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Introduction to decision analysis

Introduction to decision analysis. Jouni Tuomisto THL. Q R A. Decision analysis is done for purpose: to inform and thus improve action. Decisions by an individual vs. in a society.

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Introduction to decision analysis

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  1. Introduction to decision analysis Jouni Tuomisto THL

  2. Q R A Decision analysis is done for purpose: to inform and thus improve action

  3. 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: • 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.

  4. Probability of an event x Prize p Red Red ball 100 € • If you are indifferent between decisions 1 and 2, then your probability of x is p=R/N. Decision 1 White ball 0 € 1-p x happens 100 € Decision 2 0 € x does not happen

  5. Outcome measures in decision analysis

  6. Outcome measures in decision analysis • DALY: disability-adjusted life year • QALY: quality-adjusted life year • WTP: willingness to pay • Utility

  7. 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.

  8. DALYs in the world 2004 • Source: Wikipedia

  9. 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.

  10. Disability weights • http://en.opasnet.org/w/Disability_weights

  11. 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 Ye-0.04 Y • where W is weight and Y is age in years

  12. Discounting Wt = Wt+n (1+r)-n

  13. Age weighting with DALYsW = 0.1658 Ye-0.04 Y

  14. 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.

  15. QALY weight of disease x (standard gamble) Adjust u in such a way that you are indifferent between decisions 1 and 2. Then, your QALY weight is u(x). Utility Disease ? Live with disease Healthy u 1 Treatment 0 Dead 1-u

  16. 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.

  17. Measuring utilities Adjust u in such a way that you are indifferent between the two options. Then, your utility for option x is u(x). Utility Option ? Choose option x Best outcome u 1 Choose gamble 0 Worst outcome 1-u

  18. Utility of money is not linear

  19. CAFE clean air for Europe

  20. Value of statistical life VSL • Measure the willingness to accept slightly higher mortality risk. • E.g. a worker wants 50 € higher salary per month as a compensation for a work which has 0.005 chance of fatal injury in 10 years. • 50 €/mo*12 mo/a*10 a / 0.005 = 1200000 € / fatality • VSL is the marginal value of a small increment in risk. Of course, it does NOT imply that a person’s life is worth VSL. • A similar measure: VOLY = value of life year.

  21. The ultimate decision criterion: expected utility • Max(E(u(dj)))=Maxj (∑i u(dj,θi) p(θi) ) • Calculate the expected utility for each decision d option j. • Pick the one with highest expected utility.

  22. Which option is the best? Utility Swine flu 0.03 0.3 Healthy 1 Vaccination 0.003 Side effect 0 Swine flu 0.3 0.15 Do nothing 1 Healthy

  23. Which option is the best? u(Vaccination)=0.976 u(Do nothing)=0.895 Choose vaccination u; E(u) Swine flu 0.03 0.3;0.009 Healthy 1;0.967 Vaccination 0.003 Side effect 0;0 Swine flu 0.3;0.045 0.15 Do nothing 1;0.85 Healthy

  24. Limitations of decision trees A decision tree becomes quickly increasingly complex. This only contains two uncertain variables and max three outcomes of a variable. Swine flu 0.03 Complications Vaccination 0.003 Swine flu 0.15 Complications Do nothing Healthy

  25. Causal diagrams: a powerful tool for describing decision analysis models Swine flu Outcome Vaccination Complications

  26. Bayesian belief networks • Arrows are causal dependencies described by conditional probabilities. • P(swine flu | vaccination) • P(complications | swine flu) • P(outcome | swine flu, complicatons) • These probabilities describe the whole model.

  27. Functional models • Arrows are causal dependencies described by (deterministic) functions. • swine flu = f1(vaccination) • complications = f2(swine flu) • outcome = f3(swine flu, complicatons) • These functions describe the whole model.

  28. Functional vs. probabilistic dependency • Va1=2.54*Ch1^2 Va2=normal(2.54*Ch1^2,2)

  29. Estimating societal costs of health impacts • In theory, all costs should be estimated. • In practice, the main types considered include • Health case costs (medicine, treatment…). • Loss of productivity (absence from work, school). • WTP of the person to avoid the disease. • The societal cost of disease to other people (relatives etc) is NOT considered.

  30. St Petersburg paradox • Consider the following game of chance: you pay a fixed fee to enter and then a fair coin is tossed repeatedly until a tail appears, ending the game. The pot starts at 1 dollar and is doubled every time a head appears. You win whatever is in the pot after the game ends. Thus you win 1 dollar if a tail appears on the first toss, 2 dollars if a head appears on the first toss and a tail on the second, 4 dollars if a head appears on the first two tosses and a tail on the third, 8 dollars if a head appears on the first three tosses and a tail on the fourth, etc. In short, you win 2k−1 dollars if the coin is tossed k times until the first tail appears. • What would be a fair price to pay for entering the game? • Solved by Daniel Bernoulli, 1738

  31. St Petersburg paradox (2) • To answer this we need to consider what would be the average payout: With probability 1/2, you win 1 dollar; with probability 1/4 you win 2 dollars; with probability 1/8 you win 4 dollars etc. The expected value is thus

  32. Example of a model with causal diagram • Dampness and asthma

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