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
Lecture Overview
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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
True
Treat
False
Treat
Positive
True
Treat
False
Treat
False
Stop
True
Stop
Positive
Test
Stop
False
Test
Retest
Negative
Negative
Stop
True
Retest
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
Success
Old Treatment
(cost incurred)
Failure
(costs incurred)
Disease Strikes
Success
New Treatment
(cost incurred but
not well known)
Failure
(cost incurred – but
not well known)
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:
P A B  
PB AP( A)
P( B)
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
P A B  
PB AP( A)
P( B)
.9  .01
PA B  
 .15
.99  .05  .9  .01
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
sensitivity  prevalence
Pr ob of condition =
(sensitivity  prevalence) + (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?
Year 1
P(1)
Surgery
$
Year 2
No
occurrence
P(2)
P(3)
P(4)
No
occurrence
Local
occurrence
Treatment
$
Local
occurrence
Treatment
Metastasis
Treatment
$$
Metastasis
Treatment
Death
Death
Markov Modeling Example
Surgery
Start pop = 100
Chemo
Start pop = 100
Year
N
Surviving
HRQL
Product
N
Surviving
HRQL
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 = .03
Surgery
Start pop = 100
Year
N
Survivin
g
HRQL
Product
1
95
.54
51.3
2
87
.39
3
75
4
Chemo
Start pop = 100
N
Survivin
g
HRQL
Product
51.3
92
.39
45.1
45.1
33.9
32.9
81
.32
25.9
25.1
.35
26.3
24.7
75
.38
28.5
26.7
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
158.5
149.6
Total
142.2
Product
with
discount
136.6
Product
with
discount
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