Mathematical Optimization of Combination Therapy Regimens

Combination therapy is increasingly important, especially when resistance to drugs is a concern. However, finding the best possible doses to use can be challenging. If three drugs are to be combined, and there are 4 dose levels of each to be tested, this gives 4^3 dose combinations to test. Instead of running 64 studies, we can use mathematical modeling and simulation to gain insight into which dose levels should be combined to achieve optimal outcomes.
Essential components of optimizing outcomes include developing mathematical models of in-host disease dynamics, and quantifying the desired outcomes. Disease dynamics may be represented with semi-mechanistic models that include several cell types. Desired outcomes might include, for example, tumor size that is small at the end of treatment, but also not too large throughout the treatment period. Additionally, we don't want to use too much of any one drug, due to possible toxicity. Quantifying and giving relative weighting to these factors provide an objective that can be mathematically optimized.
I will discuss the optimal control framework and show examples in which control theory was applied to optimize combination therapy regimens. These include comparisons to more-traditional regimens, and optimization in the presence of constraints such as fixed allowable dose levels typical for patient therapies used in the clinic.