Teaching QALYs to Beginners and to Non-Beginners

Allen C. GoodmanWayne State University

iHEA/ECHE meetingsDublin Ireland

July 2014

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There is Lots of Content

• Quality of Life• Efficiency• Equity

2

Ed and Harry• At age 10, Harry and Ed

both have certain levels of health, 10 each.

• Assume that Ed (easy) can 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 Harry.

10

10

30

20

Ed

Harry 3

Harry and Ed

• What if we think that Harry and Ed should have the same QALYs? Draw 45 degree line.

10

10

30

20

Ed

Harry

• What if we think that Harry and Ed should get the same inputs?

45o

• Why?

SH = SE 8

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What’s the most cost-effective place?

• Thought experiment. Most cost effective place is where we get the highest mean score. Why?

10

10

30

20

Ed

Harry

45o

• We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = SE + SH = 10.

SE+SH=10

SE+SH=20

SE+SH= max

Mean = (0+10)/2 = 5

Mean = (8+8)/2 = 8

Mean = (20+0)/2 = 10

Highest mean!

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What do we want?

10

10

30

20

Ed

Harry

45o

SE+SH= max

A

B

C

DE

Std. Dev.

Mean.

B'

A'

C'

D'E'

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What do we want?

Std. Dev.

Mean.

B'

A'

• Utility Functions• Leveler – Will only accept

lower mean along with lower SD.

• Why?

• Utility Functions– Elitist – Will accept lower

mean with higher SD.– Why?

C'E'

D'

L1

L2

L3

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What do we want?

Std. Dev.

Mean.

B'

A'

• Utility Functions• Leveler – Will only accept

lower mean along with lower SD.

• Why?

• Utility Functions– Elitist – Will accept lower

mean with higher SD.– Why?

C'

D'

E3

E1

E2

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What do we want?

Std. Dev.

Mean.

B'

A'

• 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.

C'

D'

E3

E1

E2

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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.

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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.

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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 Mpa MPb MPc0

10 0.2389 0.2767 0.251220 0.1810 0.1957 0.165725 0.1656 0.1750 0.145030 0.1539 0.1598 0.1299

33.3333333 0.1476 0.1516 0.122035 0.1447 0.1479 0.118540 0.1372 0.1383 0.109345 0.1309 0.1304 0.101950 0.1255 0.1237 0.095660 0.1167 0.1130 0.085770 0.1097 0.1046 0.078280 0.1040 0.0978 0.072190 0.0992 0.0922 0.0672100 0.0951 0.0875 0.0631

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Marginal Product v. Input

0.000.010.020.030.040.050.060.070.080.090.100.110.120.130.140.150.160.170.180.190.200.210.220.230.240.250.260.270.280.290.30

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

Input

MP

Mpa

MPb

MPc• Equalize marginal

products• Exercise – We want to

keep MP equal• Slide line up and down,

subject to where sum of inputs = 100.

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Or …Equal inputs

Equal MPs

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

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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

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Equal Output per Person?Total QALYs v. Input

0

2

4

6

8

10

12

14

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0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105

Input

QA

LY

s

Qa

Qb

Qc

Equal inputs

Equal Outputs

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.

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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.

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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.

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