The worst drug rule revisited: mathematical modeling of cyclic cancer treatments

Abstract

In drug treatments of cancer, cyclic treatment strategies are characterized by alternating applications of two (or more) different drugs, given one at a time. One of the main problems of drug treatment in cancer is associated with the generation of drug resistance by mutations of cancerous cells. We use mathematical methods to develop general guidelines on optimal cyclic treatment scheduling, with the aim of minimizing the resistance generation. We define a condition on the drugs' potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously. We show that the general rule (best-drug-first, worst-drug-longer) is unchanged by the presence of cross-resistance. We design a systematic method to test all strategies and come up with the optimal timing and drug order. The role of various constraints in the optimal therapy design, and in particular, suboptimal treatment durations and drug toxicity, is considered. The connection with the "worst drug rule" of Day (Cancer Res. 46:3876, 1986b) is discussed.