Lecture Notes Behavioral Decision Theory | QALY Model | EUR | 2025/26

Behavioral decision theory
Three dimensions of QALY study

• In effect, we study QALYs in three dimensions:

• Under risk

• Over time (discounting)

• At the societal level (equity)

Example of three dimensions




QALY model

Start with decision node, than moving on to chance node




Cost measured in monetary terms, but utility how do we this express?

- Common model  Quality-Adjusted Life-Years (QALYs)

- Additive model:

- Let (h1, …, hT) be a health profile

- QALY model: U ( h1 , … , hT ) =∑ Q(¿ ht )¿; sum of quality measure health
stage each period (compute for each health stage utility)

- Chronic health:U ( H ,T )=Q( H )×T ; chronic health stage, utility is
always the same x total numbers of period

, • Advantages

• intuitively appealing

• easy to use in practice

• Disadvantage

• may be too simple

Questions related to QALY model

• How restrictive is the QALY model?

• How can we determine the utilities Q(H )?

•


Utility fee; vx

Weakly preferred; right x>>Y

Assumptions to utility

• Health states are chronic

• Health states are preferred to death

• Expected utility holds

,Expected Utility

• EU ( ( H 1 ,T 1 ) , p ; ( H 2 , T 2 ) ) =¿ H2 is the other health state 1-p

pU ( H 1 , T 1 )+ ( 1− p ) U ( H 2 ,T 2)

• Two points of U can be chosen freely; cardinal utility measure (to
points on a scale; 0 and 1 death and alive)

Standard gamble e.g.

• ( Back pain , 30 y . ) ( ( Full h ealt h ,30 y . ) , p , Deat h ); when indifferent between
back pain and full health due to surgery but with probabily of death

• Risk of dying ¿ improve health state

• Apply Expected Utility:

• U ( Back pain , 30 y . ) =p∗U ( Full health ,30 y . ) + ( 1− p )∗U ( Death)

• Apply scaling:

• U ( Full health, 30 y . )=1

• U ( Death)=0

• U ( Back pain , 30 y . ) =p

• If p is high you don’t want to trade of a lot of risk

• What about the 30 years?

First characterisation linear QALY model

• Pliskin, Shepard & Weinstein (1980)

• 3 conditions; then the lineair model holds

• (mutual) utility independence; QOL should be independent
from life duration; doenst matter what the health state is, if
the health state is replaced should have the same prefrences

• Dont know how long they last always have the same
probability;

• (Back Pain, rest of life)  ((FH, rest of life), 2/3,
(Death, rest of life))

• Then also should have the same risk preferences
to be

• (Back Pain, 10y.)  ((FH, 10y.), 2/3, (Death, 10y.))

, • Vice versa

• (Back pain, 20y.)  ((Back pain, 40y.), 2/3, (Back
pain, 10y.))

• Then also

• (Full health, 20y.)  ((Full health, 40y.), 2/3, (Full
health, 10y.))

Intermediate result

• The following statements are equivalent

• Utility independence holds and

• U is either additive, U(H,T) = Q(H) + L(T), or multiplicative,
U(H,T) = Q(H) * L(T)

• To arrive at the QALY model we must

• (i) exclude the additive model and (ii) ensure linearity of L(T).

• ( Back pain , 30 y . ) ( ( Full health ,30 y . ) , p , Death )

• Apply Expected Utility:

• U ( Back pain , 30 y . ) =p∗U ( Full health ,30 y . ) + ( 1− p )∗U ( Death , 30 y .)

• Apply utility independence:

• Additive:Q ¿

• Multiplicative: Q ¿)¿ L(30 y .)¿

• Apply scaling:

• Q ( Fullhealth )=1

• Q( Death)=0

• Q ( Back pain )= p in both cases which is the usual result; hence we
don’t know which to use