Are We Ready to Use Constrained Optimization in Health Outcomes Research?

Decision-analytic modeling is an accepted approach used by many health technology assessment agencies to assess the cost-effectiveness (i.e., value) of new and existing health care technologies [1,2]. These agencies (along with payers, physicians, and other stakeholders) recognize that decision analysis can be used to forecast health outcomes and to understand the value of medical technologies based on clinical trial data before they are used in clinical practice. In fact, decision modeling as an analysis tool has expanded and helps us to understand a variety of additional outcomes issues associated with health care, including the budget impact, cost of care, and risk versus benefit. Mathematical programming, mathematical optimization, and constrained optimization are terms used to describe a mathematical technique to find the best or “optimal” solution to a problem for a given set of decision variables and a series of constraints. It is a decision-analytic modeling approach that, in its simplest form, is made up of an objective function (i.e., equation) that is to be maximized or minimized subject to a set of constraint equations (i.e., limits). Finding the maximum or minimum solution for the objective function requires finding the best set of values for the decision variables. Constrained optimization is typically used to find an optimal allocation of resources. It has been used to solve problems in many fields, such as allocating available funds among different investments in financial planning, blending materials in manufacturing (e.g., blending different types of crude oils to produce different types of gasoline), or logistics planning in the military. Even in health care, these methods have been used to optimize things such as radiation administration, operating room scheduling, and staff scheduling. Nevertheless, their use is typically not seen in outcomes research. ISPOR’s task force on Constrained Optimization Methods in Health Services Research was set up to introduce the value of these methods in health systems and outcomes research. The aim is to describe problems for which these methods may be appropriate and to identify good practices for these methods (https://www.ispor.org/TaskForces/Optimization-Methods-in-Health care-Delivery.asp). The first task force report introduces the concepts of constrained optimization and presents the methodology through a simple two-dimensional example [3]. Steps to assist researchers in constructing, solving, and reporting these methods are reviewed. The approach is then compared with other decision-modeling contexts traditionally seen in health outcomes research.