Constrained optimization methods in health services research - an introduction: report 1 of the ISPOR optimization methods emerging good practices task force

Providing health services with the greatest possible value to patients and society given the constraints imposed by patient characteristics, health care system characteristics, budgets, etc. relies heavily on the design of structures and processes. Such problems are complex and require a rigorous and systematic
approach to identify the best solution. Constrained optimization is a set of methods designed to identify efficiently and systematically, the best solution (the optimal solution) to a problem characterized by a number of potential solutions in the presence of identified constraints. This report identifies: 1) key concepts and the main steps in building an optimization model; 2) the types of problems where optimal solutions can be determined in real world health applications and 3) the appropriate optimization methods for these problems. We first present a simple graphical model based upon the treatment of "regular" and "severe" patients, which maximizes the overall health benefit subject to time and budget constraints. We then relate it back to how optimization is relevant in health services research for addressing present day challenges. We also explain how these mathematical optimization methods relate to simulation methods, to standard health economic analysis techniques, and to the emergent fields of
analytics and machine learning.