Expected Value Decision Making

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Expected Value Decision Making

• Woods Hole
• Spring 2009
• 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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Exercise 1

• Part 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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Quality-adjusted life-years (QALYs)

• Quality weights (or utility weights) are anchored
  between 0 and 1 where
• the best health state (perfect health) has a
  weight of 1
• death has a weight of 0
• Sometimes states worse than death (dis utility)

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The QALY
QALY summation of TU Ttime in health
state Uutility of health state
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Euroqol

• Public domain instrument
• Societal preferences
• Many nations
• http//www.ahrq.gov/rice/EQ5Dscore.htmweights
• Multiple languages
• http//www.euroqol.org/

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Measuring Patient Preferences

• Health Status Measures - derived from
  psychology/sociology
• emphasis on measuring specific domains of health
• Value Measures (utilities, preferences) - derived
  from economics
• emphasis on assessing preferences, e.g. giving
  explicit weights to specific health states

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Measuring Utilities Directly

• Visual Analog Scale (or Feeling Thermometer)
• Scale 0 to 1
• Time-trade off
• choose a time horizon for a specific health state
• how much time in perfect health is equivalent?
• Standard gamble

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Utility assessment visual analog scale

• Patient is asked to place the arrow on the line
  that corresponds to how they feel about the
  health state of interest

0
10
20
30
40
50
60
70
80
90
100
Perfect Health
Death
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Utility assessment - time tradeoff

• Choose between
• 10 years in current health (then death)
• 9 years in perfect health (then death)

Current Health
Death
Perfect Health
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Utility assessment - time tradeoff

• Vary the amount of time spent in perfect health,
  each time asking the respondent to choose between
  current health (for 10 years) and perfect health
• When the respondent cannot choose, we say he is
  indifferent to current and perfect health use
  this value to compute utility of current health
  state.

Choose Perfect Health
Choose Current Health
Cant decide
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Utility assessment - standard gamble

• degree of willingness to gamble away a CERTAIN
  intermediate outcome for a CHANCE at a better or
  worse outcome (von Neumann and Morgenstern, 1947)
• patients with real or hypothetical health state
  are given a series of choices
• 100 certainty of remaining in current
  (intermediate) state
• try a new medication that has probability pi of
  curing you and giving you perfect health (oh,
  and, it has probability 1 - pi of immediate
  death).
• find the value of pi at which the person is
  indifferent between the sure thing and the gamble

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Utility assessment - standard gamble
The basic scenario is We have a new treatment
that can completely cure your illness and return
you to perfect health, but it has a small chance
of killing you immediately. Would you prefer to
stay as you are or take the new treatment?
Death
p(death)
Gamble
Perfect Health
Choose
Sure Thing
Health State
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Standard gamble Example
99
A patient would almost never accept a 99 chance
of death to cure a particular health state
?
1
1
A patient might be very likely to accept a 1
chance of death to cure a particular health state
?
99
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Standard Gamble

• The indifference point is assumed to be the value
  of the particular health state, as the patient
  would be willing to risk the complementary
  portion of his life to avoid that health state

p of CURE
p of Death
Preference
0.99
0.01
GAMBLE
Indifference point
0.95
0.05
GAMBLE
0.90
0.10
can't tell
0.85
0.15
Current Health
0.80
0.20
Current Health
0.75
0.25
Current Health
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Standard gamble
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Exercise 1

• Part 2

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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