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F o r u m for Health Economics & Policy
Volume 15, Issue 2 2012 Article 5
(HEALTHECONOMICS)
The Option V a l u e of Innovation
Julia Thornton Snider∗
John A. Romley†
William B. V o g t ‡Tomas J. Philipson∗∗
∗
Precision Health Economics, julia@precisionhealtheconomics.com
†
University of Southern California, romley@healthpolicy.usc.edu
‡
University of Georgia, wbvogt@uga.edu
∗∗
University of Chicago, t-philipson@uchicago.edu
DOI: 10.1515/1558-9544.1306
Copyright c 2012 De Gruyter. All rights reserved.
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The Option Value of Innovation∗
Julia Thornton Snider, John A. Romley, William B. Vogt, and Tomas J. Philipson
Abstract
Standard techniques of cost effectiveness analysis measure a technology’s benefits in terms of
expected life years (or quality-adjusted life years) gained at today’s life expectancies. However,
this approach ignores the gains which derive from the possibility that a health technology allows
an individual to survive long enough to benefit from other technological innovations which raise
life expectancy (and quality of life) in the future. Borrowing a term from the finance literature,
we refer to this source of value as the “option value” of innovation. We explain where this value
comes from and how to calculate it in a variety of standard cost effectiveness analysis contexts.
We provide a proof-of-concept using the example of the drug tamoxifen, which delayed the on-
set of breast cancer for some patients until more effective adjuvant treatment was available. We
find that incorporating option value can increase the conventionally estimated value of tamoxifen
with better adjuvant treatment by nearly a quarter (from $200,000 to $248,000 for those who ini-
tiated tamoxifen in 1999). We expect similar results for other drugs in therapeutic areas of rapid
technological advancement.
KEYWORDS: innovation, pharmaceutical, medicine, option value, cancer
∗The authors gratefully acknowledge financial support from Pfizer and comments and suggestions
from a number of Pfizer’s employees; however, the views expressed in this article are those of
the authors and not necessarily those of their institutions. Any remaining errors are those of the
individual authors.
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Introduction
Given the rapid advance of health technology in recent decades, governments and
other payers have come to desire a means for evaluating which technologies
provide the most benefit in terms of duration and quality of life, relative to their
cost. It is in this context that the field of cost effectiveness analysis (CEA) has
been developed. CEA provides researchers with a toolkit for comparing the value
of a menu of potential health interventions. By providing researchers a set of
standardized techniques, CEA aims to make the results of different studies
conducted by different researchers more comparable. Over time, researchers have
developed a vast literature which explains the benefits of CEA and outlines how
different types of studies should be conducted (Weinstein and Stason 1977;
Jennett 1992; Johannesson and Weinstein 1993; Gold 1996; Drummond 1997;
Garber and Phelps 1997; Meltzer 1997; Garber 2000).
CEA typically measures the benefits of a particular health intervention in
terms of the life years or quality-adjusted life years (QALYs) gained relative to
some benchmark (e.g. no intervention, or an older technology).1
As explained in recent work (
These benefits
are then weighed against the intervention’s net cost, that is, the cost of
implementing the intervention minus any reduction in costs it achieves relative to
the benchmark. (For example, if an intervention prevents a fraction of the cases
of disease that would have otherwise occurred, then the treatment costs for those
cases of disease are spared.) Interventions which achieve substantial gains in
terms of life years or QALYs for their cost are then favored by decision-makers.
Philipson, Becker et al. 2010), there are
several important weaknesses in the standard CEA framework. First, the
framework places equal value on each QALY saved, even though economists
typically assume that extra units of a good will be worth less when individuals are
already consuming large quantities of it. Conversely, as we have less and less of
a good, we value an additional unit of that good more and more. Thus, QALYs
near the end of life may be valued more than QALYs near the beginning. There
is evidence that these concerns are not mere economic arguments but actual forces
which influence social policy. For example, attempts to allocate health care based
on traditional cost effectiveness analyses—which value all QALYs equally
regardless of the circumstances—have provoked ire both in the context of the
Oregon Medicaid program and the National Institute for Health and Clinical
Excellence (NICE) in the United Kingdom (Oberlander, Marmor et al. 2001;
Devlin and Parkin 2004; Oberlander 2007). Similarly, work by Richardson and
Nord (Richardson and Nord 1997) has shown that people value QALYs
differently depending on their perspective: Equity considerations may play a role,
1 The benefits of an intervention may also be measured in terms of disability-adjusted life years
(DALYs) gained, or cases of disease averted, or in numerous other ways.
1
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and whether the potential beneficiary is the self or another influences people’s
judgments.
Second, the standard framework is static. An intervention which, in and
of itself lengthens life by one year is valued by assuming that its effect on lifespan
is exactly one year. But, as long as there is ongoing medical progress, this has to
be an understatement. If one medical innovation causes someone to live for an
additional year and, during that extra year, another innovation arrives that further
extends life, then the true benefit of the first innovation was the extra year of life
plus the value of the second innovation. This extra value of life-extending
innovation is called “option value.” Normally, of course, we do not know that a
second innovation is imminent. Instead we know that there is some positive
probability of an innovation. But this probability still generates an option value of
future innovation in expectation.
The term “option value” is borrowed from finance. An option (say, a call)
gives its holder the right to buy a security at a contracted price into the future.
This contract offers two sources of value: First, it has the intrinsic value of the
difference between the contract and the spot price of the security today. Second,
it has the option time value, or “option value,” of the expected benefit of having
the option to buy the security in the future at the contracted price. If the price of
the security rises, the call holder can realize a profit in the future, and buyers are
willing to pay something today for that potential future value.
Similarly, survival has an option value. If a patient survives until next
year, she will have the option of using any treatments developed between now and
then. The option of using future treatment has a value to the patient in terms of
potentially increased survival time and quality of life. The option value will be
particularly important to patients facing life-threatening conditions, a point first
made by Philipson, Becker, Goldman, and Murphy in the article “Terminal Care
and the Value of Life Near its End” (Philipson, Becker et al. 2010).
In that paper, Philipson and co-authors argue that standard techniques
understate the value of life near its end by ignoring the low opportunity cost of
medical spending near one’s death, the value of the hope of living to see new life-
prolonging innovations, and the potential positive effect on the value of life from
being frail. In this paper, we recast the value of hope as the option value of
innovation, and argue that it applies much more broadly than in end-of-life
experiences. We offer suggestions on how to incorporate the option value of
innovation in the standard CEA studies, and we illustrate the concept using the
example of two cancer drugs.
Considerations of option value are not merely academic, as the example of
innovation in AIDS drugs demonstrates. In their 2006 paper, “Who Benefits from
New Medical Technologies? Estimates of Consumer and Producer Surpluses for
HIV/AIDS Drugs,” Philipson and Jena document improvements in the treatment
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of HIV/AIDS and translate these into value accruing to consumers and producers
(Philipson and Jena 2006). Until the introduction of zidovudine (AZT) in 1987,
no treatments existed for HIV/AIDS patients. According to Philipson and Jena
(Philipson and Jena 2006), AZT helped increase a patient’s life expectancy
conditional on a new HIV infection from 23.6 years in 1986 to 25.6 years in 1989,
a gain of two years in only three years’ time. However, part of the value of AZT
was that it increased the probability of a patient living to see highly active anti-
retroviral therapy (HAART), a combination of AIDS drugs first deployed in the
developed world in 1996. Due in large part to HAART, life expectancy
conditional on new HIV infection increased to 33.2 years in 1998, a gain of nearly
8 years over 1989 and nearly 10 years over 1986 (Philipson and Jena 2006).
These rapid and substantial gains in life expectancy imply that AZT had option
value far beyond the survival gains it produced on its own.
Philipson and co-authors addressed the issues of non-linearity and option
value in their recent work on the value of end-of-life care (Philipson, Becker et al.
2010).2
2 Also, there is a fairly extensive literature on the tradeoff between static and dynamic efficiency
in pharmaceutical pricing, which hints at the possibility of option value as the funding of current
treatments creates incentives for the development of future treatments Lichtenberg, F. R. (2001).
"Probing the link between gross profitability and R&D spending." Health Aff (Millwood) 20(5):
221-222, Scherer, F. M. Ibid."The link between gross profitability and pharmaceutical R&D
spending." 216-220, Giaccotto, C., Rexford E. Santerre, et al. (2005). "Drug Prices and Research
and Development Investment Behavior in the Pharmaceutical Industry." Journal of Law and
Economics 48(1): 195-214, Vernon, J. A. (2005). "Examining the link between price regulation
and pharmaceutical R&D investment." Health Econ 14(1): 1-16, Abbott, T. A. and J. A. Vernon
(2007). "The cost of US pharmaceutical price regulation: a financial simulation model of R&D
decisions." Managerial and Decision Economics 28(4-5): 293-306, Camejo, R. C., R. R., C.
McGrath, et al. (2011). "A dynamic perspective on pharmaceutical competition, drug development
and cost effectiveness." Health Policy 100(1): 18-24.
However, the literature still lacks a broad-based explanation of these
issues and suggestions for how to remedy them in CEA. Our objectives in this
paper are threefold. First, we argue that CEA should use methods which
recognize both the option value of innovation and the non-linearity inherent in the
valuation of survival. Second, we introduce to a wider audience the (relatively
simple) methods to adjust CEA for these effects which have been recently
developed. Third, we illustrate the concept using the example of the drug
tamoxifen. Tamoxifen offered survival gains on its own by reducing the
incidence of breast cancer in some patients, and delaying onset in others. For the
latter patients, part of tamoxifen’s value was that it increased a patient’s chances
of living to the availability of more effective adjuvant treatment (Herceptin in
2006). When this option value is considered, we find that the conventionally
calculated value of tamoxifen nearly doubles as approval of the adjuvant
indication of Herceptin approaches.
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This paper proceeds as follows. First, we provide a brief guide on how the
concept of option value can be applied to the standard techniques of CEA. Next,
we provide a case study which supplies proof of concept: the option value of the
breast cancer drug tamoxifen in the early to mid-2000s, prior to the approval of
the adjuvant indication of Herceptin. Last, we conclude.
Option Value in Cost Effectiveness Analysis
The option value of innovation can be incorporated into the standard techniques
of cost effectiveness analysis. CEA typically requires information about the
survival and quality-of-life improvements of a given health innovation as well as
information about its cost. To incorporate option value into a typical CEA, we
additionally need an estimate of the improvements in medical technology—apart
from the innovation in question—which will apply to the studied population.
With this estimate in hand, incorporating option value into CEA is a relatively
straightforward process. The framework is based on the dynamic, life-cycle
utility maximization model which is the gold standard in economics for valuing
innovations; however, in practice it reduces to a simple formula whose calculation
is a spreadsheet exercise.
For example, to incorporate the option value of an innovation into the
calculation of its effect on expected remaining years of life, suppose an
innovation is introduced at time t. In each time period from time t onward, the
option value can be calculated as the product of the change in survival probability
due to the innovation times the change in survival benefits from medical advances
between time t and the time period being considered. To determine the total
option value of the innovation, simply sum over the time periods its user could
potentially live to reach.
In addition to the calculation of expected years of remaining life, option
value can similarly be incorporated into the calculation of QALYs, the economic
value of additional years of life, and the economic value of additional QALYs.3
3 This is by no means an exhaustive list. Certainly, many other types of CEA or health technology
assessment could also benefit from the inclusion of option value.
In each case the idea is the same. The option value is expressed as the survival
benefits of the innovation multiplied by the expected future advances in medical
technology. A guide to the methods for incorporating option value into the
standard valuations of CEA is presented in Table 1. In contrast, Table 2
summarizes methods for isolating the contribution of option value to total value in
these four types of CEA.
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Table 1. How to Calculate the True Total Value of an Innovation
Valuation method
How the true total value of innovation is calculated
Life Expectancy
∆ in survival
probability due to
the innovation
X
∆ in survival benefits from
medical advances between
now and that future date
Expected QALYs
∆ in survival caused
by the innovation
∆ in quality of life
caused by the
innovation
X
PLUS
X
∆ in both survival and
quality of life caused by
underlying medical advances
∆ in survival caused by
underlying medical advances
Economic Value of
Additional Life
Years
∆ in survival
probability from the
new invention
X utility (in dollars)
of a year of life
X
∆ in survival probabilities
from underlying medical
progress
Economic Value of
Additional QALYs ∆ in survival
probability from the
new invention
X utility (in dollars)
of a year of life,
accounting for its
quality
X
∆ in survival probabilities
from underlying medical
progress
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Table 2. How to Calculate the Option Value of an Innovation
Valuation
Method
How the option value of innovation is calculated
Life
Expectancy
The expected life years value of a
new drug (=∆ in expected
lifetime its survival benefits
generate, taking into account
expected future medical advances)
-less-
The life expectancy
value of a new drug
(=∆ in static life
expectancy its survival
benefits generate)
Expected
QALYs
The increase in expected QALYs
due to a new drug (= ∑ increases
in the product of quality and
quantity of life, assuming that
levels of survival, health status,
and functioning improve with
medical technology in the future)
-less-
The increase in QALYs
due to a new drug
(= ∑ increases in the
product of quality and
quantity of life,
assuming current levels
of survival, health
status, and functioning)
Economic
Value of
Additional
Life Years
Willingness-to-pay calculated
incorporating expected changes in
future survival probabilities
-less-
Willingness-to-pay
calculated using a life-
expectancy-like
approach (assuming that
future survival
probabilities will be the
same as current ones)
Economic
Value of
Additional
QALYs Willingness-to-
pay calculated
incorporating expected changes in
future quality-
adjusted survival
probabilities
-less-
Willingness-to-pay
calculated using a
quality-adjusted life-
expectancy-like
approach (assuming that
future quality-adjusted
survival probabilities
will be the same as
current ones)
These methods are probably best understood through the use of a simple
example. Consider a disease which is fatal to all patients within three years of
diagnosis. Suppose that in 2010, a new drug is introduced to treat this disease. As
shown in Figure 1, the drug raises a patient’s chance of surviving the first year
after diagnosis from 50 percent to 70 percent, however—as of 2010—all patients
die by the second year from diagnosis. Then, in 2011, medical technology
improves such that patients have a 50 percent chance of surviving the second year
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(although all patients still die by the third year from diagnosis). This means that
part of the benefit of the drug in 2010 was allowing patients to live to see 2011’s
unrelated improvement in treatment of the disease. As Figure 1 shows, the
conventional method would calculate the drug’s value ignoring future technical
improvements, as in the decision tree on the left, while the true valuation should
incorporate those improvements, as in the decision tree on the right. This is the
option value of the drug, yet this value is missed by the conventional methods of
calculating its benefit.
Figure 1. Survival after Diagnosis with a Hypothetical Disease
To see this mathematically, consider the standard way of calculating life
expectancy for newly diagnosed patients with or without the drug. Referring to
Figure 1 (and assuming for simplicity no further technical progress between 2011
and 2012), we can calculate life expectancy from the time of diagnosis without
the drug as:
LE2010 without drug = 1st year expected survival using 2010 survival
probabilities without drug
+ 2nd year expected survival using 2010 survival
probabilities without drug
+ 3rd year expected survival using 2010 survival
probabilities without drug
= 0.5 + 0.5*0.0 + 0.5*0.0*0.0 = 0.50 years.
70%
30%
50%
50%
100%
100%
100%
50%
50%
30%
70%
2011
Diagnosis
Take drug
Survive
Die
Survive
Die
Die
Die
Diagnosis
Survive
Die
Survive
Die
Die
Survival Ignoring
Technical Progress
Survival Including
Technical Progress
Year:
2010
2012
2013
Don’t
take drug
Take drug
Don’t
take drug
Survive
Die
Survive
Die
Die
50%
50%
100%
50% 50%
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Similarly, we can calculate life expectancy from the time of diagnosis with the
drug as:
LE2010 with drug = 1st year expected survival using 2010 survival probabilities
with drug
+ 2nd year expected survival using 2010 survival
probabilities with drug
+ 3rd year expected survival using 2010 survival
probabilities with drug
= 0.7 + 0.7*0.0 + 0.7*0.0*0.0 = 0.70 years.
This calculation estimates the survival benefit of the drug as 0.2 years.
However, a more accurate measure of the drug’s benefit would take into
account the fact that it increases patients’ chances of living to see additional
future improvements in medical technology (i.e. the survival gain in the second
year from diagnosis in 2011). Thus, the “true” expected remaining lifetime
without the drug is:
EL2010 without drug = 1st year expected survival using 2010 survival
probabilities without drug
+ 2nd year expected survival using 2011 survival
probabilities without drug
+ 3rd year expected survival using 2012 survival
probabilities without drug
= 0.5 + 0.5*0.5 + 0.5*0.0*0.0 = 0.75 years.
Likewise, the “true” expected remaining lifetime with the drug is:
EL2010 with drug = 1st year expected survival using 2010 survival probabilities
with drug
+ 2nd year expected survival using 2011 survival probabilities
with drug
+ 3rd year expected survival using 2012 survival probabilities
with drug
= 0.7 + 0.7*0.5 + 0.7*0.5*0.0 = 1.05 years.
It follows that the “true” survival benefit of the drug—which incorporates its
option value—is 0.3 years, and the conventional method therefore understates its
benefit by 33 percent. This analysis could easily be extended to incorporate
QALYs or the economic value of QALYs or life-years.
In general, all the specific methods invoke a common theme. The option
value of an innovation is expressed as the survival benefits of the innovation
multiplied by the expected future improvements in medical technology.
Of course in practice these future improvements in medical technology are
not known in advance and must instead be forecast. Relevant technological
improvements could take many forms, ranging from treatments for erectile
dysfunction which improve quality of life to safer automobiles which lower all-
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cause mortality. Therefore, to estimate the option value of an innovation
prospectively, the key challenge would be to articulate which are the relevant
technological improvements to forecast. This would depend on the context of the
specific innovation; however, at a minimum, it should include survival forecasts
in the therapeutic area of the innovation and in all-cause mortality. Quality of life
improvements would also be relevant to forecast but would likely face greater
data limitations. Standard forecasting methods could then be applied to predict
future improvements in medical technology.
In any case, as long as medical technology continues to advance, an
innovation’s benefits incorporating these future advances will be greater than
under the conventional method which ignores them. Therefore, as a rule, any
innovation with survival benefits will also have a positive option value.
Finally, it is worth reflecting on which types of innovations we would
expect to have the greatest option value, which in turn could inform a patient’s
decision of which treatment to choose. Because the option value of a given
treatment is equal to its survival benefits multiplied by future improvements in
medical technology, a treatment with larger survival gains will necessarily have
greater option value. Treatments which offer only quality-of-life improvements
but no survival gains do not have option value. Therefore, incorporating option
value into the calculation of a treatment’s value will favor treatments offering
lower quality-of-life but greater survival gains over treatments offering higher
quality-of-life but smaller survival gains. This could help to explain why some
patients favor aggressive treatment of terminal disease rather than palliative care,
which offers greater quality-of-life.
Case Study: The Option Value of Tamoxifen
We illustrate the concept of the option value of innovation and its effect on the
innovation’s measured value using the example of the cancer drug tamoxifen.
The U.S. Food and Drug Administration (FDA) approved tamoxifen in 1977 as
treatment for metastatic breast cancer.
In October 1998, the FDA approved a new indication for reducing the
incidence of breast cancer in high-risk women. For women with risk factors
generating a twofold-or-greater relative risk, a five-year regimen of tamoxifen has
been shown to decrease the rate of estrogen receptor-positive (ER+) tumors over
ten years from 4.3% to 2.9%, relative to placebo (Cuzick, Forbes et al. 2007).
Tamoxifen therefore increased the life expectancy of women at high risk of breast
cancer.
These women further benefited from tamoxifen’s option value.
Specifically, for tamoxifen users who went on to develop breast cancer, onset was
sometimes delayed long enough for women to avail themselves of the option of
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more effective adjuvant treatment (described below). Onset was delayed because
annual incidence rates without tamoxifen were consistently higher than annual
incidence rates with tamoxifen (indeed, the ratio of the annual rates was roughly
constant over ten years) (Cuzick, Forbes et al. 2007).
After tamoxifen was approved for prevention in 1998, there was a marked
improvement in adjuvant treatment of breast cancer. Initially, the oncology drug
Taxol, approved by the FDA in December 1992, was a standard of care. Taxol
was shown to produce an overall survival gain when used as an adjuvant for
invasive breast cancer. Specifically, when used in conjunction with anthracycline
therapy, it led to an approximate 17 percent reduction in the overall mortality
hazard over 5 years, relative to anthracycline therapy alone (De Laurentiis,
Cancello et al. 2008). In November 2006, the FDA approved a new indication for
the drug Herceptin as an adjuvant treatment for invasive breast cancer, used in
combination with Taxol.4
Romond, Perez et al. 2005
When the two drugs are used together in conjunction
with anthracycline therapy, Herceptin provides roughly an additional 33 percent
reduction in the overall mortality hazard over three years, relative to Taxol and
anthracycline therapy without Herceptin, in women with Human Epidermal
growth factor 2-positive tumors ( ).
The availability of Herceptin for adjuvant treatment means that tamoxifen
has an option value as a preventive treatment. Some of the women whose
prophylaxis failed nevertheless experienced a delay in onset, and therefore lived
long enough to receive a better prognosis with Herceptin, in comparison to Taxol
plus anthracyclines alone. These women gained a substantial option value
through their use of tamoxifen.
To illustrate the concept of option value, we provide two measures of the
economic value of additional life years due to prophylactic tamoxifen. The
conventional approach measures the survival gains from tamoxifen from both
prevention, as well as delayed onset with treatment by Taxol plus anthracyclines.
This is done by comparing the expected life years under prophylactic tamoxifen
with the expected life years without tamoxifen. The option-value approach
considers that incidence may be delayed long enough for patients to use Herceptin
as an adjuvant treatment. Under this approach we compare the expected life years
under tamoxifen, adding adjuvant Herceptin for incident cases when it becomes
available, with the control of no prophylactic tamoxifen. The rate of successful
prevention with tamoxifen was unaffected by the availability of Herceptin. Thus,
to simplify the analysis, the measures of tamoxifen’s value include only the life
expectancy gains associated with delayed onset. We focus on cases of delayed
onset rather than prevention because these are the cases which illustrate
tamoxifen’s option value.
4 Herceptin was first approved for the treatment of metastatic breast cancer in October, 1998.
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Each approach is calculated in the lifetime expected utility framework
(with expected utility measured in dollars) (Becker, Philipson et al. 2005).5
Philipson, Becker et al. 2010
We
report the details of our approach in a technical appendix. Certain assumptions are
required in order to perform the calculations. First, we need to assume an income
(or alternatively, a willingness to pay for a change in expected survival of one
year). We follow the convention of not using different values for different
patients, and assume a value of $100,000 per year ( ).
We also need to assume a utility function in order to evaluate the utility of income
and health states. As is commonly done in the literature, we use a constant
relative risk aversion utility function, taking the parameters from the results of a
wide-ranging literature review, as reported in Becker, Philipson, and Soares
(Becker, Philipson et al. 2005). For the specific utility function, please see the
technical appendix.
Next, we need to determine how long onset was delayed when prevention
failed. Over ten years, annual incidence is nearly constant at 2.9 cases per
thousand with tamoxifen and 4.3 cases per thousand without it. Hence, incidence
with tamoxifen is 29 cases (per thousand) the full ten years. In the absence of
tamoxifen, we assume that these 29 cases would occur at a rate of 4.3 per year
over the first six years, with 3.2 cases in the seventh year (for a total of 29 cases
per thousand over ten years, with none of the incidence occurring late in years
eight through ten).
Finally, we need to know the survival functions from diagnosis until death
under each technology which is being evaluated (in this case, Taxol plus
anthracyclines and Taxol plus anthracyclines and Herceptin, as it becomes
available). Estimating the survival functions turns out to be the least
straightforward task, as the randomized controlled trials from which we take the
estimated survival benefits of the three treatments only tracked patients for a few
years (Romond, Perez et al. 2005; De Laurentiis, Cancello et al. 2008), whereas
we need to know survival probabilities from diagnosis until death. To do this, we
conservatively estimate that the survival benefits of Taxol alone, and of Taxol
plus Herceptin, disappear after 5 years from diagnosis (De Laurentiis, Cancello et
al.). We take the baseline probability of survival from diagnosis from the SEER
Cancer Statistics Review (Altekruse, Kosary et al. 2009). Estimating the survival
functions requires that we assume an age at diagnosis, which is complicated by
the fact that the randomized controlled trials typically do not report the age
distribution of all patients who participated in the trial. We assume an age at
diagnosis of 50, which is roughly the median age in Romond et al.(Romond,
Perez et al. 2005) The resulting survival functions can be seen in Figure 2.
5 Note that the utility function used is taken from economics and differs from the 0-to-1 quality of
life scale commonly used in health services.
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Figure 2. Probability of Survival for a Newly-Diagnosed 50-Year-Old Patient
with Breast Cancer
Once we have calculated the survival functions for the two adjuvant
treatment options, we can use the utility function to evaluate the value of the
survival gains owing to delayed onset with prophylactic tamoxifen. Table 3
expresses these values in terms of expected life years, while Table 4 presents the
economic value of the additional life years of tamoxifen by the conventional
approach, and under the option-value approach.
From the tables, we can see that including the option value of prophylactic
tamoxifen significantly changes the assessment of its value. In terms of life
expectancy, tamoxifen provides a benefit of 1.26 years from delayed onset with
treatment by Taxol. However, once we take into account that tamoxifen increases
a patient’s chances of using Herceptin through delayed onset, it becomes apparent
that the “true” benefit of tamoxifen is much larger. For a patient who initiated
tamoxifen in 1999, the “true” survival benefit is 1.57 years, or 24 percent higher
than would be conventionally assumed. For this calculation, the true life
expectancy without tamoxifen accounts for the benefit from Herceptin to those
who live long enough to use it. The true survival benefit of tamoxifen, including
its option value, diminished over time, reaching, for example, 1.38 years among
those who initiated in 2003. The reason is that there was less time before the
availability of Herceptin for tamoxifen to improve survival by delaying onset
relative to the control of no tamoxifen.
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Table 3. The Expected Years of Life of a 50 Year-Old Female at High Risk
of HER2+ Breast Cancer, Based on Delayed Onset from Use of Tamoxifen
Initiation
Year
No
Tamox-
ifen;
Taxol
(A)
Tamox-
ifen,
Then
Taxol
(B)
Tamox-
ifen,
Then
Taxol +
Hercep-
tin
(C)
No
Tamox-
ifen,
Then
Taxol +
Hercep-
tin
(D)
Conven-
tional
Benefit of
Tamoxifen,
Ignoring
Option-
Value
(B) - (A)
True
Benefit
of
Tamox-
ifen
(C) - (D)
1999
26.7 yrs
28.0 yrs
28.7 yrs
26.9 yrs
1.26 yrs
1.57 yrs
2000
26.7
28.0
28.8
27.1
1.26
1.53
2001
26.7
28.0
28.9
27.2
1.26
1.48
2002
26.7
28.0
29.0
27.4
1.26
1.42
2003
26.7
28.0
29.1
27.5
1.26
1.38
Table 4. The Value of Delayed Onset with Tamoxifen
Value (Willingness-to-Pay)
Initiation Year
Ignoring Option-
Value
True (Including Option-Value)
1999
$200,339
$247,913
2000
200,339
241,388
2001
200,339
232,133
2002
200,339
222,498
2003
200,339
213,833
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In terms of willingness-to-pay, the conventional value of tamoxifen is
$200,339. However, once we consider the option value of tamoxifen, the true
willingness-to-pay increases is as high as $247,913 among those who initiated in
1999.
In is important to note that this case study is just one example out of many
possibilities to illustrate the concept. We expect similar results for other
treatments in therapeutic areas of rapid advancement. Moreover, by highlighting
economic value and willingness to pay, this example focused on the patient
perspective. However, examples could also be constructed which would apply to
other stakeholders in the healthcare system, such as government and private
payers.
Conclusion
In this paper, we make an argument that cost effectiveness analysis should
consider option value. Part of the value of an existing therapy derives from the
fact that it may keep people alive long enough to gain access to future medical
innovations. We illustrate the concept of option value by calculating the
economic value of additional life years gained due to therapy with tamoxifen, a
breast cancer drug approved for breast cancer prevention in 1998. Treatment with
tamoxifen improved life expectancy by reducing the incidence of breast cancer in
some patients, and delaying onset in others. For the latter patients, tamoxifen
improved the chances of living to benefit from more effective adjuvant treatment
with Herceptin. Considering the option value of tamoxifen increases estimates of
its value by nearly a quarter for those who initiated in 1999. As this example
demonstrates, the option value of an innovation is particularly stark in the case of
life-threatening diseases or rapid technological progress. (In fact, these are the
cases when we expect option value to most contribute to a drug’s value.)
However, it is positive whenever any medical progress occurs. By making
forecasts of the survival benefits of future technologies, option value can be
incorporated into all the standard cost effectiveness analysis techniques.
Including option value in such analyses leads to an improved understanding of the
value of treatments with survival benefits.
Technical Appendix: The Details of the Tamoxifen Application
To assign a monetary value to the survival benefits of a treatment (such as
tamoxifen) relative to a control, we follow the methods of Philipson, Becker,
Goldman, and Murphy (Philipson, Becker et al. 2010), which are in turn based on
Becker, Philipson, and Soares (Becker, Philipson et al. 2005).
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Given an annual income of y and a survival function S (which gives the
probability of survival in each period), we denote an individual’s lifetime indirect
utility function V(S,y).
Suppose that under the control, survival is given by S, while under
treatment improves to survival function S’. We would like to calculate the
individual’s willingness-to-pay, denoted w, for the change in survival from S to
S’. By definition, w satisfies V(S,y) = V(S’,y-w).
We assume that the individual’s period utility function can be represented as
where c is the period consumption, α is a parameter which normalizes the
consumption value of death to zero, and γ is the inter-temporal elasticity of
substitution. Following Philipson, Becker, Goldman, and Murphy (Philipson,
Becker et al. 2010), we take y = $100,000, α = -14.97, γ = 1.25, and we set the
discount rate r = 0.03.
We can then express the lifetime indirect utility function as
V(S,y) = u(y)A(S),
where A(S) is the value of an annuity which pays one dollar in perpetuity under
survival curve S.
Under these assumptions, we can the calculate the annual willingness to pay for
the treatment as
The lifetime willingness to pay is the present value of the annual willingness to
pay over the lifetime: A(S)w.
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