Teaching QALYs to Beginners and to Non-Beginners Allen C. Goodman Wayne State University iHEA/ECHE meetings Dublin Ireland July

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 Ed Harry 3

Harry and Ed What if we think that Harry and Ed should have the same QALYs? Draw 45 degree line Ed Harry What if we think that Harry and Ed should get the same inputs? 45 o Why? S H = S E  8 4

What’s the most cost-effective place? Thought experiment. Most cost effective place is where we get the highest mean score. Why? Ed Harry 45 o We can draw a line with a slope of –1. This line gives us places with equal totals. Start with S = S E + S H = 10. S E +S H =10 S E +S H =20 S E +S H = max Mean = (0+10)/2 = 5 Mean = (8+8)/2 = 8 Mean = (20+0)/2 = 10 Highest mean! 5

What do we want? Ed Harry 45 o S E +S H = max A B C D E Std. Dev. Mean. B' A' C' D' E' 6

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' L1L1 L2L2 L3L3 7

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' E3E3 E1E1 E2E2 8

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' E3E3 E1E1 E2E2 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  Q A = R A 0.6 Betty  Q B = 1.75R B 0.5 Charisse  Q c = 2.5R c 0.4 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 =

Equalize marginal products Exercise – We want to keep MP equal Slide line up and down, subject to where sum of inputs = 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 WorksheetWorksheet 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 WorksheetWorksheet Again, it’s fun to change parameters 15

Equal Output per Person? 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. 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