Economic evaluation of health programmes

Department of Epidemiology, Biostatistics and Occupational Health

Class no. 9: Cost-utility analysis – Part 2

Oct 1, 2008

Plan of class

More on using DRGs to cost hospital services in Québec

Discussion of topic for term projectAxioms of expected utility theory Methods for eliciting values or utilities

associated with health states

More on using DRGs in Québec to cost hospital days

Each hospitalisation has a NIRRU (Niveau d’Intentité Relative des Ressources Utilisées) which is a weight indicating the expected resource utilization for that DRG and level of gravity (for entire episode) Usually, secondary diagnoses add to the level

of gravity, which add to the NIRRU

Sample DRGs of various gravity levels and associated NIRRUS (Resource Intensity Weights)

DMS: Average length of stay

Example calculation

Admissions for physical health conditions: Average provincial cost in 2005 – 06 for a NIRRU of 1: $ 4 113

So an admission into APR-DRG 1 with severity 2 (Craniotomy age >17 w cc) could be attributed a cost of: 3.2688 x 4 113 = $13,445

Does not include: physician fees; opportunity cost of land and buildings

Other notes

Only the AQESSS calculates a cost per NIRRU in this way, for its clients

The MSSS excludes costs of : (1) administration and « hôtellerie » (e.g., food); and (2) buildings, maintenance. These overhead costs account for about 25% of the total

Hence in practice this system is not easy to use! Rely on goodwill of AQESSS staff!

John von Neumann and Oscar Morgenstern

John von Neumann

1944: Theory of games and economic behavior.

This book included a theory of rational decision-making under uncertainty: a normative model (i.e. a model of how people should behave, if they are to act rationally) of behavior under uncertainty.

Their approach involves assigning utility to lotteries (risky prospects).

Axioms of von Neumann- Morgenstern utility theory (1)

Win $1,000

Lose $100

p=0.9

p=0.1

Win $10,000

Lose $1000

p=0.7

p=0.3

Axiom 1: (a) Preferences exist and (b) are transitive.Pair of risky prospects y and y’:

Preferences exist: A person either prefers y to y’, or y’ to y, or is indifferent between y and y’. (Which would you prefer? Why?)They are transitive: If 3 risky prospects y, y’ and y’’, if y>y’ and y’>y’’, then y>y”

Axioms of von-Neumann Morgenstern utility theory (2)

Axiom 2: Independence: Combining each of the 2 previous lotteries with an additional lottery r in the same way should not affect your choice between the 2 lotteries

Axiom of independenceWin $1,000

Lose $100

p=0.9

p=0.1

Win $10,000

Lose $100

p=0.7

p=0.3

p=0.6

p=0.4

p=0.6

p=0.4

3rd lottery r (p, x1, x2)

3rd lottery r (p, x1, x2)

Axiom: Choice between y and y’ unaffected by addition of the same 3rd lottery with same probability of obtaining that 3rd lottery (say, p=0.9, x1=$5000, x2= - $1,000).

Is independence axiom reasonable? The Allais paradox

Experiment 1 Experiment 2

Gamble 1A Gamble 1B Gamble 2A Gamble 2B

Winnings Chance Winnings Chance Winnings Chance Winnings Chance

$1 million 100%

$1 million 89% Nothing 89%

Nothing 90%

Nothing 1%

$1 million 11%

$5 million 10% $5 million 10%

In each experiment, which gamble would you choose?

Is independence axiom reasonable? The Allais paradox

Experiment 1 Experiment 2

Gamble 1A Gamble 1B Gamble 2A Gamble 2B

Winnings Chance Winnings Chance Winnings Chance Winnings Chance

$1 million 89% $1 million 89% Nothing 89% Nothing 89%

$1 million 11%

Nothing 1%

$1 million 11%

Nothing 1%

$5 million 10% $5 million 10%

As the alternative lottery with certain outcome promises more and more (from 0 to 1 million) we are more and more inclined to choose the certain outcome. This can be viewed as rational.

Expected value of a gamble

Win $1,000

Lose $100

p=0.9

p=0.1

Win $10,000

Lose $1000

p=0.7

p=0.3

Pair of risky prospects y and y’:

In this example, E(y) = 0.9 x 1,000 -0.1 x 100 = $890; E(y’) = 0.7 x 10,000 -0.3 x 1000 = $6,700.

Utility, value and preference

Utility (NM utility): In NM jargon, a cardinal measure of preference attached to a lottery/gamble/risky or uncertain prospect

Value: Value attached to a certain outcome

Preference: generic term relevant to both NM utility and value, in the senses above

Utility, utility and utility

19th century economics: a cardinal measure of satisfaction derived from a good or bundle of goods

Modern economics: an ordinal measure of satisfaction derived from a good or bundle of goods (cardinality now thought both unrealistic and unnecessary)

Both different from NM utility defined on previous slide

Methods of measuring preferences

Response methodQuestion framing

Certainty (values) Uncertainty (utilities)

Scaling (choose a value on a scale)(Direct revealing of preference)

1Rating scale (with numbers, categories, or a line on a page)

2

Choice (which option would you prefer?)(Indirect revealing of preference)

3Time trade-offPaired comparisonEquivalencePerson trade-off

4Standard gamble

Rating scale

Rank health outcomes from most preferred to least preferred

Place outcomes on a scale: Without numbers On a line (visual analogue scale) With numbers, e.g., 0 to 100 (rating scale)

• If on a line, we get the ‘feeling thermometer’

With categories, e.g., 0 to 10

Rating scales and risk preference

Rating scales ignore the uncertainty associated with the decision to undergo a treatment

In fact people are often risk averse, sometimes risk loving

Standard gamble, which uses Axiom 2 of expected utility theory, incorporates respondents’ attitude toward risk

Time trade-off

State i for time t, then death

Healthy for time x < t, then death

Alternative 2

Alternative 1

Vary x until respondent is indifferent between the alternatives

Standard gambleHealthy

Dead

p

1-p

Healthy

State j

p

1-p

Alternative 1

Alternative 2

Alternative 1

Alternative 2

State i

State i

Above: Chronic health state preferred to death

Below: Temporary health state