Steps to Develop a Decision Tree

Developing a Decision Tree

Steps to Develop a Decision Tree

  • Define the Decision Problem:

    • Identify the core question.
    • Determine the alternatives (e.g., surgical vs. medical pathway).
    • Define the research question (e.g., best treatment for a condition).
    • Pinpoint key elements of the decision.
    • Consider subpopulations and if different models are needed for each.

  • Synthesize Evidence (Literature Review):

    • Perform a literature review to find relevant studies.
    • Identify probabilities of outcomes.
    • Determine cost definitions and estimates.
    • Look for benefits of previous interventions and their probabilities.
    • Meta-analysis is a key part of economic evaluation.

  • Describe Events within the Intervention:

    • Detail the events that make up the intervention (e.g., surgical or medical).
    • Identify potential outcomes (e.g., infection, complications, embolus, bleed, death).
    • Assign a cost and probability to each outcome.
    • Ensure all potential outcomes are accounted for.
    • Verify probabilities of occurrence sum to 100% (or 1.0).
    • Identify consequences for each occurrence.

  • Iterative Process:

    • The process is cyclical; after step four, revisit earlier steps.
    • Double-check work to ensure all potential outcomes are accounted for.

Example: Cancer Treatment Decision Tree

  • Scenario: Comparing metoclopramide and ondansetron for cancer treatment, focusing on emesis.

  • Metoclopramide Outcomes:

    • 58% chance of significant emesis.
    • 42% chance of non-significant emesis.

  • Significant Emesis Branch:

    • 66% probability of no significant Adverse Drug Events (ADEs).
    • 34% probability of significant ADEs.

  • Significant ADEs Branch:

    • 60% can be treated.
      • 78% of treated ADEs are resolved.
      • 22% of treated ADEs are unresolved.
    • 40% cannot be treated.

  • Non-Significant Emesis Branch:

    • 12% chance of significant ADEs.
    • 88% chance of no significant ADEs.

  • Important Check: At each node, the probabilities must sum to 100%.

  • Ondansetron:

    • The same decision tree structure is built for the alternative treatment, ondansetron.

  • Overall Probabilities:

    • Calculate overall probabilities for all outcomes across alternatives.
    • Example: Probability of significant emesis with no ADE for metoclopramide.
      • 0.58×0.66=0.3828≈0.3830.58 \times 0.66 = 0.3828 \approx 0.383 (38.3% chance)

  • Calculating Probabilities for Combined Outcomes:

    • Example: Significant emesis with significant ADE, treated and resolved:
      • 0.58×0.34×0.6×0.78=0.0922≈0.0920.58 \times 0.34 \times 0.6 \times 0.78 = 0.0922 \approx 0.092 (9.2% chance)

  • Verification: Sum all outcome probabilities; they should equal 1.0 or 100%.

Cost Assignment

  • Assign a cost to each potential outcome.

    • Example: Significant emesis, no ADE = $40 cost.

  • Expected Cost Calculation:

    • Expected Cost=Probability×CostExpected\ Cost = Probability \times Cost
    • Example: Expected cost for significant emesis, no ADE:
      • 0.383 \times 40 = $15.32

  • Sum all expected costs for each node.

  • Repeat for the other treatment alternative (e.g., ondansetron).

Components of a Decision Tree

  • Choice Node (Square):

    • Represents a decision point where a choice is made (e.g., treatment option).
    • Treatment for the flu: Flu Wonder vs. Flu B Gone.

  • Chance Node (Circle):

    • Represents uncertain events or probabilities outside the analyst's control.
    • Example: After choosing Flu Wonder, the chance of needing an antibiotic.

  • Example: Flu Wonder Treatment Path

    • Choice: Flu Wonder.
    • Chance: 5% chance of needing antibiotics, 95% chance of needing no antibiotics.
    • Antibiotic Needed:
      • 0.5% chance of hospitalization.
      • 99.5% chance of no hospitalization.
    • No Antibiotic Needed:
      • No further treatment.

  • Cost Identification:

    • Identify costs for each outcome (e.g., hospitalization, antibiotics, physician visits).
    • Compile costs for each node (e.g., $5 for hospitalization with antibiotic and Flu Wonder).

Decision Making with Decision Trees

  • Formulary Addition: Deciding whether to add Flu B Gone or Flu Wonder to a formulary.

  • Expected Value Calculation:

    • Expected Value=∑(Probability×Outcome)Expected\ Value = \sum (Probability \times Outcome)
    • Weighted average of all outcomes.

  • Example: Flu B Gone

    • 93% of patients do not need antibiotics, cost = $130 (physician visit + medication).
      • Physician visit: $75 + $20 (symptomatic treatment) = $95
      • Flu B Gone cost: $35
      • Total: $95 + $35 = $130

  • Calculating Expected Value for Flu B Gone: $141 per patient.

  • Calculating Expected Value for Flu Wonder: $148 per patient.

  • Conclusion: Flu B Gone is the lower-cost option.

Cost-Effectiveness Analysis

  • Plug in the costs for different outcomes.

  • Calculate ICER:

    • Differential in cost divided by the differential in effect.
    • Use days of illness as an effect.
    • ICER=Cost<em>Flu Wonder−Cost</em>Flu B GoneEffect<em>Flu Wonder−Effect</em>Flu B GoneICER = \frac{Cost<em>{Flu\ Wonder} - Cost</em>{Flu\ B\ Gone}}{Effect<em>{Flu\ Wonder} - Effect</em>{Flu\ B\ Gone}}

  • Example:

    • Cost difference = $7 (Flu Wonder vs. Flu B Gone).
    • Effect difference = 1 day of illness avoided (3.2 days with Flu Wonder, 4.2 days with Flu B Gone).
    • ICER = \frac{$7}{1} = $7\ per\ day\ of\ symptom\ avoided

  • Decision: Is $7 per day worth it for the HMO to cover Flu Wonder?

Sensitivity Analysis

  • Vary items in the study to hone in on the correct answer.

  • One-Way Sensitivity Analysis:

    • Vary one variable, keep others constant, and observe what happens.

  • Two-Way Sensitivity Analysis:

    • Vary two variables, keep others constant, and observe what happens.

  • Important Consideration: Interaction among variables is not always considered.