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Probabilistic Analysis of Decision Trees Using Symbolic Algebra

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  • Keith E. Willard
  • Gregory C. Critchfield

Abstract

Uncertainty in medical decision making techniques occurs in the specification of both decision tree probabilities and utilities. Using a computer-based algebraic approach, methods for modeling this uncertainty have been formulated. This analytic procedure allows an exact calculation of the statistical variance at the final decision node using automated symbolic manipulation. Confidence and conditional confidence levels for the preferred decision are derived from gaussian theory, and the mutual information index that identifies probabilistically important tree variables is provided. The computer-based algebraic method is illustrated for a problem previously analyzed by Monte Carlo simulation. This methodology provides the decision analyst with a procedure to evaluate the outcome of specification uncertainty, in many decision problems, without resorting to Monte Carlo analysis. Key words: decision analysis; sensitivity analysis; statistical analysis; symbolic algebra; statistical confidence; information theory. (Med Decis Making 6:93-100, 1986)

Suggested Citation

  • Keith E. Willard & Gregory C. Critchfield, 1986. "Probabilistic Analysis of Decision Trees Using Symbolic Algebra," Medical Decision Making, , vol. 6(2), pages 93-100, June.
    • Handle: RePEc:sae:medema:v:6:y:1986:i:2:p:93-100
    DOI: 10.1177/0272989X8600600206
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    References listed on IDEAS

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    1. Karen Klein & Stephen G. Pauker, 1981. "Recurrent Deep Venous Thrombosis in Pregnancy," Medical Decision Making, , vol. 1(2), pages 181-202, June.
    2. Robert D. Rifkin, 1983. "Statistical Considerations in Medical Decision Models," Medical Decision Making, , vol. 3(2), pages 197-214, June.
    3. Gregory C. Critchfield & Keith E. Willard, 1986. "Probabilistic Analysis of Decision Trees Using Monte Carlo Simulation," Medical Decision Making, , vol. 6(2), pages 85-92, June.
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    4. Ana P. Johnson-Masotti & Purushottam W. Laud & Raymond G. Hoffmann & Matthew J. Hayat & Steven D. Pinkerton, 2001. "Probabilistic Cost-Effectiveness Analysis of HIV Prevention," Evaluation Review, , vol. 25(4), pages 474-502, August.

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