Costing ‘the’ MTD … in 2-D

Abstract

ABSTRACTBackgroundI have previously evaluated the efficiency of one-size-fits-all dosing for single agents in oncology (Norris 2017b). By means of a generic argument based on an Emax-type dose-response model, I showed that one-size-fits-all dosing may roughly halve a drug’s value to society. Since much of the past decade’s ‘innovation’ in oncology dose-finding methodology has involved the development of special methods for combination therapies, a generalization of my earlier investigations to combination dosing seems called-for.MethodsFundamental to my earlier work was the premise that optimal dose is a characteristic of each individual patient, distributed across the population like any other physiologic characteristic such as height. I generalize that principle here to the 2-dimensional setting of combination dosing with drugs A and B, using a copula to build a bivariate joint distribution of (MTDi,A, MTDi,B) from single-agent marginal densities of MTDi,A and MTDi,B, and interpolating ‘toxicity isocontours’ in the (a, b)-plane between the respective monotherapy intercepts. Within this framework, three distinct notional toxicities are elaborated: one specific to drug A, a second specific to drug B, and a third ‘nonspecific’ toxicity clinically attributable to either drug. The dose-response model of (Norris 2017b) is also generalized to this 2-D scenario, with the addition of an interaction term to provide for a complementary effect from combination dosing. A population of 1,000 patients is simulated, and used as a basis to evaluate population-level efficacy of two pragmatic dose-finding designs: a dose-titration method that maximizes dose-intensity subject to tolerability, and the well-known POCRM method for 1-size-fits-all combination-dose finding. Hypothetical ‘oracular’ methods are also evaluated, to define theoretical upper limits of performance for individualized and 1-size-fits-all dosing respectively.ResultsIn our simulation, pragmatic titration attains 89% efficiency relative to theoretically optimal individualized dosing, whereas POCRM attains only 55% efficiency. The passage from oracular individualized dosing to oracular 1-size-fits-all dosing incurs an efficiency loss of 33%, while the parallel passage (within the ‘pragmatic’ realm) from titration to POCRM incurs a loss of 38%.ConclusionsIn light of the 33% figure above, the greater part of POCRM’s 38% efficiency loss relative to titration appears attributable to POCRM’s 1-size-fits-all nature, rather than to any pragmatic difficulties it confronts. Thus, appeals to pragmatic considerations would seem neither to justify the decision to use 1-size-fits-all dose-finding designs, nor to excuse their inefficiencies