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Extending Medical Preference
Models to Include Lifetime
Goals
Gordon Hazen
Northwestern University
INFORMS Pittsburgh, November 2006
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
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
QALY Model
• QALYs are the most important and broadly
used method for evaluating health quality.
QALYs s Time in state s Quality of life in s
• 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.
4
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.
5
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.
6
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
7
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.
8
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.
9
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)
10
Health Quality vs. Life Quality (cont.)
• Schwartz et al (2006): Taxonomy of reported goals
Goals
232 459
Family Professional Wealth Other
50 144 54 74 59 82 83 159
Family Financial
Job Education
Member Security
38 66 20 35
27 57 28 22
Personal Health &
Self Retire
Property Fitness
28 87 16 8
6 9 21 69
Real Personal
Property Fulfillment
26 51 17 36
Travel
Numbers of goals by categories and subcategories 25 19
elicited from subjects in the Community and Patient studies
11
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”
12
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.
13
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
14
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)
15
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.
16
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)
17
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.
18
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).
19
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
20
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
21
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 t exceeds tG
g [t tG ]
0 if not.
Only two levels {0,1} of goal achievement Can
take UG(g) = g.
22
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?
23
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.
24
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
25
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
tG Utility decreases until
kG t exceeds tG, where
time goal is achieved.
uQtG
Life duration
26
Max endurable time as usually portrayed
Stalmeier, Chapman, de Boer, Lanschot , Tech Stalmeier, Busschbach, Lamers, Krabbe, Health
Assessment in Health Care (2001) Econ (in press)
27
Max endurable time as usually portrayed
U = uQt + kG[t ≥ tG]
10
• Assume tG is uQ = 1
uQ = 0.5
uncertain with uQ = 0.2
5
distribution FG. uQ = 0
Utility
uQ = -0.2
• Then uQ = -0.5
E[U] = uQt + kGFG(t) 0 5 10 15 20
• Resulting graphs of
5
utility vs. life duration
conform to usual Life duration
portrayal.
28
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]
1 1
kG = 0 (QALY model) kG = 4 yr
% lifetime willing to trade for full health
% lifetime willing to trade for full health
0.5 0.5
0 4 8 12 16 20 0 4 8 12 16 20
Lifetime (years) Lifetime (years)
29
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
1 1
Risk of death willing to accept
Risk of death willing to accept
0.5 0.5
0 10 20 0 10 20
Lifetime Lifetime
30
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
31
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
1 th
U Q (Q(h))
U T (th ) 0 U Q (h(t ))dUT (t )
– Conclusion:
th
U (h) U (Q(h), th ) U Q (Q(h))U T (th ) U Q (h(t ))dU T (t )
0
32
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
1 th
U Q (Q(h))
th 0
U Q (h(t ))dt
– Conclusion: Sum the QALYs along the path
th
U (h) U (Q(h), th ) U Q (Q(h))th U Q (h(t ))dt
0
33
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):
U ( g , h) U ( g , Q(h), th ) U Q (Q(h))th kGU G ( g )
th
U Q (h(t ))dt kGU G ( g )
0
34
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?
35
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
36
Example Decision Analysis
• Decision to undergo carotid endarterectomy – a Markov
chain analysis performed by Matchar & Pauker (1986).
Dead $0 Dead
mexcess mexcess
1.9
Post Big Stroke
1 - Pearlydie
Well Big Stroke Big Stroke
Pbig
Pbig mstroke
Dead
Pearlydie
Stroke
mstroke $0 Dead
7.11 mexcess
Small Stroke Post Small Stroke
1 - Pbig .
Stroke
EFF = 50% mstroke
mstroke = 0.05 /yr
Pearlydie = 0.38
Pbig = 0.6667
mexcess = 0.065 /yr
m0 = 0.0111 /yr
qPBS = 0.2
qPSS = 0.8
37
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.)
38
Example Decision Analysis Results
tG = 6 years, kG = 1.2 years
Surgical efficacy EFF = 50% EFF = 37%
Intervention Surgery No Surgery Surgery No Surgery
E[QALY] 8.588 yr 8.294 yr 8.369 yr 8.294 yr
E[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 k G = 15.2 yr k G = 0.492 yr
weight k G
39
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
40
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}
41
Proportionate-duration max endurable time
preference
• tG = 5 yr, kG = 4 yr
10
uQ = 1
uQ = 0.3
uQ = 0
5 uQ = -0.3
Utility
uQ = -0.6
0 5 10 15 20
5
Lifetime
42
Proportionate-duration willingness to trade
off for full health
• tG = 5 yr, uQ = 0.3
• kG = 0 (QALY model) • kG = 4 yr
1 1
% Lifetime willing to trade
% Lifetime willing to trade
0.5 0.5
0 0
0 10 20 0 10 20
Lifetime Lifetime
43
Proportionate-duration risk of death willing to
accept for full health
• tG = 5 yr, uQ = 0.3
• kG = 0 (QALY model) • kG = 4 yr
1 1
Risk of death willing to accept
Risk of death willing to accept
0.5 0.5
0 0
0 10 20 0 10 20
Lifetime Lifetime
44
Proportionate-duration utility and the QALY
model
• Proportionate-duration utility w/o discounting
U U Q (q)t kG min{1, t tG }
k
k U Q (q) G t if t tG
U Q (q) G t if t tG tG
tG
U (q)t k U (q) kG
if t tG Q
Q G tG U Q (q)(t tG ) if t tG
tG
• 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
45
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.
46
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
47
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.
48
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.
49
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.
50
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