Decision Trees & Bayes Theorem 2016
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Transcript of Decision Trees & Bayes Theorem 2016
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Decision Decision Analysis 101Analysis 101
Stefan Tigges MD MSCRStefan Tigges MD MSCR
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What is Decision What is Decision Analysis?Analysis?
Best course of action Best course of action under conditions of under conditions of uncertaintyuncertainty
Rationalize decision Rationalize decision making making
Basic conceptsBasic concepts Expected valueExpected value Decision trees/IngredientsDecision trees/Ingredients
ExamplesExamples Audience participationAudience participation
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Key Concept: Key Concept: Expected ValueExpected Value
Average payoff of Average payoff of random trial random trial P x P x VV
P(outcome)P(outcome) Outcome valueOutcome value Expected value Expected value
may not be a may not be a possible outcomepossible outcome
Gambling exampleGambling example
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Should I Buy a Should I Buy a Ticket?Ticket?
Wikipedia: California Lottery Mega MillionsWikipedia: California Lottery Mega Millions Minimum payoff is $12,000,000Minimum payoff is $12,000,000 P(Winning) is 1/175,711,536P(Winning) is 1/175,711,536 Cost is one dollarCost is one dollar
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Should I Buy a Should I Buy a Ticket?Ticket?
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Types of Expected Types of Expected ValuesValues
Expected ValueExpected Value P(outcome)P(outcome) Value of outcomeValue of outcome
DollarsDollars Years of survivalYears of survival UtilityUtility QALYQALY
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Outcome: Utility Outcome: Utility Desirability of a Health Desirability of a Health
StateState
Expected Value= P(outcome) x ValueExpected Value= P(outcome) x Value
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Outcome: Treatment Outcome: Treatment UtilityUtility
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Decision Analysis Decision Analysis IngredientsIngredients
Comparing Comparing expected values expected values of different of different options, X vs Yoptions, X vs Y
Decision treeDecision tree OutcomesOutcomes ProbabilitiesProbabilities
Expected Value= P(outcome) x ValueExpected Value= P(outcome) x Value
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Decision Tree BasicsDecision Tree Basics
TimeTime
DecisionDecisionOptionsOptionsOutcomesOutcomes
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Decision Tree BasicsDecision Tree Basics
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Decision Tree BasicsDecision Tree Basics
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Example: R/O CADExample: R/O CAD
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First Make a ChoiceFirst Make a Choice
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PossibilitiesPossibilities
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More PossibilitiesMore Possibilities
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Final TreeFinal Tree
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And the Winner And the Winner is…is…
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Shortcomings of Decision Shortcomings of Decision AnalysisAnalysis
Risk AverseRisk Averse QALY (Y x U)QALY (Y x U)
Years survivalYears survival UtilityUtility
SubjectiveSubjective Doctor/patient/familyDoctor/patient/family
Other NumbersOther Numbers LiteratureLiterature UncertaintyUncertainty
Test accuracyTest accuracy CostsCosts
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Sensitivity AnalysisSensitivity Analysis Technique that recognizes range Technique that recognizes range
of valuesof values ProbabilitiesProbabilities OutcomesOutcomes
TypesTypes One-WayOne-Way Two-WayTwo-Way Three-WayThree-Way
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Tornado DiagramTornado Diagram
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Sensitivity Analysis: Prob Sensitivity Analysis: Prob CadCad
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One Way Sensitivity One Way Sensitivity AnalysisAnalysis
Range .05 to .95
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Tornado DiagramTornado Diagram
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Sensitivity Analysis: Cath Sensitivity Analysis: Cath MortalityMortality
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One Way Sensitivity One Way Sensitivity AnalysisAnalysis
Range .000001 to .1
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Two Way Sensitivity Two Way Sensitivity AnalysisAnalysis
Range Cath Mortality
.000001 to .1
Range CADProbability .05 to .95
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Three Way Sensitivity Three Way Sensitivity AnalysisAnalysisSensitivity Analysis on
Mortality of Cath and Sensitivity of Cath and Sensitivity of CT
Mortality of Cath
Sens
itivi
ty o
f Cat
h
0.00 0.03 0.05 0.08 0.10
0.990
0.943
0.895
0.848
0.800
Cardiac CTCoronary Cath
Sensitivity of CT = 0.800
Sensitivity Analysis on Mortality of Cath and Sensitivity of Cath and Sensitivity of CT
Mortality of Cath
Sens
itivi
ty o
f Cat
h
0.00 0.03 0.05 0.08 0.10
0.990
0.943
0.895
0.848
0.800
Cardiac CTCoronary Cath
Sensitivity of CT = 0.848
Sensitivity Analysis on Mortality of Cath and Sensitivity of Cath and Sensitivity of CT
Mortality of Cath
Sens
itivi
ty o
f Cat
h
0.00 0.03 0.05 0.08 0.10
0.990
0.943
0.895
0.848
0.800
Cardiac CTCoronary Cath
Sensitivity of CT = 0.895
Sensitivity Analysis on Mortality of Cath and Sensitivity of Cath and Sensitivity of CT
Mortality of Cath
Sens
itivi
ty o
f Cat
h
0.00 0.03 0.05 0.08 0.10
0.990
0.943
0.895
0.848
0.800
Cardiac CTCoronary Cath
Sensitivity of CT = 0.943
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Three Way Sensitivity Three Way Sensitivity AnalysisAnalysis
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Do it Yourself Decision Do it Yourself Decision AnalysisAnalysis
Problem: You chooseProblem: You choose IngredientsIngredients
Decision tree: time flows left to rightDecision tree: time flows left to right ChoicesChoices OutcomesOutcomes ProbabilitiesProbabilities ValuesValues