1. University of Minnesota Medical Technology Evaluation and Market Research Course: MILI/PUBH 6589 Spring 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 TestPositiveTrueTreatFalseTreatNegativeFalseStopRetestTrueStopRetest Model 2 TestPositiveTrueTreatFalseTreatNegativeFalseStopTrueStop

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 Disease Strikes Old Treatment (cost incurred) Success Failure (costs incurred) New Treatment (cost incurred but not well known) Success Failure (cost incurred – but not well known)

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

14. Markov Modeling Example Surgery Start pop = 100 Chemo Start pop = 100 YearN Surviving HRQLProductN Surviving HRQLProduct 195.5451.392.3945.1 287.3933.981.3225.9 375.3526.375.3828.5 453.3216.665.3925.4 535.2910.248.3516.8 612.273.235.2910.2 73.24.722.275.9 80003.24.7 Total142.2158.5

15. Markov Modeling Example w/ Discounting—r =.03 Surgery Start pop = 100 Chemo Start pop = 100 YearN Survivin g HRQLProductProduct with discount N Survivin g HRQLProductProduct with discount 195.5451.3 92.3945.1 287.3933.932.981.3225.925.1 375.3526.324.775.3828.526.7 453.3216.615.165.3925.423.2 535.2910.29.148.3516.814.9 612.273.22.735.2910.28.8 73.24.70.5822.275.94.9 800003.24.70.60 Total142.2136.6158.5 149.6

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