Phase I studies of weekly administration of cytotoxic agents: implications of a mathematical model

Certain toxic effects of cytotoxic anticancer agents typically evolve over weeks. When such agents are administered weekly, these effects are cumulative. With such schedules, good medical practice mandates dose modifications with mild or moderate toxicity in order to avoid progression to serious or life-threatening toxicity. These modifications lead to differences between scheduled and delivered doses. Phase I studies are designed to identify the maximum tolerated dose for a given schedule. Yet neither standard phase I study designs nor the theoretical literature acknowledge the existence or incorporate the impact of dose modifications upon phase I study outcomes. Our purpose was to better understand the impact of dose reductions/omissions upon outcomes of phase I studies of weekly administration of cytotoxic agents. We created a mathematical model in which toxicity was represented as a power function of dose in order to represent extremes of behavior observed with actual cytotoxic agents in the clinic. We used the model to simulate dosing and toxicity experiences across a wide range of doses. From these simulations we identified "best doses" according to a variety of traditional and novel criteria. We find the concept of maximum tolerated dose inadequate for the determination of best doses. We also suggest a strategy for a new phase I study design which can be used to estimate the "best dose" corresponding to a specified delivery rate. In summary, identification of best doses requires attention, not only to dose limiting toxic events, but also to delivered dose rates and schedule adherence.