Probabilistic threshold analysis by pairwise stochastic approximation for decision-making under uncertainty

The concept of probabilistic parameter threshold analysis has recently been introduced as a way of probabilistic sensitivity analysis for decision-making under uncertainty, in particular, for health economic evaluations which compare two or more alternative treatments with consideration of uncertainty on outcomes and costs. In this paper we formulate the probabilistic threshold analysis as a root-finding problem involving the conditional expectations, and propose a pairwise stochastic approximation algorithm to search for the threshold value below and above which the choice of conditionally optimal decision options changes. Numerical experiments for both a simple synthetic testcase and a chemotherapy Markov model illustrate the effectiveness of our proposed algorithm, without any need for accurate estimation or approximation of conditional expectations which the existing approaches rely upon. Moreover we introduce a new measure called decision switching probability for probabilistic sensitivity analysis in this paper.