Are adaptive chemotherapy schedules robust? A three-strategy stochastic evolutionary game theory model

We investigate the robustness of adaptive chemotherapy schedules over repeated cycles and a wide range of tumor sizes. We introduce a non-stationary stochastic three-component fitness-dependent Moran process to quantify the variance of the response to treatment associated with multidrug adaptive schedules that are designed to mitigate chemotherapeutic resistance in an idealized (well-mixed) setting. The finite cell (N tumor cells) stochastic process consists of populations of chemosensitive cells, chemoresistant cells to drug 1, and chemoresistant cells to drug 2, and the drug interactions can be synergistic, additive, or antagonistic. First, the adaptive chemoschedule is determined by using the N → ∞ limit of the finite-cell process (i.e. the adjusted replicator equations) which is constructed by finding closed treatment response loops (which we call evolutionary cycles) in the three component phase-space. The schedules that give rise to these cycles are designed to manage chemoresistance by avoiding competitive release of the resistant cell populations. To address the question of how these cycles are likely to perform in practice over large patient populations with tumors across a range of sizes, we then consider the statistical variances associated with the approximate stochastic cycles for finite N, repeating the idealized adaptive schedule over multiple periods. For finite cell populations, the error distributions remain approximately multi-Gaussian in the principal component coordinates through the first three cycles, with variances increasing exponentially with each cycle. As the number of cycles increases, the multi-Gaussian nature of the distribution breaks down due to the fact that one of the three subpopulations typically saturates the tumor (competitive release) resulting in treatment failure. This suggests that to design an effective and repeatable adaptive chemoschedule in practice will require a highly accurate tumor model and accurate measurements of the subpopulation frequencies or the errors will quickly (exponentially) degrade its effectiveness, particularly when the drug interactions are synergistic. Possible ways to extend the efficacy of the stochastic cycles in light of the computational simulations are discussed.