order to compare values of all future times, a calculation, net present value, is often used

NPV = 1 / (1 + δ)t Where t is number of years in the future

outcomes discounting40

Outcomes - Discounting

Aneurysm Example

If utility is 0.6 and life expectancy is 3 years

NPV would be:  Utility / (1 + δ)t

However, when is year 1?

Often, since events in year one occur on average half way through, we use 0.5 for year 1

NPV = 0.6 / (1.03)0.5 + 0.6 / (1.03)1.5 + 0.6 / (1.03)2.5

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




No aneurysm rupture

Normal survival,




No surgery



Early death,


Aneurysm rupture




Normal survival,





Ms. Brooks

No aneurysm rupture

Normal survival






Survive surgery



Early death


Aneurysm rupture





Normal survival




Key Inputs

Surgery-induced disability



Rupture risk/yr


shorter survival


Expected life span


RR rupture w/ surgery


Surgical death

Immediate death


Surgical mortality



Surg morb (disability)


Outcomes - Discounting

exponential discounting
Exponential 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 topic

Discounting – Special Topic

Think about your favorite dessert.

How much would you pay to have now?

How much would pay to have tonight?

How much would you pay to have in 1 yr?

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

exponential discounting problems with the model
Exponential DiscountingProblems 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 topic45

Discounting – Special Topic


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 preferences
Present-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 pbp

Exponential vs. PBP


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 prescriptive vs descriptive
Discounting: Prescriptive vs. Descriptive
  • We discount
  • But, should we
  • Example - perceived time
overall review

Overall Review




Measuring Utilities

Visual Analog

Standard Gamble

Time Trade-off

Quality Adjusted Life Years (QALYs)

QALYs = time (years) x quality (utils)


NPV =  Utility / (1 + δ)t