1. Estimating Outcomes in Decision Analysis Brian Harris MPP Candidate Goldman School of Public Policy University of California, Berkeley

2. Review—Last Lecture Formulate an explicit question Formulate an explicit question Make a decision tree Make a decision tree Estimate probabilities Estimate probabilities Estimate utilities Estimate utilities Compute expected utility of each branch Compute expected utility of each branch Perform sensitivity analysis Perform sensitivity analysis

3. Preview—Where We Are Going Recall Ms. Brooks and her aneurysm. We want to: Determine her utility: clip, and not clip Determine her utility: clip, and not clip Compare incremental utility and cost Compare incremental utility and cost Compare cost-per-unit of utility across private and public uses of funds. Compare cost-per-unit of utility across private and public uses of funds.

4. Overview – Today’s Lecture Outcomes Outcomes Measuring Utilities Measuring Utilities Quality Adjusted Life Years (QALYs) Quality Adjusted Life Years (QALYs) Discounting Discounting

5. Quantifying Health Outcomes Mortality Mortality Life Years Life Years number of expected years of life Significant Morbidity Significant Morbidity Paralysis, loss of sight Quality Adjusted Life Years Quality Adjusted Life Years Expected life years adjusted for the valuation of the possible states in each year Financial Valuation of these Outcomes Financial Valuation of these Outcomes Costs to patient, payor, or society Willingness to pay to avoid outcomes, obtain treatment

6. Health Outcomes – Mortality Mortality Mortality Death from disease/accident/procedure e.g. If Ms. Brooks undergoes surgery, one of the possible outcomes is mortality Life Years Life Years Calculate an expected value of life years using a probabilistically weighted average of expected life e.g. If Ms. Brooks does not undergo surgery, her life expectancy is less than if she did not have aneurysm, these outcomes are measured in expected life years

7. Health Outcomes – Morbidity Morbidity Morbidity Some health state that is less than perfect e.g. disability from stroke, chronic pain Comparison of morbidities Comparison of morbidities Difficult – apples and oranges problem e.g. which is worse: Blind v. Deaf Deaf v. Paraplegia Paraplegia v. Blind

8. Outcomes - Utility Utility is the currency of outcomes Utility is the currency of outcomes Scaled from 0 to 1 Scaled from 0 to 1 Commonly Death = 0 Commonly Death = 0 Perfect Health = 1 Perfect Health = 1 Sounds good, but how can this be measured? Sounds good, but how can this be measured?

9. Utility Measurement Utilities are commonly estimated using comparisons to the 0 and 1 anchors Utilities are commonly estimated using comparisons to the 0 and 1 anchors Methods are: Methods are: Visual Analog Scale Visual Analog Scale Standard Gamble Standard Gamble Time Trade-off Time Trade-off

10. Utility Measurement Clinical Scenario: Patient in the hospital has infection of the leg Patient in the hospital has infection of the leg Two options: BKA v. Medical Management Two options: BKA v. Medical Management BKA – below the knee amputation (1% mortality risk) BKA – below the knee amputation (1% mortality risk) Medical – 20% chance of infection worsening Medical – 20% chance of infection worsening If worse, AKA – above the knee amputation (10% If worse, AKA – above the knee amputation (10% mortality risk) mortality risk) How can we value these outcomes? How can we value these outcomes?

11. Utility Measurement Visual Analog Scale Linear Scale from 0 to 1 Linear Scale from 0 to 1 (death 0-----------------------------1.0 cure) Where is AKA? (death 0-----------------------------1.0 cure) Where is BKA?

12. Utility Measurement Visual Analog Scale Advantages: quantitative, easy to understand, visual Advantages: quantitative, easy to understand, visual Disadvantages: may bias values to the middle, seems Disadvantages: may bias values to the middle, seems disconnected from medical reality disconnected from medical reality

13. Utility Measurement--Standard Gamble Method relies on patients choosing between: 1) a certain outcome 1) a certain outcome 2) a gamble between a better outcome and a worse outcome 2) a gamble between a better outcome and a worse outcome How it works: Choice 1: You live with a BKA Choice 1: You live with a BKA Choice 2: The gamble – you might have a cure; you might die. Choice 2: The gamble – you might have a cure; you might die. Goal of method is to find the break-even point. What probability of death would you accept to avoid living with the BKA?

14. Utility Measurement – Standard Gamble

15. Standard gamble measurement involves questioning patients to determine the p at which the two outcomes are equivalent Standard gamble measurement involves questioning patients to determine the p at which the two outcomes are equivalent Using expected utilities, the value of p [p = P(cure)] gives the utility: Using expected utilities, the value of p [p = P(cure)] gives the utility: Utility (BKA) x Prob (BKA) = Utility (BKA) x Prob (BKA) = Utility(cure) x (p) + Utility(death) x (1-p) Utility(cure) x (p) + Utility(death) x (1-p) [Note that here, P(BKA) = 1.] [Note that here, P(BKA) = 1.] You can demonstrate that the utility of BKA = p: Utility (BKA) = [Utility(cure) x (p) + Utility(death) x (1-p)] = [1.0 * p + 0 * (1-p)] = p

16. Utility Measurement – Standard Gamble In utility estimation utilizing the standard gamble measurement, using the simple comparison described, the value of p, the probability of perfect health needed to make the patient indifferent between the two choices is the estimated utility of the outcome. In utility estimation utilizing the standard gamble measurement, using the simple comparison described, the value of p, the probability of perfect health needed to make the patient indifferent between the two choices is the estimated utility of the outcome. Advantages: the incorporation of risk into the model, comparison or choice between different outcomes. Advantages: the incorporation of risk into the model, comparison or choice between different outcomes. Disadvantages: possible nonrealistic choices patients may be asked to make, the difficulty of understanding the question (especially for non-gamblers), and the difficulty for some in understanding a math equation. Disadvantages: possible nonrealistic choices patients may be asked to make, the difficulty of understanding the question (especially for non-gamblers), and the difficulty for some in understanding a math equation.

17. Utility Measurement – Time Trade-off Time Trade-off involves patients choosing between: Time Trade-off involves patients choosing between: quality of life vs. length of time alive quality of life vs. length of time alive We want to determine when patients are equivocal between choice: Time A * Utility A = Time B * Utility B Time A * Utility A = Time B * Utility B e.g. -- If you have a life expectancy of 30 years with a BKA, how much time would you give up to live in your current state? time would you give up to live in your current state? Would you give up 5 years? 3 years? 1 year? 30 years * Utility (BKA) = (30-x) years * 1.0 30 years * Utility (BKA) = (30-x) years * 1.0 If you’re willing to give up 3 years, that means the utility of BKA is: If you’re willing to give up 3 years, that means the utility of BKA is: = [(30-3)*1/ 30] = 27/30 = 0.9 = [(30-3)*1/ 30] = 27/30 = 0.9

18. Utility Measurement – Time Trade-off Time trade off can be used to measure the utility of an outcome in the fashion described. Like standard gamble, patients need to understand subtlety of questions being asked. Time trade off can be used to measure the utility of an outcome in the fashion described. Like standard gamble, patients need to understand subtlety of questions being asked. Advantages: the simplicity of the choice between different outcomes, consideration of long-term outcomes. Advantages: the simplicity of the choice between different outcomes, consideration of long-term outcomes. Disadvantages: fails to incorporate risk, lack of clarity of when time traded occurs, different valuation of time during life, and the theoretical lack of realism of the choice. Disadvantages: fails to incorporate risk, lack of clarity of when time traded occurs, different valuation of time during life, and the theoretical lack of realism of the choice.

19. Utility Measurement – Health State Excluding Clinical Problem 0 to 1 utility scaling is simple and useful for determining the utility of different outcomes for a single patient. 0 to 1 utility scaling is simple and useful for determining the utility of different outcomes for a single patient. However, comparisons across patients or across programs raises the issue of ‘Is a utility of 1 really available?’ However, comparisons across patients or across programs raises the issue of ‘Is a utility of 1 really available?’ Consider: (a) polio vaccinations for children, and (b) hip replacement surgery for 85-year old patients. Consider: (a) polio vaccinations for children, and (b) hip replacement surgery for 85-year old patients. Typically (on average) the health state of a polio-free 5-year old will be very close to 1, whereas the health state of an 85- year old even with a perfectly functioning hip will typically be less than one. Typically (on average) the health state of a polio-free 5-year old will be very close to 1, whereas the health state of an 85- year old even with a perfectly functioning hip will typically be less than one.

20. Utility Measurement – Chaining The utility of the health state of the 85-year old can be determined by “chaining”. The utility of the health state of the 85-year old can be determined by “chaining”. Consider first the clinical situation under review: what is the utility, on a 0 to 1 scale, of a hip with reduced function and some pain? Let us say utility =.8. Consider first the clinical situation under review: what is the utility, on a 0 to 1 scale, of a hip with reduced function and some pain? Let us say utility =.8. Consider next the utility of an 85-year old with no hip problems, but some other reduced function or chronic pain. Here, perhaps overall utility =.9. Consider next the utility of an 85-year old with no hip problems, but some other reduced function or chronic pain. Here, perhaps overall utility =.9. Total utility for the bad-hip case =.8 *.9 =.72 Total utility for the bad-hip case =.8 *.9 =.72 Here, the perfect-hip case utility = 1 *.9 =.9 Here, the perfect-hip case utility = 1 *.9 =.9

21. Utility Measurement – Additional Information Multi-Attribute Health Status Classification System Multi-Attribute Health Status Classification System Developed by Health Utilities, Inc. Developed by Health Utilities, Inc. Available at: http://www.healthutilities.com/overview.htm Available at: http://www.healthutilities.com/overview.htm

22. Utilities in Decision Analysis Now that we have methods to estimate utilities, these can be used in the DA Now that we have methods to estimate utilities, these can be used in the DA However, our outcomes often include both mortality and morbidity However, our outcomes often include both mortality and morbidity Want a way to add in life expectancy Want a way to add in life expectancy Quality Adjusted Life-Years (QALYs) Quality Adjusted Life-Years (QALYs)

23. QALYs QALYs are generally considered the standard unit of comparison for outcomes QALYs are generally considered the standard unit of comparison for outcomes QALYs = time (years) x quality (utils) QALYs = time (years) x quality (utils) e.g. 30 years after BKA, util(BKA) = 0.9 e.g. 30 years after BKA, util(BKA) = 0.9 = 30 x 0.9 = 27 QALYs = 30 x 0.9 = 27 QALYs

24. QALYs

25. QALYs Aneurysm Example We said life expectancy is reduced by 2/3, so instead of 35, it is = 35 *.333 = 11.67 We said life expectancy is reduced by 2/3, so instead of 35, it is = 35 *.333 = 11.67 Here, we have assigned a utility of.5 to surgery- induced disability, so QALYs = Here, we have assigned a utility of.5 to surgery- induced disability, so QALYs = years * utils = 11.67 *.5 = 5.8 years * utils = 11.67 *.5 = 5.8

26. Outcomes - Discounting However, are all years considered equal? However, are all years considered equal? Consider: Favorite Meal Consider: Favorite Meal Extreme Pain Lifetime Income

27. Outcomes - Discounting Generally, present > future Generally, present > future One common way to value the different times is discounting One common way to value the different times is discounting Essentially this year is worth δ more than next year Essentially this year is worth δ more than next year δ is commonly set at 0.03 or 3% δ is commonly set at 0.03 or 3% In order to compare values of all future times, a calculation, net present value, is often used In order to compare values of all future times, a calculation, net present value, is often used NPV = 1 / (1 + δ) t Where t is number of years in the future NPV = 1 / (1 + δ) t Where t is number of years in the future

28. Outcomes - Discounting Aneurysm Example Aneurysm Example If utility is 0.5 and life expectancy is 3 years If utility is 0.5 and life expectancy is 3 years NPV would be:  Utility / (1 + δ) t NPV would be:  Utility / (1 + δ) t However, when is year 1? Often, since events in year one occur on average half way through, we use 0.5 for year 1 However, when is year 1? Often, since events in year one occur on average half way through, we use 0.5 for year 1 NPV = 0.5 / (1.03) 0.5 + 0.5 / (1.03) 1.5 + 0.5 / (1.03) 2.5 NPV = 0.5 / (1.03) 0.5 + 0.5 / (1.03) 1.5 + 0.5 / (1.03) 2.5 NPV = 0.5 * {(1.03) -0.5 + (1.03) -1.5 + (1.03) -2.5 } NPV = 0.5 * {(1.03) -0.5 + (1.03) -1.5 + (1.03) -2.5 }

29. Outcomes - Discounting

30. Another issue is partial years Another issue is partial years Can use similar adjustment: Can use similar adjustment: Exponent is half way through time period Exponent is half way through time period Numerator is multiplied by fraction of year Numerator is multiplied by fraction of year e.g. disability for 1.6 years, utility of 0.5 e.g. disability for 1.6 years, utility of 0.5 NPV =  Utility / (1 + δ) t NPV =  Utility / (1 + δ) t NPV = 0.5 / (1.03) 0.5 + 0.5*0.6 / (1.03) 1.3 NPV = 0.5 / (1.03) 0.5 + 0.5*0.6 / (1.03) 1.3

31. Discounting – Special Topic Issues with exponential discounting: Issues with exponential discounting: Relatively easy to manipulate Relatively easy to manipulate However, assumes same difference between any two time periods is the same value difference However, assumes same difference between any two time periods is the same value difference Consider: Consider: today vs. tomorrow and 10 yrs vs. 10 yrs + 1 day Essentially, “today” versus all other time periods is valued higher for many outcomes Essentially, “today” versus all other time periods is valued higher for many outcomes

32. Discounting – Special Topic Importance of discount rate chosen: Importance of discount rate chosen: Imagine a benefit of $1,000,000 to be received in 30 years Imagine a benefit of $1,000,000 to be received in 30 years Present value of this benefit at different discount rates: Present value of this benefit at different discount rates: 1% -- $741,923 3% -- $411,987 8% -- $99,377 17% -- $9,004

33. Overall Review Outcomes OutcomesMortalityMorbidity Measuring Utilities Measuring Utilities Visual Analog Standard Gamble Time Trade-off Quality Adjusted Life Years (QALYs) Quality Adjusted Life Years (QALYs) QALYs = time (years) x quality (utils) QALYs = time (years) x quality (utils) Discounting Discounting NPV =  Utility / (1 + δ) t