Decision and Cost-Effectiveness Analysis
Elective, Training in Clinical
Research
UCSF Department of Epidemiology
and Biostatistics EPI 213
Jan-Feb 2004
ATCR DCEA Lecture 2, January
13, 2004, Dr. Caughey / substitute:
Decision Analysis: Utilities and QALYs
Objectives:
·
To understand techniques to measure utilities
·
To understand how to calculate Quality-Adjusted Life Years
·
To understand discounting
Reading:
Shlipak MG, Chapter 2. Decision Analysis, in
Friedland DJ et al Evidence-Based Medicine: A Framework for
Clinical Practice. Appleton & Lange, 1998.
In the last
lecture, we introduced decision analysis and went through the
steps of making a decision tree. In this lecture, we’ll move on
to some important refinements in DA. The topics are
1. Utilities/utility measurement
2. Quality-adjusted life years
3. Discounting
1. Utilities and utility measurment
Utility is a
quantitative measure of the strength of a patient’s preference
for a particular state of health, or outcome.
In other words,
how do we value our health compared with other potential states
of health?
Examples:
Disability from a stroke
stable exertional angina
chronic pain
Why do this
quantitatively?
Let’s return to aneurysm example. There are two parts of the
analysis that require good utility assessments.
As discussed, clipping surgery can cause disability. The quality
of life depends on the severity of the disability – mild vs.
moderate/severe.
Also, being at risk of an aneurysm rupture can cause anxiety
that reduces quality of life, and hence reduces the utility of
being in the at-risk state. Considering this factor makes the no
surgery arm less attractive. This anxiety does not affect the
surgery arm; clipping reduces risk to zero, and thus is assumed
to reduce the anxiety to zero.
We’ll return to how these utilities are assessed at the end of
the lecture.
How do you decide what the utility
of health states is?
3 common methods used for
estimating utilities:
Visual analog scale/Interval
scaling
Standard Gamble
Time trade-off
To illustrate these methods,
consider the following clinical scenario:
A
patient in the hospital has a serious infection of the lower leg.
The surgeon advises a below-the-knee amputation (BKA), rather than
medical management. The reason she gives is that the infection has
about a 20% chance of spreading further up the leg, and an 80%
chance of being cured, with medical management. If the infection
spreads, the procedure would have to be an above-the-knee amputation
(AKA), a more serious procedure. The chance of dying is about 10% if
the infection were to spread; the mortality from a BKA is only 1%.
Which option (BKA or medical management) is better? It turns out the
right answer depends on how the patient values living with a BKA
versus with an AKA.
This
method uses a simple linear scale to determine a patient’s relative
preferences. (It’s basically a ruler.)
(death
0-----------------------------1.0 cure)
Where is the AKA?
(AKA--------------------------------1.0 cure)
Where is the BKA?
Advantages:
Quantitative
Easy to understand
Visual
Disadvantages:
May bias values to the middle.
Seems disconnected from medical
reality.
Method of utility assessment that
forces patients to choose between
a.
a certain outcome
b.
a gamble to achieve a better outcome while risking ending up
with a worse outcome
Sort of like the old game show,
“Lets make a deal.”
How it works:
Choice A:
You live with a BKA
Choice B:
Take a chance – you might have a cure; you might die.
Which do you choose? Doesn’t it
depend on the likelihood of cure vs. death? What risk of death would
you accept to avoid living with the BKA? How does this lead us to
the utility?
Remember the concept expected
utility. If you cannot decide between the 2 choices, then your
expected utility is the same for both (Choice A = Choice B).
The choice is represented like this:
Steps in the Standard Gamble.
(The other methods have steps too;
we show standard gamble because it’s the most complicated.)
Ask the “subject” to
1. Rank the 3 outcomes (perfect
health, BKA, death).
2. Imagine that they have the
intermediate outcome (BKA); you provide details about limitations on
mobility, etc.
Tell the subject that
3. You are doing this to try to
determine the relative value they place on living with this
intermediate state (BKA), by comparison with the best (perfect
health) and the worst (death).
4. There is a procedure (or pill, or
test) that has the possibility of restoring them to perfect health
(or whatever the best outcome is). However, there is a down side to
this procedure. Sometimes, it results in death (or whatever the
worst outcome is).
Then determine “100- p.”
5. “I’m now going to ask you what
chance of dying you would be willing to take with this procedure.
Remember, if it works, you will be restored to perfect health.”
6. Approach it from the bottom
(“Would you be willing to take a one in a million chance of dying?”)
and from the top (“...a 1 in 2 chance of dying?”). Keep narrowing: a
one in 10,000 chance? a 1 in 5 chance? until you arrive at the point
where the subject has a hard time deciding.
7. Verify by re-phrasing to
determine p (“...a 999,999 in a million chance of living
through the surgery?”; “ ...a 1 in 2 chance of living?”, etc.)
Once you find the probability “p” of
cure at which A = B, then from the equating of expected utility
value
Utility (BKA) x Probability (BKA) =
Utility(cure) x (p) + Utility(death) x (1-p)
you can demonstrate that the utility
of BKA = p:
Utility (BKA) =
[Utility(cure) x (p) + Utility(death) x (1-p)] / Probability (BKA)
= [1.0 * p + 0 * (1-p)] / 1.0 = p
Advantages:
Reflects the uncertainty of the
future.
Portrays the element of risk.
Disadvantages:
Hard for some people to understand,
especially those who have never gambled.
Involves a math equation.
This method of utility assessment
involves trading off the quality of life vs. length of time alive.
Simple concept:
Time A * Utility A = Time B *
Utility B
So, let’s say you have a life
expectancy of 30 years of life with a BKA; how much time would you
give-up to live in your current state?
Would you give up 5 years? 3 years?
1 year?
30 years * Utility (BKA) = (30-x)
years * 1.0
If you’re willing to give up 3
years, that means the utility of BKA is 0.9 [= (30-3)/ 30].
Advantages:
Portrays long-term outcomes.
Easy to understand.
Helpful for portraying chronic
diseases.
Disadvantages:
Does not reflect the element of
risk.
Makes all years in the future appear
to be equal.
Final thoughts on Utilities:
1.
Very subjective. To some extent this is desirable – capturing
patient preferences even if apparently nonrational. But some
subjectivity represents measurement problems (the methods may yield
inconsistent results with no “gold standard”, and are hard to
standardize). Research to improve measurement is ongoing.
2.
Important to realize that the utilities can change over time.
3.
It really matters who is deriving the utility. In some
situations the patient should, and their rankings will depend
on who they are. For example, for BKA -- teenagers, vascular
surgeons, patients, professional athletes. Some economists say
society should decide utility values, which may overstate disutility
(eg, people living with AIDS rate their quality of life as higher
than those in society contemplating living with AIDS).
2. Quality-adjusted life-years:
What does this term mean? What’s a
Quality-Adjusted Life Year (QALY)? It’s really pretty
straightforward:
QALY(s) = Year(s) * Quality (i.e.,
utility)
Example: 2 years * 0.9 utility = 1.8
QALYs.
Another
example:
|
|
Patient A |
Patient B |
|
Year
|
Quality |
Quality |
|
1 |
0.95 |
0.8 |
|
2 |
0.95 |
0.8 |
|
3 |
0.9 |
0.75 |
|
4 |
0.8 |
0.75 |
|
5 |
0.0 |
0.5 |
|
|
QALYs = 3.6 |
QALYs = 3.6 |
Are QALYs
better than Life Years?
Given how subjective utilities are,
how does measuring QALYs help? It represents the best estimate of
the quality of life. To not use QALYs ignores the obvious
differences in the desirability of different health states. Utility
assessments and QALYs, though imperfect, begin to quantify these
differences.
For the aneurysm example, there are
no definitive published studies for the health states with
disutility
(disability due to brain surgery and anxiety due to risk of
rupture). Nor were there resources to conduct utility assessments
(these studies are expensive!). So another approach was used:
applying the most relevant estimates from the literature.
Gage and colleagues used time tradeoff and standard gamble
methods to obtain utility valuations for permanent disability
states after stroke for 83 patients with atrial fibrillation
(Gage 96). Utility for mild strokes was 0.76, and for moderate
and major strokes averaged 0.25. Since these two levels of
disability occur with equal frequency after surgery, the tree
uses 0.50 as the utility. The risk of death is 3-fold higher
with disability (Strauss 98), so we lowered life expectancy by
2/3. Thus, QALYs are reduced by 83% (50% reduction for
disutility; a further 67% reduction for shorter life).
Thus, with QALYs substituted for
utilities (but not yet portraying worry), the tree looks like below.
Note that the disability branch reflects decreases due to lower
utility and lower life expectancy. Other branches have utility =
1.0; differences in QALYs reflect unequal life years.
Here’s how worry is incorporated:
Prior cost-effectiveness analyses
of aneurysm treatment assumed that untreated patients would be
burdened by concern that their aneurysm could rupture, and
estimated a utility of 0.95 (Kallmes 98, King 95). This burden
should depend on rupture rates, so we assumed that the utility
for untreated patients would vary with the rupture rates as
follows: RU = 1 – 5 * (Rupture rate). The factor 5 is an
estimate of the emotional dimension of living with a low-risk,
high consequence condition (Gage 96). For an aneurysm with 1%
yearly rupture rate, this reproduces the prior estimate of 0.95
and is similar to the mildly impaired emotional state
(“occasionally fretful, angry, irritable, anxious, depressed, or
suffering” = 0.93) in the Health Utilities Index Mark 2
(Torrance 96). For an aneurysm with 0.05% yearly rupture rate
(our example), the formula produces a utility of 0.9975.
The tree below shows the effect of
worry. Only the no surgery branches are affected. Given the low
rupture rate in our example, worry doesn’t affect QALYs much. With a
higher rupture rate (as we’ll examine in a later lecture), worry
creates a larger effect. The “worry” factor amplifies the loss in
QALYs by about 25%, compared with considering only the years of life
lost due to aneurysm rupture.
3. Discounting
Is it right to simply add QALYs over
time? Should we really treat present and future QALYs equally? The
answer is no: We need to capture the real “time preference” people
have – valuing events in the present more than events in the future.
Example:
Let’s say (hypothetically), I agree to buy you an ice cream cone, or
your equivalent favorite dessert…
Who would want the dessert today? Or
in 5 years?
Most people want to delay bad events
or health states, but have good events occur as soon as possible.
(This holds true for all except physicians-in-training. We
MD’s are pretty accepting of delayed gratification.)
Discounting is the method to adjust future health outcomes and costs
to their value in the present. Value in the present is called “net
present value”, or NPV. This technique has long been used to
represent time preference for costs. Recently a consensus has been
reached to discount health outcomes. Not doing so leads to some
logical conundrums in CEAs.[1]
On average people exhibit time preferences for health outcomes
similar to those for costs.
The recommended discount rate (for both health and costs) is 3%
(0.03), suggested by the U.S. Panel on Cost-Effectiveness in Health
and Medicine. Other rates can be used to reflect special conditions
such as the discount rate used internally by an HMO for financial
planning.
As
we’ve talked about all along, everything in decision analysis has to
be done quantitatively. Each year in the future will be de-valued at
a constant rate (the discount rate). Here is the formula for
discounting:
The NPV of a utility value occurring x years in the future
=
Utility
(1+D)x
where D is the discount rate.
So, if D = 3%, then events occurring 1-5 years into the future are
adjusted as follows:
0.97, 0.94, 0.92,
0.89, 0.86.
For Utility = 1.0, D = 3%, and x = 10 years, the NPV for a year of
“perfect health” is:
1.0/(1+0.03)10
= 0.74.
This can get subtle: Events happening “in year x” of a simulation
are not happening exactly “x years into the future”. More precisely,
they are happening on average [x-0.5] years into the future. For
example, events during “year 2” probably occur on average 1.5 years
from the start of the analysis. Thus, a half-year adjustment is
sometimes used:
Utility
(1+D)[x – 0.5]
Thus, a utility of 1.0 in year 2 translates to a NPV of 1.0/(1+0.03)1.5
= 0.957. Alternatively, a full-year adjustment is sometimes used, so
events in year x are discounted by (x-1); this may be slightly
inaccurate but is acceptable.
In the aneurysm example,
discounting is very important, because most of the health states
occur substantially into the future. The QALY total without
rupture, with life expectancy of 35 years, is discounted by 39%
overall. This represents the discounting of each year, and then
summing across years. The QALY total with rupture is discounted
less (24%), since many individuals live only an average of 17.4
years. Life with disability is discounted least (17%) since it
occurs in the near future.
The tree with
discounted values is below. The drop in QALYs due to discounting is
slightly larger for no surgery 13.4 (38.5%) than for clipping 12.3
(38.3%). As a result, the difference in QALYs between the strategies
also decreases, from 2.77 to 1.63. Almost all of the change in the
difference (93%) is due to the overall effects of discounting; just
7% is due to the differential effects of discounting on the two
strategies
Quick
Review:
Utilities – ways of measuring and valuing health states between
perfect health and death.
Utility assessment – Visual analog scale, standard gamble, time
trade-off
Quality-adjusted life expectancy – utility * time
Discounting – way of de-valuing future health states relative to the
present
Additional reading /
references
Kallmes DF et al. Guglielmi detachable coil embolization for
unruptured aneurysms in non-surgical candidates: a
cost-effectiveness exploration. Am J Neuroradiol 1998;18:167-176.
King
JT et al. Elective surgey for asymptomatic, unruptured, intracranial
aneurysms: a cost-effectiveness analysis. J Neurosurg
1995;83:403-412.
Strauss DJ et al. Long-term survival of children and adolescents
after traumatic brain injury. Arch Phys Med Rehabil
1998;79:1095-1100.
Gage
BF et al. Cost-effectiveness of warfarin and aspirin for prophylaxis
of stroke in patients with nonvalvular atrial fibrillation. JAMA
1995;274:1839-1845.
Gage BF et al. The effect of stroke and stroke
prophylaxis with aspirin or warfarin on quality of life. Arch Intern
Med 1996;156:1829-1836.
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