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Topics:- QALYs
- Monetary valuation of health
- Time preference (discounting)
- Utility measurement (mainly in situations of risk)
- Equity
We study QALYs in three dimensions:
1. Randomness of allocation (risk and uncertainty)
2. Allocation over time (discounting)
3. Aggregation/Allocation among people (equity)
,Lecture 1&2: theoretical foundations
Estimating a monetary value of a QALY
In economic evaluation we compare costs and benefits, but how can we express
benefits numerically (assign a monetary value to it)?
Estimate the willingness to pay and the value of life.
Value of life = €WTP/reduction in risk.
The main advantage of putting a monetary value to health (so CBA instead of
CUA) is that CBA enables comparing health programs to non-health programs.
However, there are several difficulties in estimating WTP for health:
1. Sensitivity to irrelevant information
- Starting point bias = answers depend on the starting point given
(e.g. in the first choice). Higher starting points cause higher valuation
for the same good.
- Range effect = range bias means that the elicited WTP depends on if
and, if so, which comparators are used in the question. A separate
evaluation may for instance lead to a higher value than when the
valuated item is compared to a better item.
- WTP/WTA disparity = People are often found to be willing to pay
much less than they are willing to get for that same good once that is
already in their possession. This is hard to explain from traditional
economic theory. One of the most important explanations is loss
aversion: once you own something, then giving it up feel like a loss,
and you need more compensation than for something that you don’t
possess.
-
2. Insensitivity to relevant information
- Scope effects = WTP values are not sensitive to the amount of the
good that is being valued. The WTP for a QALY is also not constant over
QALY changes. If the QALY increases twice as much, the WTP does not
increase twice as much.
The QALY model: main purpose
is to represent preferences: the
value of a health improvement to
an individual. In a linear QALY
model, this is the product of
gains in quality of life (utility) and
the length of life:
Main advantage:
- Intuitively appealing.
- Easy to use in practice.
Disadvantages:
- May be too simple.
Calculating Expected Utility:
EU [(Q1, T1), p, (Q2, T2)] =
pU(Q1, T1) + (1-p)U(Q2,T2)
,EU [(minor health problems, 10y), 0.5 (major health problems, 10y) =
0.5*10*H(minor health problems) + (1-0.5)*10*H(major health problems)
We measure expected utility most often with standard gamble questions. SG
questions involve risk. We search for an indifference point and apply this to
expected utility. For example, someone is indifferent between:
( Back pain , 30 y . ) ( ( Full health ,30 y . ) , p , Death )
We can apply scaling to this indifference by saying that Full Health has a utility of
1 and Death has a utility of 0:
U ( Full health, 30 y . )=1
U ( Death)=0
U ( Back pain , 30 y . ) =p
The answer a respondent is giving, is the utility he/she assigns to back pain.
Assumptions linear QALY model:
U(Q,T) = H(Q) * T
1. Mutual utility independence
a. Life duration is utility independent from health quality:
(Back pain, 20y.) ((Back pain, 40y.), 2/3, (Back pain, 10y.))
Then also
(Full health, 20y.) ((Full health, 40y.), 2/3, (Full health, 10y.))
b. Health quality is utility independent from life duration:
(Back Pain, rest of life) ((FH, rest of life), 2/3, (Death, rest of
life))
Then also
(Back Pain, 10y.) ((FH, 10y.), 2/3, (Death, 10y.))
2. Constant proportional trade-off: for each health state Q there exists a
number q such that Y years in Q is equivalent to qY years in perfect health
(Q, Y) is equivalent to (perfect health, qY) for all Y
( Back pain , 40 y . ) ( FH , 30 y . )
30
TTO: H ( Back pain )= .
40
( Back pain , 10 y . ) ( FH ,7.5 y )
7.5 30
TTO: H ( Back pain )= =
10 40
(Back pain, T 1 y .) ( FH , T 2 y .) ( Back pain , α T 1 y . ) ( FH , α T 2 y ) , α ≥ 0
CPT excludes the additive QALY model:
If life duration is 0 (α=0), then the additive QALY model can not be
applied. In that case, we prefer the full health state over the back
, pain health state, when life duration is longer than 0. However,
when life duration is 0, then we don’t have a preference. By the law
of CPT, we cannot have H(BP)<H(FH) for α>0 and H(BP)=H(FH) for
α=0.
3. Risk neutrality with respect to life duration
a. Risk neutrality wrt life duration holds if for a fixed health status level
all treatments with equal expected life duration are equivalent.
L(T) = linear
The linear QALY model:
The assumption of risk neutrality is not empirically realistic, because it does
not incorporate discounting and risk aversion.
Plausible explanations for concave utility of life duration are:
- People are risk averse with respect to life years
- Decreasing marginal utility, with people valuing additional life-years less
the higher their life expectancy
- The discounting of future utility.
Assumptions generalized QALY model:
U(Q,T) = H(Q) * L(T) with L(0) = 0
1. Mutual utility independence
2. Constant proportional trade-off
3. Standard gamble invariance & zero-condition
a. Standard gamble invariance: in place of risk neutrality, a
condition on SG for life duration is adopted: probability
equivalence
( Back pain, 20 y . ) ( ( Full health , 40 y . ) , p , Death )
U(FH) = 1; U(D) = 0
We say that back pain is probability equivalent with respect to
the end points Full health and Death. If people are risk neutral, then
the probability equals:
20y certain = p*1*40 + (1-p)*0*0 20y = p*40 p=0.5
Standard gamble invariance allows for risk aversity and risk
seeking.
Gamble (40y, ½, 0y) Certain (20y)
Risk neutral =
Risk averse <
Risk seeking >
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