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## Expected Value Theory

Aka: Expected Value Theory, Expected Utility Theory, Expectancy Value Theory, Time Trade Off, Standard Gamble, Visual Analogue
2. Definition
1. Expected Value Theory
1. Choose an option with the highest expected value (based on the probability of that value occurring)
2. This highest value option is independent of individual discretion (the calculation is the same for all people)
3. The expected value calculation often runs counter to the decision maker's intuition
2. Expected Utility Theory
1. Options are assigned an amount of satisfaction (or utility) an individual would experience for each option
2. Accounts for risk aversion, personal preference and situational circumstances (beyond expected value based decision)
3. Evaluation: Assigning value to outcomes
1. Standard Gamble
1. State of current illness for T time versus therapy with known risk of cure or death
1. State of current illness for T1 time versus Perfect health for T2 time
2. Patient imagines living 10 years in their current state of health
1. How many years of perfect health (T2) are worth the same as living 10 years (T1) in your current health state?
3. Visual Analogue
1. Rate health states beween death (0) and perfect health (100)
4. Example: Expected Value
1. Possible outcomes for theoretical cancer treatment
1. Chemotherapy agent A
1. Odds: 50% chance of 10 year survival
2. Expected Value (EV): 5 years
2. Chemotherapy agent B
1. Odds: 90% chance of 2 year survival
2. Value Value (EV): 1.8 years
2. Interpretation
1. Expected value of choosing Chemotherapy agent A (5 years) is significantly more than agent B (1.8 years)
5. Example: Expected Utility
1. Possible outcomes for theoretical cancer management
1. No treatment
1. Odds: 50% chance of 10 year survival in current state of health
2. Expected value (EV) = 5 years
3. Time Trade Off (TTO) = 0.3
1. Patient assigns 3 years of perfect health equivalent to 10 years in current state of health
4. Quality Adjusted Life Year (QALY) = TTO x EV = 0.3 x 5 = 1.5 years
2. Chemotherapy agent B
1. Odds: 90% chance of 2 year survival in perfect health
2. Expected Value (EV): 1.8 years
2. Interpretation
1. Expected utility of Chemotherapy with agent B (1.8 years perfect health) exceeds the QALY (1.5 years) of status quo
6. Resources
1. Expectancy Value Theory (Wikipedia)
1. https://en.wikipedia.org/wiki/Expectancy-value_theory
7. References
1. Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course

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