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In general, QWB
scales report a numeric value representing the quality of life, for each
of a set of “health conditions.”
One such health condition, for instance, might be “confined to a
wheelchair.” After a large number of patients are surveyed for their
opinions on what life would be like with each health condition, each
condition is assigned a value on a scale of 0 to 1, with 1 being perfect
health and 0 being as good as dead. So,
for instance, the QWB for “confined to a wheelchair” might end up with
a value of 0.5 – having to spend one’s life in a wheelchair might be
judged as having only half the quality of perfect health.With these
considerations, the formula for QALY is:
QALY
= QWB x probability
X duration
“Probability”
is the statistical probability that the health condition related to the
QWB will occur. “Duration” is the expected duration of that health
condition. Assuming a
therapy has a 25% chance of preventing a patient from having to spend the
rest of his life in a wheelchair (a health condition that has a QWB of
0.50), and also assuming the patient has a life expectancy of 20 years,
then the QALY for that therapy would be calculated as QWB x probability x
duration = 0.5 x 0.25 x 20 = 2.5.
Note that a
therapy might impact on several different “health conditions.”
For instance, a drug used for cancer chemotherapy might have a 25%
chance of curing a particular type of cancer; but at the same time it
might also have a 20% chance of causing severe nausea for up to six
months, and a 5% chance of causing severe heart failure.
To compute a QALY for this therapy, one would have to total the
quality effects of the drug related to all three health conditions (i.e.,
curing the cancer, producing nausea, and causing heart failure).
Such an endeavor is not trivial.
To illustrate,
assume this chemotherapy was being contemplated for a 60 year old man,
whose life expectancy if cancer is cured would be 18 years, and whose life
expectancy were he to develop heart failure from the chemotherapy would be
five years.
The essential
data for calculating an overall QALY for this therapy in this patient is
given in the following table:
| Effect of therapy |
QWB value |
Probability |
Duration (years) |
| Curing cancer |
1.0 |
0.25 |
18 |
| Producing nausea |
0.75 |
0.2 |
0.5 |
| Causing heart failure |
0.6 |
0.05 |
5 |
This table
reflects the fact that the chemotherapy we’re considering for this
patient has a 25% chance of curing his cancer (i.e., the probability of
achieving this effect of therapy is 0.25).
Further, if the therapy does cure cancer, our patient will probably
live another 18 years, and will have a “normal” quality of life (i.e.,
the QWB value for a cancer cure is 1.0). Therefore, contribution to the
overall QALY calculation from “cancer cure” (the QALYcure)
1 x .25 x 18 = 4.5. This
means that for every patient like this one who receives this chemotherapy,
we might expect to gain 4.5 quality-adjusted life years.
Unfortunately,
our proposed therapy also has some detrimental effects.
It has a 20% chance of producing nausea for up to 6 months, and the
nausea is so severe that the patient’s quality of life for that period
of time will be significantly reduced. Indeed, the QWB score of .75
indicates that the presence of such nausea would make life itself worth
only 75% of its usual value. Because the nausea, if it occurs, will reduce
our patient’s quality of life by 25% for six months, the contribution of
this “effect of therapy” to our overall QALY (the QALYnausea)
is - 0.25 x 0.2 x 0.5 = - .025.
Our proposed
chemotherapy also has the propensity to cause heart failure.
In considering its effect on the QALY, we need to consider that
this heart failure is fundamentally different from the nausea we’ve just
discussed. Not only does the heart failure reduce the quality of life
while the patient remains alive, but it also reduces the duration of life.
This difference requires a two-part calculation to assess the
effect of heart failure on the overall QALY. It requires the calculation
of a quality of life component, and a duration component.
The quality of
life component contributed by the proposed therapy’s propensity to cause
heart failure is calculated using logic similar to that used for nausea.
There is a 5% chance our therapy will cause heart failure, which can be
expected to persist for 5 years, and which will reduce the patient’s
quality of life during that time by 40%. Thus, the calculation for the
quality of life component is - 0.4 x 0.05 x 5 =
- 0.1.
The need to
calculate a duration component arises from the fact that, if a patient
develops heart failure as a side effect of the chemotherapy, and if that
patient would otherwise have been cured of his cancer, then in effect the
heart failure will produce a reduction in survival of 13 years.
In other words, the heart failure will reduce the 18 years our
patient could have expected to live with a cancer cure, to 5 years. This
duration component is calculated as follows:
Pcancercure
X Pheartfailure
X Duration,
where
Pcancercure
is the probability that the
cancer will be cured, Pheartfailure
is the probability that heart failure will develop, and Duration is the
reduction in survival caused by the heart failure.
This calculation thus becomes: 0.25 x 0.05 x 13 = 0.1625.
The total
contribution to the QALY resulting from the propensity of our therapy to
cause heart failure (the QALYheartfailure) is the quality of
life component plus the duration component, or 0.1 + 0.1625 = 0.2625. (We are
assuming here that if the cancer is not cured, then the production of
heart failure will not further reduce survival.)
Now we can
calculate total QALY for the proposed chemotherapy as follows:
QALYrx
= QALYcure
+ QALYnausea
+ QALYheartfailure.
(Remember that
since
“nausea” and “heart failure” detract, not add, to the quality of
life, they are negative values, and will lessen the overall QALY.) Thus, the
QALY we could expect to achieve if we were to use this chemotherapy (i.e.,
the QALYrx,)
is 4.5 - 0.025 - 0.2625 = 4.21.
We would next
use the same methodology to calculate a QALYnorx,
(the QALY score we would expect
if we did not use the chemotherapy). Assume we did this, and the answer we got was 0.82.
(The low QALY here is reflective of the fact that, without
chemotherapy, early death would most likely ensue.) Thus, the QALY
difference is 4.21 – 0.82 = 3.39.
This number reflects the difference in outcomes (as measured by
QALY) between using and not using the chemotherapy.
Finally, we are
ready to calculate the cost-effectiveness of this chemotherapy. If the
cost of the chemotherapy is $50,000, then its cost-effectiveness would be:
$50,000/ 3.39 = $14,749 per QALY.
The chemotherapy would cost society $14,749 for every quality-adjusted life
year it gained us. Considering
that many commonly used treatments in medicine yield cost-effectiveness
values in the tens of thousands of dollars, this therapy looks reasonably
economical.
Note that, in
this example, the relatively high cure rate provided by the chemotherapy
along with the QWB score of 1.0 for a “cure,” strongly outweighs the
relatively small negative contributions resulting from the possible side
effects of severe nausea and heart failure.
The severe nausea, while a significant problem with an appreciable
incidence, reduces the QALY only marginally because of its relatively
short duration. Severe heart failure has a significantly poor QWB and
shortens life substantially, but because of its low probability, the
magnitude of its contribution to the overall QALY is also relatively low.
This sort of
calculation, while complex, is still eminently doable.
As long as we have reliable QWB values for a comprehensive list of
medical conditions, values for the probabilities of the important effects
of various medical therapies, and values for the duration of those
effects, then we can easily calculate QALY scores for virtually any
therapy we desire.
Ethical
considerations in calculating cost-effectiveness
As we have seen,
the ethical problem in designing a prioritized list of health care
services centers around the issue of which quality measures to include in
the cost-effectiveness calculation.
To see how
ethical considerations create a problem, let’s re-examine the
cost-effectiveness calculation for our 60 year-old cancer victim – but
this time, let’s add a complication. In addition to having cancer, assume he is now also confined
to a wheelchair, and that we have decided to factor this disability into
the QALY calculation. Further,
assume that the QWB for the health condition of being confined to a
wheelchair has been determined to be 0.5.
If we cure his cancer, he will still have a life expectancy of 18
years, and the probability that we will cure his cancer with our
chemotherapy is still 0.25. Thus, his QALY calculation for being confined
to a wheelchair is 0.5 x 0.25 x 18 = 2.25.
The new QALYrx
then becomes 4.21 (the previous QALYrx)
minus 2.25 = 1.96; and the QALY difference (QALYrx
– QALYnorx)
becomes 1.96 – 0.82 = 1.14.
The cost-effectiveness in this case is $50,000/1.14 = $43,859 per quality
adjusted life year. Providing
this chemotherapy to a patient confined to a wheelchair, then, looks far
less economical than providing it to a patient who is not disabled.
We can thus
easily see how factoring every underlying disability into a QALY score
(i.e., the standard method) will always
bias the resultant cost-effectiveness calculation against patients with
disabilities. The federal government was right, in other words, to
criticize the Oregon rationing plan as being in violation of the American
Disability Act.
On the other
hand, if we follow our FCEO standard, the
quality adjustment for being confined to a wheelchair would not
be used (from Rule # 1, since being
wheelchair-bound has no relationship to the effectiveness of the
chemotherapy), so for this patient the more favorable cost-effectiveness
value would apply. Thus, our
ethical standards determine the results of the cost-effectiveness
calculation, and thus determine the order of priority in rationing.
Implications
of who determines quality of life.
Another
way that ethical standards impact on cost-effectiveness calculations has
to do with the issue of who one surveys when the QWB values are being
assigned.
Are
patients being surveyed who have the condition being assessed, or are
individuals being surveyed who do not
have that condition? This is
an important consideration since, as is now well-recognized, patients who
are living with a disability (paraplegia, for instance), tend to rank
their own quality of life higher than would a person without that
disability (who is being asked about her quality of life if she were to
develop the disability).
This
fact has significant implications regarding the calculation of QALYs.
For instance, say we’re assessing a therapy that has the
potential to prevent paraplegia. If
the QWB score for paraplegia is derived from a survey of people who
actually have paraplegia, any treatment whose cost effectiveness is
measured using that QWB score won’t look as efficient as it would if we
had surveyed people who do not have paraplegia.
(This is because, since the QWB would be higher from a survey of
people with paraplegia, the QALYnorx
would also be higher. Therefore the QALYrx
– QALYnorx
would
be lower, and the results of a cost-effectiveness calculation for a
therapy that prevented paraplegia would be less favorable.)
This
example establishes a general rule. If
the QWB score for a disability is derived from a survey that includes
patients who have that disability, then both the QWB and the QALY will
tend to be higher than if the survey was derived solely from people who do
not have that disability. This would mean that any therapy that cures,
improves, or prevents that disability would end up with a relatively
unfavorable cost-effectiveness value, and would thus be disadvantaged in a
priority ranking. Conversely, a therapy that had, as a side effect, the
property of causing that disability would end up with a relatively
favorable cost-effectiveness value. Thus,
QWB values should be measured, whenever possible, by surveying patients
who do not have the health condition being assessed.
It
is important to note that this general rule only
holds if the FCEO standard is to be used.
Recall that under the FCEO standard, the quality measures for a
disability will not be included in the cost-effectiveness calculation for
a treatment, unless that disability materially affects the results
obtained with that treatment (see Appendix A). Under the more typical
application of cost-effectiveness, however (i.e., if the FCEO standard is
not going to be used), the quality measures for a disability would
be included in the cost-effectiveness calculation, regardless of whether
that disability affected the efficacy of the treatment. In this case,
excluding patients with the disability from participating in the QWB
survey would disadvantage them even further (since excluding them would
result in a lower QWB score and a lower QALY score, and thus a less
favorable cost-effectiveness calculation.)
Implications
of including "duration" in cost-effectiveness calculations.
By definition,
QALY measurements must factor in the expected duration of the benefits and
harms of the treatment being considered.
We ought to be quite clear about what this means.
Sometimes, the
duration of a benefit (or harm) is dependent only on characteristics of
the treatment. For instance, the duration of nausea caused by the
chemotherapy in the examples we’ve been using is 6 months.
That value is purely a function of the chemotherapy itself.
However, in many
cases the expected duration of a benefit or harm is directly related to
the age of the patient in whom the therapy is being contemplated.
In the example of our 60-year-old patient, his life expectancy,
judged to be 18 years if the cancer could be cured, featured prominently
in the calculations of cost-effectiveness.
If this patient had been 30 years old, his life expectancy would
have been nearly 50 years, and the cost-effectiveness would have
calculated out much more favorably.
Most methods of
computing cost-effectiveness, by including the expected duration of
benefit in the calculations, are automatically biasing the calculations
according to age. While,
according to the FCEO standard, it is ethically permissible to do this
(based on the concept of total lifetime risk being equal for all
individuals), it is not required that we do so.
If we do decide
to continue biasing cost-effectiveness calculations by age, we should not
allow that fact to remain “hidden.”
Perhaps we should rename the process “age-adjusted
cost-effectiveness.” While
such a term could legitimately be considered a redundant one, at least it
lets everyone know exactly what’s being done.
If we decide not
to let age become a factor in rationing health care services, then we will
need to devise a new methodology for calculating QALYs.
For instance, the “duration” of benefit of a life-saving
therapy might be assigned a standard value for all patients.
To do this will be seen by some as being more fair to the elderly;
but in terms of the ideal of equalizing the lifetime opportunities of all
individuals, others will see it as being unfair to the youthful.
The point, once
again, is that our ethical principles will determine our methodology for
calculating cost-effectiveness, and therefore largely will determine how
our health care services are rationed.
If we don’t specifically articulate those ethical principles,
then the equations we use for doing our calculations will articulate them
for us.
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