Post on 19-Dec-2015
transcript
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
• 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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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
• 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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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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Health Quality vs. Life Quality (cont.)
• 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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Health Quality vs. Life Quality (cont.)
• 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
• 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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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
• 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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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
• 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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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)
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0 4 8 12 16 20
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Lifetime (years)
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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
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0 10 20
0.5
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Lifetime
Ris
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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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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
• 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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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
• 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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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
ime
will
ing
to tr
ade
0 10 200
0.5
1
Lifetime
% L
ifet
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will
ing
to tr
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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
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0 10 200
0.5
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Lifetime
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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
• 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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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.