Two-stage stochastic programming for interdisciplinary pain management

Abstract

The goal of this research is to find an optimal adaptive treatment strategy to assist physicians in prescribing treatments for patients with chronic pain. This research proposes a two-stage stochastic programming (2SP) method to optimize a treatment procedure for interdisciplinary pain management. The 2SP model incorporates non-convex nonlinear mixed integer constraints, which are constructed based on data from a real pain management program. We derive a piecewise linear approximation method to approximate the non-convex nonlinear constraints in the 2SP model. Consequently, we formulate an equivalent mixed integer linear programming (MILP) model and then solve it using a commercial mixed-integer programming solver. A comparison of the policies generated by the MILP model with the policies generated by the original nonlinear 2SP model shows that, given limited CPU time, the policies generated by the MILP model outperform those of the original nonlinear 2SP model.

Keywords:

• Linear approximation
• MILP
• MINLP
• pain management
• regression
• two-stage stochastic programming

Acknowledgements

This research is funded by National Science Foundation grant CMMI-1434401.