• Option 2: Survive for A years in health state H, followed by death.
• A is fixed, B is moved around to find indifference. When Alt 1 and Alt 2 are equally
preferred…
• A x U(Health State) + U(Death) = B x U(Perfect Health) + U(Death)
• A x H + 0 = B x 1 + 0 H = B/A
• If H is considered worse than death, there’s a slight modification:
• B x U(Health State) + (A – B) x U(Perfect Health) = U(Death)
• A is kept fixed, and B is moved around to find indifference.
• BH + (A – B) = 0 H = 1 – A/B
• TTO has similar assumptions to QALY, and can be vulnerable to time discounting effects.
• (Mixes time discounting with health state utility, just as SG mixes risk aversion/seeking.)
18
Chronic condition better than death
19
Valuation
TimeA
H
B
Full Health = 1
Death = 0
Area = B x 1 = B
Area = A x H = AH
If both choices are equally preferred, then
B = AH H = B/A
Option 1: B years of full health
Option 2: A years of state H
Chronic condition worse than death
20
Valuation
Time
A
H
B
Full Health = 1
Death = 0
Area = B x 1 = B
Area = (A – B) x H
New choices are needed:
Option 1: Death
Option 2: B years of full health,
followed by (A – B) years of state H.
(Sometimes the order is flipped)
If both choices are equally preferred…
B + (A – B) x H = 0
H = B/(B – A) < 0
As before, this is usually capped at -1.
Temporary Health State
21
Valuation
TimeA
H
B
S
Death = 0
Area = A x S
Area = (A – B) x 1
If both choices are equally preferred, then
B = AH H = B/A
As before, S is a
temporary state with
known utility.
Now we assume B periods of H are
followed by (A – B) of full health.
Full Health = 1
Area = B x H
If both choices are
equally preferred:
A – B + BH = AS
H = 1 – A/B x (1 – S)
Option 1: A years of S
Option 2: B years of H, and (A – B) years of full health
Multiattribute Approaches
• Multiattribute Utilities (MAU) allow us to approximate a calculation of
utilities for more complicated health states, in which more than one
attribute is important.
• These utilities, appropriately scaled, can be used as QALY weights.
• Each MAU consists of a health questionnaire, and a formula that maps
each possible combination of answers (health state) into an utility value.
• The mapping formula may, for example, use weights from SG or TTO
evaluations of key health states. Linear regression is used to find weights
for individual attributes.
• Why not use TTO/SG for all health states? Some are not plausible (e.g. no
trouble moving, confined to bed), while the number of possible states in
some MAU may be unwieldy.
• The EQ-5D, one of the most popular MAU, has 243 possible health states.
22
The EQ-5D (Required in UK, common elsewhere)
• Rates 5 Dimensions of Health: Mobility (MOB), Self-Care (CARE), Usual Activities
(ACT), Pain/Discomfort (PAIN) and Anxiety/Depression (DEP).
• Disutility of each can be rated is none/moderate/severe (1/2/3).
• 243 possible health states, written as 5-digit sets, e.g. (1,1,3,1,2)
• Each of the 10 possible non-’none’ answers (PAIN2,CARE3,MOB2, etc.) is assigned
a weight. (Weight for all ‘none’ answers is 0.)
• Weights for key health states (42 or 17 of 243) are obtained via TTO. Weights for
each answer are derived via linear regression.
• To obtain the total utility score for a health state, the weights for each answer are
added together and subtracted from 1 (perfect health).
• e.g. U(1,1,3,1,2) = Weight for ACT3 + Weight for DEP2
23
FYI: The ED-5D Equation (Richardson/McKie/Bariola)
• You do not need to memorize this formula.
• In the formula, a variable such as MOB2 is equal to 1 if the answer is
included in the health state, and 0 if it is not.
• ANY(A) = 1 if any answer =/= 1, 0 otherwise.
• ANY(B) = 1 if any answer = 3, 0 otherwise.
• Utility = 1 – [MOB + CARE + ACT + PAIN + DEP + ANY]
• Utility = 1 – [(.069MOB2 + .314MOB3) + (.104CARE2 + .214CARE3) +
(.036ACT2 + .094ACT3) + (.123PAIN2 + .386PAIN3) + (.071DEP2 +
.236DEP3) + (.081ANY(A) + .269ANY(B)]
24
PURPOSEFUL READING (3-2-1) REPORT Version 2.0
Lightly Adapted from a template by Geraldine Van Gyn.
Question 1: In your own words, what are the 3 most important concepts, ideas or issues in the
reading? Briefly explain why you chose them.
Concept 1 (In your own words) (2 marks)
Concept 2 (In your own words) (2 marks)
Concept 3 (In your own words) (2 marks)
Question 2: What are 2 concepts, ideas or issues in the article that you had difficulty
understanding, or that are missing but should have been included? In your own words, briefly
explain what you did to correct the situation (e.g. looked up an unfamiliar word or a missing
fact), and the result. Cite any sites or sources used in APA format.
Issue 1 (In your own words) (1 mark)
Citation 1 (in APA format) (1 mark)
Issue 2 (In your own words) (1 mark)
Citation 2 (in APA format) (1 mark)
Question 3: What is the main economic story of the reading? (Economics studies the allocation
of scarce resources.)
Story (In your own words) (2 marks)
1
ECON 317 SPRING 2020 – INDIVIDUAL ASSIGNMENT
4
TO BE SUBMITTED VIA COURSESPACES BY 11:59 PM ON FEBRUARY 11th, 2020
Name (First, Family)
Last 3 digits of Student ID#
TO SPEED UP MARKING, PLEASE ANSWER THE QUESTIONS IN THE FORMS AND SPACES
PROVIDED. THE T.A. RESERVES THE RIGHT TO NOT MARK ANY QUESTIONS THAT ARE NOT
ANSWERED IN THE EXPECTED LOCATIONS.
By submitting this assignment you agree to the following honor code, and understand that any
violation of the honor code may lead to penalties including but not limited to a non-negotiable
mark of zero on the assignment:
Honor Code: I guarantee that all the answers in this assignment are my own work. I have cited
any outside sources that I used to create these answers in correct APA style.
Marking scheme – Make sure you answer all the questions before handing this in!
Question Marks
1 a 1
2
2
a
3
b
3
c 3
3
a 3
b 3
c 3
4
a
2
b 2
c
4
Total 38
2
1. [Reading] Read the following article:
John, T. M., Millum, J. & Wasserman, D. (2017). How to Allocate Scarce Health Resources
Without Discriminating Against People with Disabilities. Economics and Philosophy, 33, 161-
186. Retrieved from https://doi-org.ezproxy.library.uvic.ca/10.1017/S0266267116000237
The choice of this article (as opposed to other candidates for this assignment’s reading) was
inspired by a current ECON 317 student who is interested in both philosophy and economics.
a. (12 marks) Write a 3-2-1 report using the form on the ECON 317 Coursespaces site.
2. [Standard Gamble] Answer the following calculation questions, putting your answer in the
spaces provided. Show your work (among other things, it allows us to give you part marks).
You will find Lecture 10 and the associated required readings very useful for this question.
a. (3 marks) You are using a standard gamble to evaluate the QALY weight of a health state H,
which is chronic and preferred to death. The respondent tells you they are indifferent between
the following two options:
Option 1: Spend the rest of their life in health state H.
Option 2: Take a pill that has a 43% chance of restoring them to perfect health for the rest of
their life, and a 57% chance of killing them instantly.
QALY weight for state H: __________
Work:
https://doi-org.ezproxy.library.uvic.ca/10.1017/S0266267116000237
3
b. (3 marks) You are using a standard gamble to evaluate the QALY weight of a health state H,
which is chronic and worse than death. The respondent tells you they are indifferent between
the following two options:
Option 1: Die instantly.
Option 2: Take a pill that has a 75% chance of restoring them to perfect health for the rest of
their life, and a 25% chance of leaving them in state H for the rest of their life.
QALY weight for state H: __________
Work:
c. (3 marks) You are using a standard gamble to evaluate the QALY weight of a health state H,
which is temporary and better than death. The respondent tells you they are indifferent
between the following two options:
Option 1: Spend the rest of the year in state H.
Option 2: Take a pill that has a 25% chance of restoring them to perfect health for the rest of the
year, and a 75% chance of leaving them in state S for the rest of the year. State S has a known
QALY weight of 0.24.
QALY weight for state H: __________
Work:
4
3. [Time Trade-Off] Answer the following calculation questions, putting your answer in the
spaces provided. Show your work (among other things, it allows us to give you part marks).
You will find Lecture 10 and the associated required readings very useful for this question.
a. (3 marks) You are using a time trade-off method to evaluate the QALY weight of a health state
H, which is chronic and preferred to death. The respondent tells you they are indifferent
between the following two options:
Option 1: Spend 17 years in perfect health, and then die.
Option 2: Spend 50 years in health state H, and then die.
QALY weight for state H: __________
Work:
b. (3 marks) You are using a time trade-off method to evaluate the QALY weight of a health state
H, which is chronic and worse than death. The respondent tells you they are indifferent between
the following two options:
Option 1: Die instantly.
Option 2: Spend 8 years in perfect health, then spend 2 years in health state H, then die.
QALY weight for state H: __________
Work:
5
c. (3 marks) You are using a time trade-off method to evaluate the QALY weight of a health state
H, which is temporary and better than death. The respondent tells you they are indifferent
between the following two options:
Option 1: Spend 8 years in state S, which has a known QALY weight of 0.43.
Option 2: Spend 4 years in health state H, then spend 4 years in perfect health.
QALY weight for state H: __________
Work:
4. [Discounting] Answer the following calculation questions, putting your answer in the spaces
provided. Show your work (among other things, it allows us to give you part marks).
You will find Lecture 11 very useful for this question.
a. (2 marks) It is currently year 0. The social discount rate is 5% per year. Calculate the present
value of 10 QALY received in Year 20. Give your answer to two decimal places (e.g. 3.33).
P = ____________________
Work:
6
b. (2 marks) It is currently year 0. The relevant discount rate is 2% per year. Calculate the year 10
value (future value) of $100 today. (Put another way: if you save $100 today, and your savings
account pays you 2% interest per year, how much money will you have ten years from now?)
Give your answer to the nearest cent (e.g. $3.33).
F = ___________________
Work:
c. (4 marks) It is currently 2020. A new treatment is being developed that is expected to provide
benefits equivalent to 1,000 QALY in 2030. Researching this treatment is expected to cost a total
of $1,000, $500 of which were paid five years ago (2015), and $500 of will have to be paid in
2025. Calculate the $/QALY of this treatment in present value terms. Discount QALY by 5 % a
year, and costs by 10 % a year. Give your answer to the nearest cent (e.g. 3.33 $/QALY).
(Hints: Find the present value of the costs, then find the present value of the QALY. Divide the
present value of the costs by the present value of the QALY. Note that if the present is 2020, then
2015 is in the past, and 2025 is in the future.)
$/QALY in present worth terms: ___________________
Work:
ECON
3
1
7
The Economics of Canadian Health Care
Lecture
11
: Health, Wealth and Time –
An Introduction to Discounting
January
2
9
th,
20
20
Version 1
Learning Objectives
• To understand the basic math behind time discounting.
• To be able to convert between present and future values, given an
interest (discount) rate.
• To understand some of the controversies and difficulties involved in
applying discounting to health care evaluation.
2
Required Reading
• Paulden, M. (201
4
). Time Preference and Discounting. In Encyclopedia of
Health Economics. Retrieved from https://doi-
org.ezproxy.library.uvic.ca/
10
.101
6
/B97
8
-0-
12
-37
5
678-7.00506-X
3
https://doi-org.ezproxy.library.uvic.ca/10.10
16
/B978-0-12-375678-7.00506-X
Optional Reading 1: Official Documents
• CADTH. (20
17
). Guidelines for the Economic Evaluation of Health Technologies:
Canada– 4th Edition. Retrieved from https://www.cadth.ca/dv/guidelines-
economic-evaluation-health-technologies-canada-4th-edition
• Section 7. Discounting, explains Canada’s guidelines for economic evaluation of
health technology.
• HM Treasury. (20
13
). The Green Book: appraisal and evaluation in central
government. London: TSO. Retrieved from
https://www.gov.uk/government/publications/the-green-book-appraisal-and-
evaluation-in-central-governent
• Annex 6, Discount Rate, explains the UK treasury’s guidelines for economic
evaluation of public projects. Includes a discussion of the Ramsey formula.
4
https://www.cadth.ca/dv/guidelines-economic-evaluation-health-technologies-canada-4th-edition
https://www.gov.uk/government/publications/the-green-book-appraisal-and-evaluation-in-central-governent
Optional Reading 2: Controversy and Impact
• Severens, J.L. & Milne, R. J. (2004). Discounting Health Outcomes in Economic Evaluation: The
Ongoing Debate. Value In Health, 7(4), 397-401. Retrieved from
http://onlinelibrary.wiley.com/doi/10.1111/j.
15
24-4733.2004.74002.x/abstract
• A very short, but very thorough, summary of the issues regarding discounting and health care.
• Westra, T. A. et al. (2012). On Discounting of Health Gains from Human Papillomavirus Vaccination:
Effects of Different Approaches. Value in Health, 15(3), 562-567.Retrieved from
http://dx.doi.org/10.1016/j.jval.2012.01.005
• Would you like to see exactly what happens when you apply different discount rates to a
preventive health intervention? This is the paper for you. Only lack of time kept this from being a
case study in the lecture.
• Boardman, A. E., Moore, M. A. & Vining, A. R. (2010). The Social Discount Rate for Canada Based on
Future Growth in Consumption. Canadian Public Policy, 36(3), 325-343. Retrieved from
http://www.jstor.org/stable/20799660
• A thorough discussion of the appropriate social discount rate for public projects in Canada. More
geared to monetary costs than health benefits, which is why it didn’t make it into the lecture.
5
http://onlinelibrary.wiley.com/doi/10.1111/j.1524-4733.2004.74002.x/abstract
http://dx.doi.org/10.1016/j.jval.2012.01.005
http://www.jstor.org/stable/20799660
A preview of Cost-Benefit/Effectiveness Analysis
• Economic Evaluations typically report QALY gained / $ spent.
• Problem: A QALY or $ today is not the same as a QALY or $ a century from now.
• $ Cost: Suppose the cost is $100. If it’s to be paid next year, we can put less than
$100 in an interest-bearing account and be able to afford it.
• QALY: Suppose someone is in chronic pain. Relief (QALY) gained today is more
valuable than the same relief ten years from now. For different reasons…
• …it’s also more valuable than the same QALY gain 300 years from now.
• Solution: Discount health gains and costs. BUT this is tricky and controversial.
• We’ll start with the easy bit: discounting monetary costs. After using this as an
introduction to how discounting works…
• …we’ll think a bit about the (unresolved) issue of discounting health benefits.
6
Future Value, F
• Consider a one-year time horizon, and assume that a health authority (HA)
can borrow and invest (e.g. in a savings account) at an interest rate i.
• The HA wants to buy a hospital bed for $P, today.
• Case A: It doesn’t have that $P, so it will have to borrow the money.
• If the HA borrows $P for one year, at an interest rate of i…
• At the end of one year it will have to pay P x (1 + i) dollars.
• We say that the future value, F, of P dollars today is P x (1 + i) dollars a year
from now.
• Case B: The health authority DOES have $P to spare. It can buy the bed
directly… BUT it could have invested the $P instead, in which case it would
have had $P x (1 + i) dollars one year from now, after the investment grew.
• Again, the future value, F, of P dollars today is the P x (1 + i) dollars a year
from now that the HA gives up
7
The basics of Present Value and Future Value
• We can also go the other way around:
• Given the HA and borrow and invest at an interest rate of I per year, the present
value, P, of F dollars one year from now is F/(1 + i).
• Why? Because to have F dollars one year from now, you need to save P dollars
today (the present).
• If you save F/(1 + i) dollars today, one year from now you’ll have (1 + i) times
that, which is F.
• When we only consider two time periods, today and one year from now,
• P = (1 + i) x F
• Given you can borrow and invest at an interest rate of i per year…
• The present value, P, is the amount you need to give up today to have F dollars
a year from now.
• The future value, F, is what you must give up one year from now to have P
dollars today.
8
Example: A one-year loan
• Suppose you can lend and borrow at 10% interest (i = 0.1)
• If you want an extra $10 today, you must pay $11 a year from now.
• The future value of $10 today is $11 a year from now.
• Suppose you want to buy something for $11 a year from now.
• You only need to lend $10 today, and you’ll be paid back $11 a year
from now. (Maybe you lend to a bank, by depositing the money…)
• The present value of $11 a year from now is the $10 you’ll have to set
aside today.
9
Compound interest
• What if the loan is for more than one year?
• Each period’s interest is added to the principal.
• Next period’s interest is calculated over the original amount and all
accumulated interest.
• F = P + i x P + i x (P + iP) + … = P x (1 + i) x (1 + i) x …
• ? = ?(? + ?)?
• Example: Suppose you borrow $100 at 10% for 2 years.
• F = $100 + 0.1 x $100 + 0.1 x ($100 + 0.1 x $100)
• F = $100(1 + 0.1)2 = $1
21
10
Application: Saving up
• You want to save up for a $100,000 MRI machine 10 years from now.
• You can lend (or save) money at 10% yearly interest.
• How much money do you need to put in the bank today?
• F = 100,000, i = 0.1, N = 10, P = to be determined
• F = P(1 + i)N ? = ?(? + ?)−?
• P = 100,000(1 + 0.1)−10 = $38,554.33
• Considerably less than $100,000!
11
Discounting Costs
• It’s common when talking about costs to put them in present value terms:
that is, to discount them. The rate i that is used is the discount rate.
• It’s also common to do this with benefits that can be put in dollar terms: if I
give you a hundred dollars today, that’s different than giving you a hundred
dollars ten years from now (even adjusting for inflation).
• There’s an opportunity cost to paying something today instead of paying it
later – you could have used those resources for something else, and you
have time to save up for a delayed cost. It makes sense to take that into
account when considering costs.
• Similarly, if you get something today instead of ten years from now, that’s
an extra ten years to do something with it – an opportunity ‘benefit’. If
we’re talking about a gift of money, then again it makes sense to take this
into account when valuing it.
12
What about discounting health?
• There is no consensus yet regarding discounting and health.
• Most countries/studies use a flat % for health benefits and monetary costs, but
that’s more pragmatic than soundly reasoned.
• A few basic, unanswered (but heavily studied) questions:
• Should we (society and individuals) discount health benefits at all?
• Should health benefits and monetary costs be discounted at the same rate?
• Should the rate of discount be constant over time?
• How should we calculate the discount rate(s) for policy use?
13
Why discount health benefits at all?
• Consumption Smoothing: If there is diminishing marginal utility to
health consumption, then individuals and social planners can
maximize (aggregate) utility by consuming more today and less
tomorrow. (Assumes consumption of health increases over time.)
• Risk of Catastrophe: The farther in the future a health benefit is, the
more likely it becomes that the individual (or society) won’t be
around to enjoy it.
• Pure Time Preference: Time and again, humans have been found to
have myopic preferences, and be impatient.
• Utilitarians (who believe individuals are the best judges of their own
welfare) would say this should be taken into account.
14
Some arguments against discounting health
• Catastrophic Risk is much less of an issue for most societies than for most
individuals, so a social planner should not emphasize it.
• Some view myopia as irrational, and a threat to social welfare…
• …particularly of future generations, who are harmed by excessive discounting.
• QALY measures both time and quality of life. Quality weights for QALY are often
obtained via Time Trade Off (TTO) and Standard Gamble (SG) experiments. Both of
these – especially TTO – include a time preference component.
• If health is measured in QALY, and the QALY are discounted using 1/(1+i)N, then they
will be double-discounted, understating health benefits.
• Discounting is especially harmful to preventive health care, where costs are
immediate and benefits are both uncertain and in the future. Discounting benefits
will favor, and may create/reinforce a bias toward, acute care.
15
What is it worth to live forever?
• There’s also the issue of how discounting interacts with ‘a QALY is a QALY’.
• Suppose you get a payment of $A a year, starting today, and the appropriate
discount rate is constant at i per year.
• The present value of this payment is A + A/i. (Math on the next slide.)
• Since QALY weight for perfect health is 1, this means that under discounting,
a human life is worth 1 + 1/i or less. If i=5%, then this maximum is 21 QALY.
• A treatment that gives 1 year of full life to 22 people, starting this year, is
preferred to a treatment that grants a full life of perfect health to a newborn
who will otherwise die immediately.
• The higher i is, the worse the situation becomes.
16
For those who want to see the math…
• Let Year 0 be the present, and the relevant discount rate be i per year.
• The present value of a payment A in year N is A/(1+i)N.
• If we receive a payment of A every year from Year 0 to year infinity, this is
a geometric series of the form A + Ar + Ar2 + … , where r = 1/(1+i).
• It’s well known that the sum of such a series is A/(1-r).
• 1-r = 1 – 1/(1+i) = ((1+i) – 1)/(1+i) = i/(1+i)
• 1/(1-r) = (1+i)/i = 1/i + 1 = 1 + 1/i
• So the sum of the series is A x (1 + 1/i) = A + A/i, q.e.d.
17
Should QALY and $ use the same discount rate?
• Suppose QALY are discounted by LESS than $ costs. Then QALY/$
(cost-effectiveness) will be higher the longer a social planner waits,
leading to eternal delay (or as close as bureaucracy will allow).
• To see this: consider an instant intervention that costs $1 and
provides 1 QALY. Suppose i is 0% for QALY and 100% for $costs.
• Cost-effectiveness: 1 QALY/$ if done today, 2 QALY/$ if done a year
from now, N QALY/$ if done N years from now.
• However, the possibility of double-discounting mentioned earlier is an
argument against uniform discounting (using the same rate for both).
18
Should the discount rate vary with time?
• Empirically, most humans appear to exhibit variable time preference.
• For events near us in time, we have fairly high discount rates.
• For events in the far future, we have lower discount rates.
• For example… Would you rather have $10 now or $15 next year?
• Would you rather have $10 20 years from now, or $15 in 21 years?
• (Most people answer ‘$10 now’ and ‘$15 in 21 years’.)
• A variable discount rate would match this empirical finding, and also make
interventions with long-term benefits (e.g. vaccination) more appealing.
• One possibility: 6% for 1 to 10 years in the future, 2% thereafter.
19
How should we calculate the discount rate?
• The UK Treasury uses the Ramsey rule to approximate a social discount rate:
i = μg + L + δ
• ? = elasticity of marginal utility of consumption (1 for the UK)
• ? = growth rate of real per capita consumption (2% for the UK)
• ?? as a whole accounts for diminishing marginal utility of consumption.
• L = risk of a catastrophic event (1% for the UK)
• ? = a measure of ‘pure’ time preference, or myopia (0.5% for the UK)
• i = social discount rate estimate (about 3.5% for the UK)
• (For full details, see Annex 6 of the ‘Green Book’.)
20
What about Canada? (CADTH, 2017)
• Canada assumes the real interest rate on government bonds is the opportunity
cost of government investment, and approximates the social discount rate.
• Since health is mostly a provincial matter, and federal bonds tend to move with
provincial bonds, the discount rate used is that on provincial government bonds.
• CADTH recommends that both costs and outcomes be discounted by the same
rate, while acknowledging “outcomes should be discounted using … interest on
provincial bonds, minus the growth rate of the cost-effectiveness threshold
(i.e., the estimated health expected to be forgone as a result of any new costs
that must be accommodated within a budget-constrained system)” (CADTH,
2017).
• (The cost-effectiveness threshold is, for example, the limit on how many $
society is willing to pay for an additional QALY.)
• Currently, the reference discount rate is 1.5% (real, per year).
21
