Stephen T. Parente, Ph.D. Carlson School of Management, Department of Finance

1. University of MinnesotaMedical Technology Evaluation and Market Research Course: MILI/PUBH 6589Spring Semester, 2012 Stephen T. Parente, Ph.D. Carlson School of Management, Department of Finance

2. Lecture Overview • Statistical Uncertainty • Baye’s Rule • Practice Exercise • Markov Modeling • Group Project work

3. Statistical Uncertainty • Model Uncertainty • How do you know if the CE analysis you have purchased are using the right model? • Tough one! • In the Monte Carlo analysis, do any of the draws give crazy results?

4. Statistical Uncertainty: Example Model 1 Model 2

5. Randomness in health & cost outcomes • Like uncertainty over parameter estimates, there may be uncertainty over outcomes and costs. • Can use information on distribution of outcome and costs from clinical trial data or other datasets • How might you do this? What is the goal? • Use Monte Carlo methods here • Markov Models

6. Randomness in health & cost outcomes: Example

7. Bayes’ Rule • How should one rationally incorporate new information into their beliefs? • For example, suppose one gets a positive test result (where the test is imperfect), what is the probability that one has the condition? • Answer: Bayes’ Rule! • Particularly useful for the analysis of screening but it applies more broadly to the incorporation of new information

8. Bayes’s Rule • Bayes rule answers the question: what is the probability of event A occurring given information B • You need to know several probabilities • Probability of event given new info = F(prob of the event, prob of new info occurring and the prob. of the new info given the event)

9. Bayes’s Rule • Notation: • P(A) = Probability of event A (unconditional) • P(B) = Probability of information B occurring • P(B|A) = Probability of B occurring if A • P(A|B) = Probability of A occurring given information B (this is the object we are interested in • Bayes’s Rule is then:

10. Baye’s Rule Example • Cancer Screening • Probability of having cancer = .01 • Probability that test is positive if you have cancer = .9 • Probability of false positive = .05 • Use Baye’s rule to determine the probability of having cancer if test is positive

11. Baye’s Rule Another Formulation • There is another way to express the probability of the condition using Bayes’s Rule: • Sensitivity is the probability that a test is positive for those with the disease • Specificity of the test is the probability that the test will be negative for those without the disease

12. Markov Modeling • Methodology for modeling uncertain, future events in CE analysis. • Allows the modeling of changes in the progression of disease overtime by assigning subjects to differ health states. • The probability of being in one state is a function of the state you were in last period. • Results are usually calculated using Monte Carlo methods.

13. No occurrence No occurrence Local occurrence Local occurrence Treatment Treatment $ Metastasis Metastasis Treatment $$ Treatment Death Death Markov Modeling Example • Three initial treatments for cancer—chemo, surgery and surgery+chemo. • What is the CE of each treatment? Year 1 Year 2 P(1) Surgery $ P(2) P(3) P(4)

14. Markov Modeling Example

15. Markov Modeling Example w/ Discounting—r = .03

16. Practice Exercise • Use Baye’s rule to determine the probability that given a positive test for Lung Cancer. • Find the prevalence of lung cancer from the web • Suppose that the probability of a false positive is .005 • The probability of have lung cancer if test is positive is .95

17. Group Project Time