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 crossresistance 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-druglonger) 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.

Evolution of acquired resistance to anti-cancer therapy

“…Later on, we designed a stochastic process approach to identify optimum dose administration strategies where the birth and death rates of both sensitive and resistant cells are dependent on a temporally varying drug concentration profile [82, 83]. Katouli and Komarova developed a methodology for identifying the optimal scheduling for cyclic treatment strategies – alternating administration of two drugs [110]. The authors utilized their framework published earlier [51] and incorporated the phenomenon of cross-resistance, in which one mutation confers simultaneous resistance to two drugs.…”

Pharmacokinetics and Drug Interactions Determine Optimum Combination Strategies in Computational Models of Cancer Evolution

“…Building on the Goldie-Coldman framework, Day introduced a ‘worst-drug rule’(30) that proposed administering the less effective drug earlier or more frequently than other drugs in a combination therapy regimen. This rule was later extended to the case of cross-resistant drugs by Katouli and Komarova(31). Lavi and colleagues used a structured population approach to explore the role of heterogeneity and density dependence in multi-drug resistance(36), based on previous work by Lorz and others which treats resistance as a continuous physiological variable(37).…”

Optimal treatment and stochastic modeling of heterogeneous tumors

“…Day computationally investigated relaxation of the symmetry assumptions and found that some non-alternating schedules could outperform the alternating schedule in that scenario [24]. In particular Day proposed a ‘worst drug first’ rule, this rule was investigated in further depth by Katouli and Komarova who considered a wide range of possible cyclic therapies [62]. In later works Murray and Coldman [72] and Coldman and Murray [20] extended the original model of Coldman and Goldie [19] to allow for toxicity constraints on normal tissues, simultaneous administration of multiple drugs, and included the possibility of inter-patient heterogeneity.…”