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 project  Axioms 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: $  So an admission into APR-DRG 1 with severity 2 (Craniotomy age >17 w cc) could be attributed a cost of: x = $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 independence Win $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) Axiom: Choice between y and y’ unaffected by addition of the same 3 rd lottery with same probability of obtaining that 3 rd lottery (say, p=0.9, x1=$5000, x2= - $1,000).

Is independence axiom reasonable? The Allais paradox Experiment 1Experiment 2 Gamble 1AGamble 1BGamble 2AGamble 2B WinningsChanceWinningsChanceWinningsChanceWinningsChance $1 million100% $1 million89%Nothing89% Nothing90% Nothing1% $1 million11% $5 million10%$5 million10% In each experiment, which gamble would you choose?

Is independence axiom reasonable? The Allais paradox Experiment 1Experiment 2 Gamble 1AGamble 1BGamble 2AGamble 2B WinningsChanceWinningsChanceWinningsChanceWinningsChance $1 million89%$1 million89%Nothing89%Nothing89% $1 million11% Nothing1% $1 million11% Nothing1% $5 million10%$5 million10% 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, x 100 = $890; E(y’) = 0.7 x 10, 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  19 th 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 method Question framing Certainty (values)Uncertainty (utilities) Scaling (choose a value on a scale) (Direct revealing of preference) 1 Rating scale (with numbers, categories, or a line on a page) 2 Choice (which option would you prefer?) (Indirect revealing of preference) 3 Time trade-off Paired comparison Equivalence Person trade-off 4 Standard 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 gamble Healthy Dead p 1-p Healthy State j p 1-p Alternative 1 Alternative 2 Alternative 1 Alternative 2 State i Above: Chronic health state preferred to death Below: Temporary health state