Contributions to the Theory of Sensitivity and Stability Analysis of Multi-criteria Decision Models, with Applications to Medical Decision Making

Abstract

Patients are faced with multiple alternatives when selecting the preferred method for colorectal cancer screening, and there are multiple criteria to be considered in the decision process. We model patients’ choices using a multi-criteria decision model, and propose a new approach for characterizing the idiosyncratic preference regions for individuals and for groups of similar patients.

We propose an extension of the sensitivity and stability analyses for Analytic Network Models developed by May et al. (2013). We study ANP models to understand how preference regions are created, and how boundaries can be characterized, as the number of criteria increases. For the two-criteria and three-criteria sensitivity and stability analyses, piecewise linear functions and triangular mesh generation, respectively, are used to approximate the boundaries between two adjacent preference regions. We use optimization methods to find the best approximations for the core stability and solution stability regions for cases where two and three criteria are perturbed simultaneously, and there exist an arbitrary number of alternatives. We define sensitivity and stability measures that can be implemented in practice, and that can be considered as a starting point in any medical decision making process.

We apply our newly developed methodology to randomly chosen patients, and show how insights derived from the sensitivity and stability of patients’ preferences might be used within the medical decision making process. Individualized stability analysis is informative, but the generalization to groups of similar patients may be even more important for healthcare providers. Our comparisons reveal that a patient’s age may be an effective discriminating factor that should be taken into consideration when extending the individualized sensitivity and stability analysis to groups of patients with similar characteristics.