Epi
Decision Analysis
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Decision Analysis
, Decision Tree, Chance Graph
See Also
Incremental Cost Effectiveness Ratio
(
ICER
)
Expected Value Theory
(or
Expected Utility Theory
,
Time Trade Off
,
Standard Gamble
,
Visual Analogue
)
Quality Adjusted Life Year
(
QALY
)
Definitions
Sum of probabilities
Sum of probabilities for a given situation = 1
Example: P(infected) + P(not infected) = 1
Conditional probability
Probability of X given Y uses vertical pipe notation (|)
Example: Probability of STD given multiple sexual partners
P(STD | multiple-partners)
Where P (A | B) = Probability of A given B
Technique
Decision Tree (Chance Graph)
Definition
Models sequential events with conditional probabilities
Nodes
Decision node (Square)
Chance node (Circle)
Probability assigned to each branch from a chance node
All node branches add to 1
Outcome node (Triangle)
Each outcome node is assigned a value
Values may be relative value, utility,
QALY
Values may also be Life (1) or Death (0)
Values may be cost (cost effectiveness analysis)
Rollback Analysis
For a given decision node choice, conditional probabilities are multiplied for each outcome node
Cost Effectiveness Analysis
Outcome nodes are assigned cost unit values
Sensitivity Analysis ("What-if")
Expected values are calculated for a range of chance node probabilities
Example
Treatment success varies between 10 and 30%
Expected values are calculated and plotted for each treatment success probability between 10-30%
Fatal reaction rate is known and plotted
Threshold at which the expected value for treatment success exceeds the risk of fatal reaction
Example
Decision node - Treatment X Given
Chance node - Fatal Reaction: P(rxn) = 0.10
Outcome node: 0 (dies)
Chance node - no fatal reaction: 1-P(rxn) = 0.90
Chance node - Treatment success: P(cure) = 0.20
Outcome node: 1 (survives)
Chance node - Treatment fails: 1 - P(cure) = 0.80
Outcome node: 0 (dies)
Expected Value Calculation if treatment given
Fatal Reaction = (0.1 * 0) = 0
No Fatal Reaction = (tSuccess + tFail) * 0.9
Treatment success (tSuccess) = (0.2 *1) = 0.2
Treatment fails (tFail) = (0.8 * 0) = 0
Expected Value = 0 + (0.2 + 0) * 0.9 = 0.18
Decision node - Treatment X Not Given
Chance node - Improves: P(cure) = 0.15
Outcome node: 1 (survives)
Chance node - Succumbs: P(cure) = 0.85
Outcome node: 0 (dies)
Expected value calculation if treatment not given
Spontaneous cure = (0.15 * 1) = 0.15
Patient succumbs = (0.85 * 0) = 0
Expected Value = (0.15 + 0) = 0.15
Analysis
Expected Value calculated for treatment branch is slightly higher (0.18) compared with non-treatment branch (0.15)
Resources
Decision Tree (Wikipedia)
https://en.wikipedia.org/wiki/Decision_tree
References
Desai (2014) Clinical Decision Making, AMIA’s CIBRC Online Course
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