Optimal locations for traumatic brain injury units: a pilot model

WB Vogel, Ph.D., MJ Côté, Ph.D., S Syam, Ph.D., Diane Cowper, M.A.,Gretchen Stephens, M.A., and Barbara Bates, M.D.

VA RR&D Brain Rehabilitation Research Center, VA RR&D/HSR&D Rehabilitation Outcomes Research Center; Malcom Randall VA Medical Center, Gainesville, FL

Objectives: The objective of this research is to demonstrate a prototype mathematical optimization model for locating traumatic brain injury (TBI) treatment units geographically. The goal of the model is to allocate a limited number of TBI treatment units to existing VA medical centers so as to minimize the sum of patient travel costs and VA treatment costs while ensuring service for those veterans diagnosed with TBI in VISN 8. Through developing a prototype for VISN 8, we demonstrate both the capabilities of the model and the feasibility of constructing such a model for the entire VA system.

Methods: We present a mixed integer programming model where the objective function to be minimized is the sum of patient travel costs and VA patient treatment costs. The constraints in this model represent the geographical origins of VA TBI patients. Patients' zip codes of residence from the VA's Patient Treatment File (PTF) comprise a key data element for this model. Combined with the zip codes of VA treatment sites, we estimated the travel distances for VA TBI inpatients in VISN 8 over the past three years. We calculated approximate travel costs based on these travel distances and combined them with estimates of the VA costs of providing care to these patients (from the VA Health Economics Resource Center's Average Cost Dataset) to parameterize the objective function. We solved this optimization model under varying configurations to demonstrate both how the model operates and how optimal geographic locations vary as model parameters and constraints are changed.

Results: We demonstrate how the optimal number of TBI units varies with changes in travel, production costs, and patient volume and location. We also exercise the model to present estimates of the expected costs of closure of a TBI unit and their attendant incidence. Such exercises can be extremely useful in informing policymakers about the often otherwise hidden costs of resource allocation decisions.

Conclusions: Our prototype model demonstrates both the usefulness of a more sophisticated analytical approach to planning decisions as well as the feasibility of constructing such a model for the VA nationwide. We believe that our work demonstrates a powerful new method for informing and supporting important resource allocation decisions within VA rehabilitation.

Funding Acknowledgment: This pilot work was funded by the VA Rehabilitation Research and Development Service through the VA RR&D Brain Rehabilitation Center at the Malcom Randall VA Medical Center in Gainesville, FL.