Extending the Qaly Model to Incorporate Goals that Are Not Time Modulated

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Extending the Qaly Model to Incorporate Goals
that Are Not Time Modulated

• Gordon Hazen
• Northwestern University

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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.

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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)

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Problems with QALYs (cont.)

• 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.
• Such behavior cannot be accommodated within the
  QALY model.

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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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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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Assumptions underlying the QALY model (Miyamoto
et al 1998)

• 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.

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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.
• B3. Conditional utility 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 implies
• U(g,q,t) UQ(q)UT(t) ? kG(1?UG(g))

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Utility function incorporating extrinsic goals

• The utility model
• U(g,q,t) UQ(q)UT(t) ? kG(1?UG(g))
• Interpretation
• UQ(q)UT(t) QALYs
• UG(g) Utility for goal achvmnt level g
• kG(1?UG(g)) Penalty for less-than-full goal
  achievement
• kG Tradeoff weight for goal achvmt

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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 exceeds tG.

Only two levels of goal achievement ? Can take
UG(g) g.
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Interpretation of kG when there is a tG-survival
duration surrogate
U(g,q,t) UQ(q)UT(t) kG(1 g) kG / tG
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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Goal model allows max endurable time
Health profile h Survive for duration t in
unde-sirable health state with utility uQ lt 0.
U(h) uQt ? kG(1? g) Utility of h decreases
until t exceeds tG, where time goal is achieved.
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Goal model allows tradeoff reluctance
UQ(q0) 0.30, tG 1 yr

• If reduction in survival time interferes with
  goal achievement, then it may make sense not to
  trade away time for health improvement.

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Example Decision Analysis

• Decision to undergo carotid endarterectomy a
  Markov chain analysis performed by Matchar
  Pauker (1986)
• 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 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
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Conclusion

• Von Neuman-Morganstern 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.