University of Minnesota

Medical Technology Evaluation and Market

Research Course: MILI/PUBH 6589

Spring Semester, 2012Stephen T. Parente, Ph.D.

Carlson School of Management, Department of Finance

Lecture Overview

• Statistical Uncertainty• Baye’s Rule• Practice Exercise• Markov Modeling • Group Project work

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?

Statistical Uncertainty: Example

Model 1 Model 2

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

Randomness in health & cost outcomes: Example

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

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)

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:

)(

)(

BP

APABPBAP

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

15.01.9.05.99.

01.9.

BAP

)(

)(

BP

APABPBAP

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

Prob of condition = sensitivityprevalence

(sensitivityprevalence)+ (1- specificity)(1 prevalence)

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.

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 $$

DeathP(4)

No occurrence

Local occurrence

Metastasis

Treatment

Treatment

Death

Markov Modeling Example

Surgery

Start pop = 100

Chemo

Start pop = 100Year N

SurvivingHRQL Product N

SurvivingHRQL Product

1 95 .54 51.3 92 .39 45.1

2 87 .39 33.9 81 .32 25.9

3 75 .35 26.3 75 .38 28.5

4 53 .32 16.6 65 .39 25.4

5 35 .29 10.2 48 .35 16.8

6 12 .27 3.2 35 .29 10.2

7 3 .24 .7 22 .27 5.9

8 0 0 0 3 .24 .7

Total 142.2 158.5

Markov Modeling Example w/ Discounting

—r = .03Surgery

Start pop = 100

Chemo

Start pop = 100Year N

Surviving

HRQL Product Product with

discount

N Survivin

g

HRQL Product Product with

discount

1 95 .54 51.3 51.3 92 .39 45.1 45.1

2 87 .39 33.9 32.9 81 .32 25.9 25.1

3 75 .35 26.3 24.7 75 .38 28.5 26.7

4 53 .32 16.6 15.1 65 .39 25.4 23.2

5 35 .29 10.2 9.1 48 .35 16.8 14.9

6 12 .27 3.2 2.7 35 .29 10.2 8.8

7 3 .24 .7 0.58 22 .27 5.9 4.9

8 0 0 0 0 3 .24 .7 0.60

Total 142.2 136.6 158.5 149.6

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

Group Project Time