Extending Medical Preference Models to Include Lifetime Goals Gordon Hazen Northwestern University INFORMS Pittsburgh, November 2006

Extending Medical Preference Models to Include Lifetime

Goals

Gordon HazenNorthwestern University

INFORMS Pittsburgh, November 2006

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Outline of talk

• QALYs/ Problems with QALYs• Health quality versus life quality: Extrinsic goals• Revising the QALY assumptions• Survival-duration surrogates• Filling gaps in the QALY model• Utility over health profiles• Example decision analysis• Proportionate-duration surrogates• Open issues

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Outline of talk


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QALY Model

• QALYs are the most important and broadly used method for evaluating health quality.

• Panel on Cost Effectiveness in Health and Medicine (Gold et al. 1996): Medical CE studies should incorporate morbidity and mortality consequences into a single measure using QALYs.

s

Time in state s Quality of life in sQALYs

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Problems with QALYs

• Numerous studies have demonstrated that the correlation between one’s current health and the time-tradeoff or standard gamble utility for that health state is at best modest. (Tsevat 2000)

• Willingness to trade away time often much less than one might expect.– Miyamota and Eraker (1988): Subjects might accept a

tradeoff of life duration for improved health quality when remaining lifetime was long, but decline such tradeoffs if remaining lifetime was short.

• This behavior cannot be accommodated within the QALY model.

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Problems with QALYs (cont.)• Maximum endurable time: Subjects can tolerate no more

than a particular time in an undesirable health state, beyond which each additional increment of time decreases overall utility. – Miyamoto et al (1998) report a patient who regarded his health

state as almost intolerable, but who wanted to live at least 5 more years to see his son graduate from high school.

– Sutherland et al (1982): 6-9/20 MET preferences among physicians and scientists, depending on health state evaluated.

– Stalmeier et al (2001) report:• > 50% MET preferences for low QALY health states among

students;• 10/14 MET preferences among migraine patients • 12/27 MET preferences among esophagectomy patients

• Such behavior cannot be accommodated within the QALY model.

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Outline of talk


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Health Quality vs. Life Quality

• Hypothesis (Tsevat): QALYs capture quality of health, but not quality of life.

• Goals related to quality of health tend to be ongoing – their impact is modulated by duration– increase mobility– eliminate pain– reduce emotional stress.

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Health Quality vs. Life Quality (cont.)

• Goals related to quality of life may be extrinsic – their impact is not modulated by duration:• an author might want to complete a book;

• a politician might strive to achieve higher office;

• an engineer or architect might endeavor to see a project to completion;

• many individuals seek to have children and raise families.

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• Schwartz et al (2006): – Community Study

• Random-digit dialing telephone interviews• 50 Chicago-area residents

– Patient Study• In-person interviews• 100 inpatients (University of Illinois Hospital, Jesse Brown

VA Hospital)

– In each study, participants provided up to five goals (three 5-year goals, one 10-year goal, one life goal)

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• Schwartz et al (2006): Taxonomy of reported goals

Goals232 459

Education20 35

Family50 144

Health &Fitness21 69

PersonalFulfillment

17 36

Professional54 74

Travel25 19

Wealth59 82

FamilyMember

27 57

Self28 87

Job38 66

Retire16 8

FinancialSecurity28 22

RealProperty26 51

PersonalProperty

6 9

Other83 159

Numbers of goals by categories and subcategorieselicited from subjects in the Community and Patient studies

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Representative Goals by Category(Schwartz et al 2006)

• Education: “finish college”, “go back to school”

• Family– Self: “Get married”, “Have children”– Family member: “See daughter finish high school”, “See son get married”

• Health and Fitness: “lose weight”, “complete marathon”

• Personal Fulfillment: “spend more time in charitable activity”, “write a book”

• Professional– Job: “get a job”, “own a business”– Retirement: “retire”

• Travel: “travel to Europe”, “travel”

• Wealth– Real Property: “buy a house”, “invest in property”– Personal Property: “buy a new car”, “own a boat”

• Financial Security “become financially secure”, “win the lottery”

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QALY model and Extrinsic Goals

• In the QALY model, quality of health is given weight proportional to health duration.

• It follows that the QALY model cannot directly account for extrinsic goals, whose importance is by definition independent of duration.

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Outline of talk


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Assumptions underlying the QALY Model

• Assumptions on preferences yielding the QALY form: Pliskin et al. (1980), Miyamoto et al. (1998), and Miyamoto (1999).

• Preference model:– Quality/life duration pairs (q,t).– Theorem (Miyamoto et al 1998):

A1 & A2 U(q,t) = UQ(q)UT(t)

(Generalized QALY model)

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Assumptions underlying the QALY model (Miyamoto et al 1998)

Quality/life duration pairs (q,t).

A1. The zero condition: Preferences between states of health disappear when survival duration is zero, that is, for all states q, q of health, (q,0) ~ (q,0).

A2. Generalized utility independence (GUI) for lifetime (Standard gamble independence).

Any two conditional preference relations over lifetime gambles, given health states q and q not equivalent to death, are either identical or reversed.

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Failure of the zero condition for extrinsic goals

• Goal achievement/ Quality/ Life duration triples (g,q,t)• Goal achievement may be preferred to non-achievement

even if life duration is zero:

(g = Achieved, q, t = 0) (g = Not achieved, q, t = 0)

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Revised assumptions allowing for extrinsic goals

Goal/ quality/ life-duration triples (g,q,t).

B1. Conditional zero condition:

For each level g of extrinsic goal achievement, preferences for health quality disappear when life duration is zero, that is, for all health states q, q,

(g,q,0) ~ (g, q,0).

B2. Generalized utility independence (GUI) for lifetime.Any two conditional preference relations over lifetime gambles, given health states q and q not equivalent to death, and goal achievement levels g and g, are either identical or reversed.

B3. Additive independence of extrinsic goal attainment and health quality given life duration.

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Revised assumptions allowing for extrinsic goals

Goal / quality / life-duration triples (g,q,t).

Theorem (Hazen 2003): B1+B2+B3 are equivalent to

U(g,q,t) = UQ(q)UT(t) + kGUG(g).

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Utility function incorporating extrinsic goals

The utility model:

U(g,q,t) = UQ(q)UT(t) + kGUG(g)

Interpretation:

UQ(q)UT(t) QALYs

UG(g) Utility for goal achievement level g

kG Tradeoff weight for goal achievement

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Outline of talk


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Survival-duration surrogate for extrinsic goal achievement

• Achievement of an extrinsic goal may require time commitment – say estimated time commitment is tG.

• Simple and convenient surrogate for goal achievement: Whether survival duration t exceeds tG.

1 if exceeds [ ]

0 if not.G

G

t tg t t

Only two levels {0,1} of goal achievement Can take UG(g) = g.

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Interpreting kG when there is a survival-duration surrogate

AssumptionsUG(g) = g (survival duration surrogate)UT(t) = t (no discounting)

ThereforeU(g,q,t) = UQ(q)t + kG [t ≥ tG].

Assessment question: What quality-of-life decrement q* q would you be just willing to accept to increase survival duration from just below tG to just above tG?

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Interpreting kG when there is a survival-duration surrogate (cont)

• Therefore

(g=0, q*, tG-) ~ (g=1,q, tG+)

U(g=0, q*, tG-) = U(g=1,q, tG+)

1tG + kG0 = UQ(q) tG + kG1

• Solve to obtain

kG / tG = 1 – UQ(q).

• Conclusion: kG / tG is the quality of life increment that one would be just willing to sacrifice to increase survival from slightly below tG to slightly above tG.

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Outline of talk


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Goal model allows max endurable time

Health profile h: Survive for duration t in undesirable health state with utility uQ < 0.

U = uQt + kG[t ≥ tG]

Utility decreases until t exceeds tG, where time goal is achieved.

k G

t G

u Q t G

Util

ity

Life duration

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Max endurable time as usually portrayed

Stalmeier, Busschbach, Lamers, Krabbe, Health Econ (in press)

Stalmeier, Chapman, de Boer, Lanschot , Tech Assessment in Health Care (2001)

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Max endurable time as usually portrayed

U = uQt + kG[t ≥ tG]

• Assume tG is uncertain with distribution FG.

• Then

E[U] = uQt + kGFG(t)

• Resulting graphs of utility vs. life duration conform to usual portrayal.

0 5 10 15 20

5

5

10

uQ = 1uQ = 0.5uQ = 0.2uQ = 0uQ = -0.2uQ = -0.5

Life duration

Util

ity

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Goal model allows tradeoff reluctance• If reduction in survival time interferes with goal achievement, then it

may make sense not to trade away time for health improvement.

uQ = 0.30, tG = 5 yr U = uQt + kG[t ≥ tG]

0 4 8 12 16 20

0.5

1

Lifetime (years)

% li

fetim

e w

illin

g to

trad

e fo

r fu

ll he

alth

0 4 8 12 16 20

0.5

1

Lifetime (years)

% li

fetim

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illin

g to

trad

e fo

r fu

ll he

alth

kG = 0 (QALY model) kG = 4 yr

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Goal model allows reluctance to gamble

• Risks of death may be declined to the extent they interfere with goal achievement.uQ = 0.30, tG = 5 yr U = uQt + kG[t ≥ tG]

kG = 0 (QALY model) kG = 4 yr

0 10 20

0.5

1

Lifetime

Ris

k of

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g to

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0 10 20

0.5

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Lifetime

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Outline of talk


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Extending to utility over health profiles

• Health profile h: A function which assigns health state q = h(s) to every time instant s in some interval [0, th].

• The informal approach for QALYs (Pliskin et al 1980):– Assumption Q1: For any health profile h there is a level q = Q(h)

of health quality such that h ~ (q,th). – Assumption Q2: Q(h) satisfies the time-weighted average

equation

0

1( ( )) ( ( )) ( )

( )

ht

Q Q TT h

U Q h U h t dU tU t

– Conclusion:

0( ) ( ( ), ) ( ( )) ( ) ( ( )) ( )

ht

h Q T h Q TU h U Q h t U Q h U t U h t dU t

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Extending to utility over health profiles

• The informal approach for QALYs (Pliskin et al 1980), with no time discounting:– Assumption Q1: For any health profile h there is a level q = Q(h)

of health quality such that h ~ (q,th).– UT(t) = t – Assumption Q2: Q(h) satisfies the time-weighted average

equation

0

1( ( )) ( ( ))

ht

Q Qh

U Q h U h t dtt

– Conclusion: Sum the QALYs along the path

0( ) ( ( ), ) ( ( )) ( ( ))

ht

h Q h QU h U Q h t U Q h t U h t dt

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Extending to utility over health profiles and extrinsic goals

• Extrinsic goal achievement is not time-modulated, so does not accrue over time, but instead is associated holistically with the entire life profile of an individual.

• For modeling purposes, then, we consider preferences over pairs (g,h), where h is a health profile and g is a level of extrinsic goal achievement.

• Assumption Q1 extended: For any health profile h and goal achievement level g, there is a level q = Q(h) of health quality such that (g,h) ~ (g,q,th).

• Conclusion (under no time discounting):

0

( , ) ( , ( ), ) ( ( )) ( )

( ( )) ( )h

h Q h G G

t

Q G G

U g h U g Q h t U Q h t k U g

U h t dt k U g

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Extending to utility over health profiles and extrinsic goals

• Note: Q(h) is assumed to not depend on g. – Reasonable because the additive form

U(g,q,t) = UQ(q)UT(t) + kGUG(g) implies q,t utility independent of g, so why not h utility independent of g?

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Outline of talk


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Example Decision Analysis• Decision to undergo carotid endarterectomy – a Markov

chain analysis performed by Matchar & Pauker (1986).

$01.9

$07.11

EFF = 50%mstroke = 0.05 /yr

Pearlydie = 0.38Pbig = 0.6667

mexcess = 0.065 /yrm0 = 0.0111 /yr

qPBS = 0.2qPSS = 0.8

mstroke

mexcess

Pearlydie

1 - Pearlydie

Pbig

mexcess

Pbig mstroke

1 - Pbig .

mstroke

mexcess

Well

Stroke

Big Stroke

Small Stroke

Post Big Stroke

Big Stroke

Post Small Stroke

Stroke

Dead

Dead

Dead

Dead

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Example Decision Analysis

• We add an extrinsic goal represented by survival-duration surrogate tG = 6 yr.

• We take goal weight kG= 1.2 yr. (Willing to decrease health quality by kG/tG = 0.20 in order to increase survival duration from just below the 6-year survival goal to just above it.)

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Example Decision Analysis Results

tG = 6 years, kG = 1.2 years

Surgical efficacy

Intervention Surgery No Surgery Surgery No Surgery

E[QALY] 8.588 yr 8.294 yr 8.369 yr 8.294 yrE[U G ] (= P(Goal achieved)) 0.558 0.577 0.552 0.577

Overall E[U ] when k G = 1.2 yr 8.057 yr 7.786 yr 7.768 yr 7.786 yr

Threshold value for the tradeoff weight k G

EFF = 50% EFF = 37%

k G = 15.2 yr k G = 0.492 yr

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Outline of talk


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Partial goal achievement

• Proportionate-duration surrogate for degree of goal achievement:

g = min {1,t / tG}

= survival time as a percentage up to 100% of a critical duration tG.

• U(g,q,t) = UQ(q)UT(t) + kGmin{1,t/tG}

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Proportionate-duration max endurable time preference

• tG = 5 yr, kG = 4 yr

0 5 10 15 20

5

5

10

uQ = 1uQ = 0.3uQ = 0uQ = -0.3uQ = -0.6

Lifetime

Util

ity

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Proportionate-duration willingness to trade off for full health

• tG = 5 yr, uQ = 0.3

• kG = 0 (QALY model) • kG = 4 yr

0 10 200

0.5

1

Lifetime

% L

ifet

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will

ing

to tr

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0 10 200

0.5

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Lifetime

% L

ifet

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will

ing

to tr

ade

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Proportionate-duration risk of death willing to accept for full health

• tG = 5 yr, uQ = 0.3

• kG = 0 (QALY model) • kG = 4 yr

0 10 200

0.5

1

Lifetime

Ris

k of

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0 10 200

0.5

1

Lifetime

Ris

k of

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Proportionate-duration utility and the QALY model

• Proportionate-duration utility w/o discounting

( ) min{1, }

( ) if ( ) if

( ) if ( ) ( )( ) if

Q G G

GQ GG

GQ GG

GQ G G Q G Q G G

G

U U q t k t t

kU q t t tk

tU q t t tt

kU q t k t t U q t U q t t t t

t

• This is equivalent to:• UQ(q) + kG/tG QALYs per unit time up to time tG

• UQ(q) QALYs per unit time after time tG

• This is a modified QALY model

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Proportionate-duration utility and the QALY model

• Theorem: Suppose degree of extrinsic goal achievement is measured by the proportionate-duration surrogate, and there is no time discounting. Then the utility of a health profile h is equivalent to the QALY of a modified health profile hG in which all health states q occupied before time tG are replaced by states q+ having health quality UQ(q+) = UQ(q) + kG/tG.

• Implication: Standard software can be used to compute extrinsic-goal utility with a proportionate-duration surrogate goal.

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Outline of talk


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Open issues

• Multiple simultaneous goals• Future goals

– Once current goal(s) are achieved, future goals are likely to arise. Should this be modeled? If so, how?

– Note that no one asks this kind of question for QALYs - ongoing goals represented by QALYs are assumed never to change.

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Open issues

• Population issues– Heterogeneous goals across a population – how to

account for these?

– Heterogeneous parameters kG, tG – how to account for these?

– Note for QALYs, all that matters is the population average QALY for each health state, so heterogeneity issues are not as significant for the QALY model.

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Conclusion

• Utility functions that include an extrinsic goal component – can account for observed violations of the QALY

model (maximum endurable time preference, reluctance to trade off time for quality)

– can do so prescriptively, thereby providing a coherent basis for including such goals in decision and cost-effectiveness analyses.

Documents

Extending Medical Preference Models to Include Lifetime Goals Gordon Hazen Northwestern University INFORMS Pittsburgh, November 2006