Teaching QALYs to Beginners and
to Non-Beginners
Allen C. Goodman
Wayne State University
iHEA/ECHE meetings
Dublin Ireland
July 2014
1
There is Lots of Content
• Quality of Life
• Efficiency
• Equity
2
Ed and Harry
• At age 10, Harry and Ed
30
both have certain levels of
health, 10 each.
• Assume that Ed (easy) can
Ed
gain health at a lower
incremental cost than Harry
(hard). Hence, a given level
of expenditures will give Ed
20 incremental points but
would give Harry only 10.
• Suppose half of the people
are like Ed and half are like
10
Harry.
10
20
Harry
3
Harry and Ed
30
• What if we think that
Harry and Ed should
have the same QALYs?
Draw 45 degree line.
45o
Ed
SH = S E  8
• What if we think that
Harry and Ed should
get the same inputs?
10
• Why?
10
20
Harry
4
What’s the most cost-effective place?
Highest mean!
30
Mean = (20+0)/2 = 10
• Thought experiment.
Most cost effective
place is where we get
the highest mean score.
Why?
• We can draw a line
with a slope of –1.
This line gives us
places with equal
totals. Start with S = SE
+ SH = 10.
45o
SE+SH= max
Ed
SE+SH=20
Mean = (8+8)/2 = 8
SE+SH=10
10
Mean = (0+10)/2 = 5
10
20
Harry
5
What do we want?
E
Mean.
30
D
SE+SH= max
45o
D'
Ed
C'
C
B
E'
B'
A'
A
10
10
20
Harry
Std. Dev.
6
What do we want?
• Utility Functions
• Leveler – Will only accept
lower mean along with
lower SD.
• Why?
L3
L2
Mean.
L1
D'
C'
E'
B'
A'
• Utility Functions
– Elitist – Will accept lower
mean with higher SD.
– Why?
Std. Dev.
7
What do we want?
• Utility Functions
• Leveler – Will only accept
lower mean along with
lower SD.
• Why?
Mean.
E3
D'
C'
E2
B'
A'
• Utility Functions
E1
– Elitist – Will accept lower
mean with higher SD.
– Why?
Std. Dev.
8
What do we want?
• So, it’s not altogether clear
that we always want to
raise the mean.
• The levelers here, want to
push up the lower end,
and this lowers the SD.
• Means fewer special
programs.
Mean.
E3
D'
C'
E2
B'
A'
E1
Std. Dev.
9
Let’s Think more About Calculations
• We don’t live in a 2-person world.
• We don’t live in a world where everyone has linear or
logarithmic functions.
• Most of these are not analytically tractable.
10
Let’s look at 3 people
• Alex  QA = RA0.6
• Betty  QB = 1.75RB0.5
• Charisse Qc = 2.5Rc0.4
• Total Resources = 100
• We want the most cost effective place. Maximize total
output.
11
Cost-Effectiveness?
• Equalize marginal
products
• Exercise – We want to
keep MP equal
• Slide line up and down,
subject to where sum of
inputs = 100.
Resources
0
10
20
25
30
33.3333333
35
40
45
50
60
70
80
90
100
Mpa
0.2389
0.1810
0.1656
0.1539
0.1476
0.1447
0.1372
0.1309
0.1255
0.1167
0.1097
0.1040
0.0992
0.0951
MPb
0.2767
0.1957
0.1750
0.1598
0.1516
0.1479
0.1383
0.1304
0.1237
0.1130
0.1046
0.0978
0.0922
0.0875
MPc
0.2512
0.1657
0.1450
0.1299
0.1220
0.1185
0.1093
0.1019
0.0956
0.0857
0.0782
0.0721
0.0672
0.0631
12
Or …
MP
• Equalize marginal
products
• Exercise – We want to
keep MP equal
• Slide line up and down,
subject to where sum of
inputs = 100.
Marginal Product v. Input
Equal inputs
0.30
0.29
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.20
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
Mpa
MPb
MPc
Equal MPs
0
5
10 15 20 25
30 35 40
45 50 55 60
65 70 75
80 85 90 95 100 105
Input
13
For more advanced students, we can
calculate
• What are the steps?
• Use an initial allocation – 1/3 each will work
• Compare MP
• Take resources from the lower MP to the higher MP
• Look at Worksheet
• It’s fun to change parameters
14
What if we want equal output?
• What are the steps?
• Use an initial allocation – 1/3 each will work
• Compare Outputs
• Take resources from the higher output to the lower output
• Look at Worksheet
• Again, it’s fun to change parameters
15
Equal Output per Person?
Total QALYs v. Input
20
Equal inputs
18
16
QALYs
14
Equal Outputs
12
10
8
Qa
6
Qb
4
Qc
2
0
0
5
10
15
20
25
30
35
40
45
50
55
Input
60
65
70
75
80
85
90
95 100 105
Things to Look For
• You can also maximize utility. It’s easy to program, but too much to
do right here, right now.
• Cost-effective does NOT mean everyone gets same amount.
• Everyone getting same amount does not maximize output OR utility.
17
Extensions
• EXCEL has a “Solver” function.
• It will take motivated students a couple of hours to get
comfortable with it.
• It works fine, but it takes away the “fun” or learning.
• Still, after they’ve figured out the principles, there’s nothing
wrong with using it.
18
Take Away
• We often set up first order conditions but do not solve
because a lot of seemingly simple problems are not
analytically tractable, especially when N > 2.
• We preach about marginal conditions, but don’t really show
students how to solve.
• We talk about Equity v. Efficiency, but again, we don’t give
good examples.
• Everyone has EXCEL – let’s use it.
19