Decision Trees

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Decision Trees

• Farrokh Alemi, Ph.D.

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Coming Up

• How to construct a decision tree?
• Components of a tree
• Interviewing decision makers
• How to analyze a decision tree?
• Mathematical expectations.
• Folding back

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Example

• A preferred provider organization (PPO) has
  approached the benefit manager of a company of
  992 employees.
• The PPO offered to discount hospitalization
  services by 6 and outpatient services by 15 if
  the company would remove co-payments for
  employees utilizing the PPO

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Components of a Tree

• Decision
• Square node, two arcs and options
• Sequence of events
• Circle node, arcs and events
• Probabilities
• Consequences
• Utilities or costs

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The Analysis Process Matters

• It informs that a decision is looming
• Reassures that the analysis is fair
• It removes decision makers from day-to-day
  concerns
• It provides new insights while facilitating
  discussion

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Process

• Interview decision makers and construct a
  preliminary tree
• Present tree and show how various concerns are
  captured
• Solicit a list of new concerns
• Revise tree

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New Concerns

• Separate general outpatient care from mental
  health care
• Focus on employees who file claims
• The PPO clinic might have less efficient
  practices
• Lower co-pay may lead to over utilization
• Group practices are more efficient than solo
  practices
• Clinicians may generate their own demand
• Show discounts

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Estimating Probabilities from Data, Experts
Literature
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Estimating Costs

• Review of cases at the employer site
• Average cost of the sample
• Review of cases at the PPO
• Adjusted for case mix difference (PPO patients
  30 sicker)

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Analysis of Trees

• Folding back
• Replace a node with its expectation
• Continue until the decision node

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Net Impact

• Expect cost under continue
• Expected cost after joining PPO 871.08
• Savings per family per year 597.86
• Sensitivity analysis
• Not sensitive to 5 changes in hospitalization
  rate
• Not sensitive to 5 changes in clinic visit rate
• Sensitive to changes in calculation of cost of
  hospitalization and case mix differences

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Myth of Analysis

• All options are depicted
• Wait for a better offer
• All consequences are enumerated
• Other health care organizations were on the board
  of the employer
• Assess utilities and fold back using expected
  utilities
• Data are valid
• Sensitivity analysis see if small differences in
  estimates will change conclusions

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Make Your Own

• Think through what is the unit of analysis (who
  decides)
• Start with the decision
• Think through possible events and consequences
• Think through issues that should be captured
• Make a draft
• Revise to incorporate new issues