A model-based framework for assessing schedule dependence of therapeutic window for three-drug combinations
Authors: Yuan Lin , Stoddard Madison , Chen Andrew , Bottino Dean , Chakravarty Arijit 
Published: February 2025

OBJECTIVES: Combination therapies hold great promise in the management of adversarial diseases such as cancer and infectious diseases, but they are limited in their potential by drug tolerability. A systematic evaluation of the impact of dose scheduling on the therapeutic window of combination therapies can provide valuable insights into their design. Here we present a simplified quantitative systems pharmacology framework for the assessment of schedule dependence for combination therapies that can provide a basis for the rigorous assessment of such combinations, focused on cancer as a motivating example.METHODS: We used a simplified tumor dynamics model with subpopulations of cancer cells being resistant to none, one, two or three drugs in all possible combinations. Tumor dynamics were simulated based on an exponential growth model that suffered growth penalties dependent on the drug concentrations [1]. To determine the effect of a three-drug combination on tumor growth, we simulated the concentrations of three drugs using a one-compartment pharmacokinetic model. Final tumor volume and peak toxicity were used to compare the effectiveness of various dosing strategies and interaction combinations. For the toxicity constraint, we simulated a neutropenia-like toxicity for all three drugs (which we have previously shown to be proportional to the peak moving average of drug concentrations over 18 days [2]).RESULTS: Our model suggests that the impact of drug synergy and antagonism are strongest when drugs are dosed synchronously. In particular, simultaneously dosing three drugs with overlapping toxicities is vulnerable to the extent of (undesirable) synergy in their toxicities. The time-sensitivity— that is, the magnitude of the changes in efficacy associated with small changes in schedule— varies with phase offset of drug dosing. On the flip side, dosing completely asynchronously in our model provides the greater opportunity for the emergence of resistant populations. A potential compromise is the simultaneous dosing of two of the three drugs, which results in an intermediate toxicity. CONCLUSIONS: Our work provides a generalized framework for the design of three-drug combinations that can readily be extended to the optimization of specific drug combinations. At the same time, the model provides some fundamental strategic insights about multi-drug combinations. First, the degree of synergy for efficacy and toxicity play a strong role in feasibility. Second, the toxicity constraint will limit the feasibility of effective disease control for many multidrug combinations. Third, drugs that are strongly synergistic in their efficacy may be highly time-sensitive in their dosing, which can be impractical in a clinical setting. Finally, striking a balance between efficacy and toxicity may be easier to achieve for drugs that have independent effect on efficacy (additive), but have non-overlapping toxicity profiles. Citations: 1. Bottino D, Chakravarty A. (2016) Modeling Tumor Growth in Animals and Humans: An Evolutionary Approach. In: Bonate P., Howard D. (eds) Pharmacokinetics in Drug Development. Springer, Cham. https://doi.org/10.1007/978-3-319-39053-6_11.2. Patel M, Palani S, Chakravarty A, Yang J, Shyu WC, Mettetal JT. Dose schedule optimization and the pharmacokinetic driver of neutropenia. PLoS One. 2014 Oct 31;9(10):e109892. doi: 10.1371/journal.pone.0109892. PMID: 25360756; PMCID: PMC4215876.