PURPOSE: A critical challenge in applying formal decision analysis to routine medical care is the assessment of utilities from individual patients, which can be quite difficult and time-consuming. Fortunately for many problems it is not necessary to know the decision maker's complete multiattribute utility function in order to infer which course of action is preferred. Here I describe the application of a robust multivariate sensitivity analysis method to the task of guiding utility assessment based on partial information.

METHOD: Optimizing Multivariate Sensitivity Analysis uses a collection of mathematical methods to process decision trees and influence diagrams in which some probabilities and utilities are specified as symbolic functions of random variables. The decision models include partial information on the unknown probabilities and utilities in the form of constraints on the variables; the analysis can be extended to include features of the second-order probability distributions the variable values, though it is not necessary to provide or assume any particular second-order distributions. The method uses symbolic Bayesian inference to compute a polynomial expression for the expected utility of each decision strategy, and bounded global optimization to solve problems using these symbolic expected utilities. The method does not involve Monte Carlo sampling; it returns closed-form symbolic functions and bounded interval results. All variables are allowed to change simultaneously.

RESULTS: The method selects the set of non-dominated strategies which includes the efficient set of strategies that are optimal for some feasible assignments to the random variables in the decision model. Strategy selection uses polynomial optimization problems to describe the best- and worst-case performance of each strategy relative to its competitors. Also, the method computes the preference region for each selected strategy, which is the system of inequalities that defines the values of the random variables for which that strategy is preferred. Now, instead of assessing the precise value of every variable used to specify an individual decision maker's utilities, the analyst need only establish which preference region the variables fall into in order to recommend a plan of action. Textual and graphical techniques are provided for summary and visualization of the multidimensional preference regions.

CONCLUSION: Optimizing Multivariate Sensitivity Analysis computes results useful for making inferences from partial information about probabilities and utilities and for guiding additional utility assessment.