Costing ‘the’ MTD
Authors: Norris David C. 
Published: June 2017

Background:

Absent adaptive, individualized dose-finding in early-phase oncology trials, subsequent registration trials risk suboptimal dosing that compromises statistical power and lowers the probability of technical success (PTS) for the investigational drug. While much methodological progress has been made toward adaptive dose-finding, and quantitative modeling of dose-response relationships, most such work continues to be organized around a concept of ‘the’ maximum tolerated dose (MTD). But a new methodology, Dose Titration Algorithm Tuning (DTAT), now holds forth the promise ofindividualized‘MTDi’ dosing. Relative to such individualized dosing, current ‘one-size-fits-all’ dosing practices amount to aconstraintthat imposescostson society. This paper estimates the magnitude of these costs.

Methods:

Simulated dose titration as in (Norris 2017) is extended to 1000 subjects, yielding an empirical MTDidistribution to which a gamma density is fitted. Individual-level efficacy, in terms of the probability of achieving remission, is assumed to be an Emax-type function ofdose relative to MTDi, scaled (arbitrarily) to identify MTDiwith the LD50of the individual’s tumor. (Thus, a criterion 50% of the population achieve remission under individualized dosing in this analysis.) Current practice is modeled such that all patients receive a first-cycle dose at ‘the’ MTD, and those for whom MTDi< MTDtheexperience a ‘dose-limiting toxicity’ (DLT) that aborts subsequent cycles. Therapy thus terminated is assumed to confer no benefit. Individuals for whom MTDi≥MTDthetolerate a full treatment course, and achieve remission with probability determined by the Emaxcurve evaluated at MTDthe/MTDi. A closed-form expression is obtained for the population remission rate, and maximized numerically over MTDtheas a free parameter, thus identifying the best result achievable under one-size-fits-all dosing. A sensitivity analysis is performed, using both a perturbation of the assumed Emax function, and an antipodal alternative specification.

Results:

Simulated MTDifollow a gamma distribution with shape parameterα ≈1.75. The population remission rate under one-size-fits-all dosing at the maximizing value of MTDtheproves to be a function of the shape parameter—and thus the coefficient of variation (CV)—of the gamma distribution of MTDi. Within a plausible range of CV(MTDi), one-size-fits-all dosing wastes approximately half of the drug’s population-level efficacy. In the sensitivity analysis, sensitivity to the perturbation proves to be of second order. The alternative exposure-efficacy specification likewise leaves all results intact.

Conclusions:

The CV of MTDidetermines the efficacy lost under one-size-fits-all dosing at ‘the’ MTD. Within plausible ranges for this CV, failure to individualize dosing can effectively halve a drug’s value to society. In a competitive environment dominated by regulatory hurdles, this may reduce the value of shareholders’ investment in the drug tozero.

Epilogue:

The main result on one-size-fits-all dosing is generalized to regimens with several dose levels. Implications for the ongoing ALTA-1L trial are briefly explored; the 2 dose levels in the brigatinib arm of this trial may lend it a competitive advantage over the single-dose crizotinib arm.