Introduction to decision analysis
Jouni Tuomisto
THL
Decision analysis is done for purpose:
to inform and thus improve action
Q
R
A
Decisions by an individual vs. in a
society
• In theory, decision analysis is straightforward with a single
decision-maker: she just has to assess her subjective
probabilities and utilities and maximize expected utility.
• In practice, there are severe problems: assessing probabilities
and utilities is difficult.
• However, in a society things become even more complicated:
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–
–
–
There are several participants in decision-making.
There is disagreement about probabilities and utilities.
The decision models used are different.
The knowledge bases are different. NOTE! In this course,
"knowledge" means both scientific (what is?) and ethical (what
should be?) knowledge.
Probability of an event x
p
Decision 1
1-p
Red ball
White ball
Prize
100 €
0€
x happens 100 €
Decision 2
x does not
happen
0€
• If you are indifferent between decisions 1 and 2,
then your probability of x is p=R/N.
Outcome measures in decision analysis
Outcome measures in decision
analysis
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–
–
–
DALY: disability-adjusted life year
QALY: quality-adjusted life year
WTP: willingness to pay
Utility
Disability-adjusted life year
– The disability-adjusted life year (DALY) is a
measure of overall disease burden, expressed as
the number of years lost due to ill-health, disability
or early death. (Wikipedia)
– Originates from WHO to measure burden of disease
in several countries in the world.
DALYs in the world 2004
– Source: Wikipedia
How to calculate DALYs
– DALY= YLL+YLD
– YLL=Years of life lost
– YLD=Years lived with disability
– YLD = #cases*severity weight*duration of disase
– More DALYs is worse.
Weighting of DALYs
– Discounting
– present value Wt = Wt+n*(r+1)-n
– Where W is weight, r is discount rate, and n is
number of years into the future and t is current time
– Typically, r is something like 3 %/year.
– Age weighting
– W = 0.1658 Y e-0.04 Y
– where W is weight and Y is age in years
Discounting Wt = Wt+n (1+r)-n
Present value of a future outcome at different discount
rates
Net present value
1.2
1
0.8
0
0.01
0.03
0.05
0.6
0.4
0.2
0
0
20
40
Years into the future
60
Age weighting with DALYs
W = 0.1658 Y e-0.04 Y
Age weighting in DALY
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
20
40
60
Age (years)
80
100
Estimating QALY weights
• Time-trade-off (TTO): Choose between:
– remaining in a state of ill health for a period of time,
– being restored to perfect health but having a shorter life
expectancy.
• Standard gamble (SG):
– Choose between:
– remaining in a state of ill health for a period of time,
– a medical intervention which has a chance of either
restoring them to perfect health, or killing them.
• Visual analogue scale (VAS): Rate a state of ill health on
a scale from 0 to 100, with 0 representing death and 100
representing perfect health.
QALY weight of disease x (standard
gamble)
Utility
Disease
?
Healthy
1
Dead
0
Live with
disease
u
Treatment
1-u
• Adjust u in such a way that you are
indifferent between decisions 1 and 2.
• Then, your QALY weight is u(x).
Standard descriptions for QALYs
• E.g. as the EuroQol Group's EQ5D questionnaire
• Categorises health states according to the
following dimensions:
– mobility,
– self-care,
– usual activities (e.g. work, study, homework or
leisure activities),
– pain/discomfort
– anxiety/depression.