Expected Value Decision Making

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Expected Value Decision Making

• Woods Hole
• Spring 2008
• Suzanne Bakken, RN, DNSc
• Columbia University

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Behavioral Objectives

• Identify the components of expected value
  decision making
• Construct and solve a decision tree using a
  decision analysis software package

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Outline

• Probability in evidence-based practice
• Expected value decision making
• Building a decision tree with Data

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Probability in Evidence-based Practice

• Characterization of test performance positive
  predictive value, negative predictive value
• Diagnostic decision support systems
• Expected value decision making

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Quantifying Uncertainty

• Probability as a language for expressing
  uncertainty
• Bayes theorum for probability revision

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Probability Fundamentals

• Strength of belief
• A number between 0 and 1 that expresses an
  opinion about the likelihood of an event
• Probability of an event that is certain to occur
  is 1
• Probability of an event that is certain to NOT
  occur is 0

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Definitions

• Prior probability - the probability of an event
  before new information (finding) is acquired
  pretest probability or risk
• Posterior probability - the probability of an
  event after new information (finding) is
  acquired posttest probability or risk
• Probability revision - taking new information
  into account by converting prior probability to
  posterior probability

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Role of Probability Revision Techniques
Prior Probability
Posterior Probability
Before Finding
After Finding
Abnormal Finding
1
0
Probability of Disease
Diagnosis
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Role of Probability Revision Techniques
Posterior Probability
Prior Probability
After Finding
Before Finding
Negative Finding
1
0
Probability of Disease
Diagnosis
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Probability in Evidence-based Practice

• Characterization of test performance positive
  predictive value, negative predictive value
• Diagnostic decision support systems
• Expected value decision making

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What is a Decision?

• A decision is an irreversible choice among
  alternative ways to allocate valuable resources

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What makes a health care decision hard?

• Complexity
• Uncertainty including limited information
• Dynamic effects
• High stakes
• Unclear alternatives
• Unclear preferences

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Are These Decisions?

• A person with appendicitis is uncertain whether
  there will be unpleasant side effects from the
  appendectomy he is about to have.
• A nurse is considering whether he should apply
  restraints to a patient who is at risk for
  falling.
• A MD is uncertain about whether her patient will
  suffer side effects from his antiretroviral
  therapy.
• A woman with breast cancer is wondering whether
  she should have a lumpectomy or a mastectomy.
• A NP is trying to decide if she should screen for
  strep throat in someone who presents with a sore
  throat.

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Decision Analysis Expected Value Decision Making

• Prescriptive
• Analytic
• Explicit

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Basic Concepts

• Biological events random
• Outcomes of illness uncertain
• Outcomes of treatments uncertain
• Must choose between treatments - a gamble
• Utility - a measure of preference
• Expected value - result expected on average

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Steps in Decision Analysis

• Create a decision tree
• Identify and bound problem
• Structure the problem
• Characterize information needed
• Calculate the expected value of each decision
  alternative
• Choose the decision alternative with the highest
  expected value (payoff, utility)
• Use sensitivity analysis to test the conclusions
  of the analysis

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Whose View?

• Individual patient
• Physician
• Society
• Government
• Healthcare institutions

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Create the Decision Tree

• Define the decision problem
• Identify the decision alternatives
• List the possible clinical outcomes of each of
  the decision alternatives
• Represent the sequence of events leading to the
  clinical outcomes by a series of chance nodes and
  decision nodes
• Choose a time horizon for the problem
• Determine the probability of each chance outcome
• Assign a value (preference, utility, payoff) to
  each clinical outcome

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Simple Decision Tree
Outcome Treatment with disease
Outcome Treatment without disease
Outcome Treatment with disease
Outcome Treatment without disease
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Identify Decision
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Represent Sequence of Events
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Represent Sequence of Events
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Assign Probabilities

• Determine probabilities for each chance node
• Probability of X occurring plus probability of X
  not occurring is equal to 1
• Sum of probabilities of all branches emanating
  from a chance node must equal 1

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Assign Values

• Utilities, preferences, payoffs
• Mortality
• Length of survival
• Cost
• Quality of life
• Quality of life years

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Standard gamble
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Exercise 1
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Folding Back Manually

• Probabilities x utilities at each chance node
• Highest expected value goes forward if multiple
  decision nodes

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Folding Back the Tree
No cure
U.2
Disease present
p.90
No cure
U.2
Do not operate
Survive
p.10
p.10
p.10 p.90
U1
Cure
Try for the cure
p.90 p.10
p.90

U20


Cure
Disease absent
Disease present
Operative death U0 Operative death U0
p.10
Cure
p.02 p.98
U1
Palliate
p.10 p.90
Operative death
Operate
Survive
U0
U.2
p.01 p.99
p.90
No Cure
Disease absent
U1
Survive
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Folding Back the Tree
No cure
U.2
Disease present
p.90
No cure
U.2
Do not operate
Survive
p.10
p.10
p.10 p.90
U1
Cure
Try for the cure
p.90 p.10
p.90

U1


Cure
Disease absent
Disease present
Operative death U0 Operative death U0
p.10
p.02 p.98
Palliate
.1 X 1 .90 X .2 .28
Operative death
Operate
Survive U20
U0
p.01 p.99
p.90
Disease absent
U1
Survive
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Fold It Again
No cure
U.2
Disease present
p.90
No cure
U.2
Do not operate
Survive
p.10
p.10
p.10 p.90
U1
Cure
Try for the cure
p.90 p.10
p.90

U1


Cure
Disease absent
Disease present
Operative death U0
p.10
U .98 X .28 .02 X 0 .27
Palliate
Operative death
Operate
U0
p.01 p.99
p.90
Disease absent
U1
Survive
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Try for Cure Vs. Palliative
No cure
U.2
Disease present
p.90
Do not operate
p.10
p.10
U1
Cure
Try for the cure
p.90

U .90 X .92 .10 X 0 .83

Disease absent
Disease present
p.10
U .98 X .28 .02 X 0 .27
Palliate
Operative death
Operate
U0
p.01 p.99
p.90
Disease absent
U1
Survive
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Final Fold - Operate Vs. Do Not Operate
Do not operate
U .83
U .27
Operate
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What Happens If You Change the Numbers?

• Cost
• Probabilities
• Values associated with living and dying

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Exercise 2