Decision and Cost-Effectiveness Analysis
Elective, Training in Clinical Research
Department of Epidemiology and Biostatistics EPI 213
ATCR DCEA Lecture 2,
January 13, 2004, Dr. Caughey / substitute:
Decision Analysis: Utilities and QALYs
\l 1 "Objectives"
understand techniques to measure utilities
level0 \h \r0 seq level1 \h \r0 seq level2 \h \r0 seq
level3 \h \r0 seq level4 \h \r0 seq level5 \h \r0 seq
level6 \h \r0 seq level7 \h \r0 To understand how to
calculate Quality-Adjusted Life Years
Shlipak MG, Chapter 2. Decision Analysis, in Friedland
DJ et al Evidence-Based Medicine: A Framework for
Clinical Practice. Appleton & Lange, 1998.
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
1. Utilities and utility
Utility is a quantitative measure of the strength of a
patient’s preference for a particular state of health,
other words, how do we value our health compared with
other potential states of health?
Disability from a stroke
stable exertional angina
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.
do you decide what the utility of health states is?
common methods used for estimating utilities:
Visual analog scale/Interval scaling
illustrate these methods, consider the following
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.
Visual analog scale:
This method uses a simple linear scale to determine a
patient’s relative preferences. (It’s basically a
(death 0-----------------------------1.0 cure)
Where is the AKA?
Where is the BKA?
bias values to the middle.
disconnected from medical reality.
Method of utility assessment that forces patients to
gamble to achieve a better outcome while risking ending
up with a worse outcome
of like the old game show, “Lets make a deal.”
Choice A: You live with a BKA
Choice B: Take a chance – you might have a cure; you might
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
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.
other methods have steps too; we show standard gamble
because it’s the most complicated.)
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.
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).
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.)
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)
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
Reflects the uncertainty of the future.
Portrays the element of risk.
for some people to understand, especially those who have
Involves a math equation.
method of utility assessment involves trading off the
quality of life vs. length of time alive.
Time A * Utility A = Time B * Utility B
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].
Portrays long-term outcomes.
Helpful for portraying chronic diseases.
not reflect the element of risk.
all years in the future appear to be equal.
Final thoughts on Utilities:
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.
Important to realize that the utilities can change over
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
2. Quality-adjusted life-years:
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.
QALYs = 3.6
QALYs = 3.6
Are QALYs better than Life Years?
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.
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.
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
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
Here’s how worry is incorporated:
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.
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.
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
Let’s say (hypothetically), I agree to buy you an ice
cream cone, or your equivalent favorite dessert…
would want the dessert today? Or in 5 years?
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. 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
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 =
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:
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.
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
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
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
Gage BF et al. Cost-effectiveness of warfarin and
aspirin for prophylaxis of stroke in patients with
nonvalvular atrial fibrillation. JAMA
BF et al. The effect of stroke and stroke prophylaxis
with aspirin or warfarin on quality of life. Arch Intern