Extending Medical Preference Models to Include Lifetime Goals

1
Extending Medical Preference Models to Include
Lifetime Goals

• Gordon Hazen
• Northwestern University
• INFORMS Pittsburgh, November 2006

2
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

3
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

4
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.

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Problems with QALYs

• Numerous studies have demonstrated that the
  correlation between ones 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
• gt 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.

7
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

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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

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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.

14
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) B1B2B3 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

21
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

22
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.

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
Assumptions UG(g) g (survival duration
surrogate) UT(t) t (no discounting) Therefore
U(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 (g0, q, tG?-) (g1,q,
  tG) U(g0, q, tG?-) U(g1,q, tG) 1?tG
  kG?0 UQ(q) tG kG?1
• 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.

25
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 lt 0.
U uQt kGt tG Utility decreases until t
exceeds tG, where time goal is achieved.
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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 kGt tG
• Assume tG is uncertain with distribution FG.
• Then
• EU uQt kGFG(t)
• Resulting graphs of utility vs. life duration
  conform to usual portrayal.

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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 kGt tG
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 kGt tG
kG 0 (QALY model)
kG 4 yr
31
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

32
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

• Conclusion

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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

• Conclusion Sum the QALYs along the path

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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)

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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?

36
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).

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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
40
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

41
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) kGmin1,t/tG

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Proportionate-duration max endurable time
preference

• tG 5 yr, kG 4 yr

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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

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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

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Proportionate-duration utility and the QALY model

• Proportionate-duration utility w/o discounting

• 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-durat
  ion 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.

47
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.