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## Expected Value Theory

*Aka: Expected Value Theory, Expected Utility Theory, Expectancy Value Theory, Time Trade Off, Standard Gamble, Visual Analogue*

- See Also
- Definition
- Expected Value Theory
- Choose an option with the highest expected value (based on the probability of that value occurring)
- This highest value option is independent of individual discretion (the calculation is the same for all people)
- The expected value calculation often runs counter to the decision maker's intuition

- Expected Utility Theory
- Options are assigned an amount of satisfaction (or utility) an individual would experience for each option
- Accounts for risk aversion, personal preference and situational circumstances (beyond expected value based decision)

- Expected Value Theory
- Evaluation: Assigning value to outcomes
- Standard Gamble
- State of current illness for T time versus therapy with known risk of cure or death

- Time Trade Off (TTO)
- State of current illness for T1 time versus Perfect health for T2 time
- Patient imagines living 10 years in their current state of health
- How many years of perfect health (T2) are worth the same as living 10 years (T1) in your current health state?

- Visual Analogue
- Rate health states beween death (0) and perfect health (100)

- Standard Gamble
- Example: Expected Value
- Possible outcomes for theoretical cancer treatment
- Chemotherapy agent A
- Odds: 50% chance of 10 year survival
- Expected Value (EV): 5 years

- Chemotherapy agent B
- Odds: 90% chance of 2 year survival
- Value Value (EV): 1.8 years

- Chemotherapy agent A
- Interpretation
- Expected value of choosing Chemotherapy agent A (5 years) is significantly more than agent B (1.8 years)

- Possible outcomes for theoretical cancer treatment
- Example: Expected Utility
- Possible outcomes for theoretical cancer management
- No treatment
- Odds: 50% chance of 10 year survival in current state of health
- Expected value (EV) = 5 years
- Time Trade Off (TTO) = 0.3
- Patient assigns 3 years of perfect health equivalent to 10 years in current state of health

- Quality Adjusted Life Year (QALY) = TTO x EV = 0.3 x 5 = 1.5 years

- Chemotherapy agent B
- Odds: 90% chance of 2 year survival in perfect health
- Expected Value (EV): 1.8 years

- No treatment
- Interpretation
- Expected utility of Chemotherapy with agent B (1.8 years perfect health) exceeds the QALY (1.5 years) of status quo

- Possible outcomes for theoretical cancer management
- Resources
- Expectancy Value Theory (Wikipedia)

- References
- Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course