Multi-Objective Two-Stage Stochastic Programming for Adaptive Interdisciplinary Pain Management with Piece-Wise Linear Network Transition Models

摘要

Pain is the most common symptom when a patient visits a physician. People experience pain throughout their lifetime at different degrees. If short term pain is not treated properly, then it can become long term pain, which is also known as chronic pain. The Eugene McDermott Center for pain management at UT Southwestern Medical Center conducts a two-stage pain management program for chronic pain. This research uses a two-stage stochastic programming approach to optimize personal adaptive treatment strategies for pain management. The goal is to generate adaptive treatment strategies using statistics based optimization approaches that can be used by physicians to prescribe treatment to the patients. Transition models predict how a patient with certain characteristics will react to treatments. This research uses Piece-wise Linear Networks (PLN) to represent transition models. A mixed integer linear program is developed to integrate those PLN transition models into an optimization problem.;In this research we have considered five pain outcomes. To balance between different pain outcomes in the objective, we developed a survey for physicians, which is actually a pairwise comparison of different levels of different pain outcomes. Survey inputs are subjective and vary from physician to physician. In other words, inputs from multiple surveys are not entirely consistent. To get consistent weights for different levels of different pain outcomes in the two-stage stochastic program, we developed a convex quadratic programming model.;To speed up the solution process, we developed additional constraints based upon 3-way treatment interactions. These 3-way treatment interaction constraints are totally consistent with two-way treatment interaction constraints. These additional constraints do not eliminate real integer solutions, but they may eliminate fractional solutions in the branch-and-bound algorithm. We then solved the original MILP with these additional logical style constraints to see the improvement in MILP.