Abstract We present a novel paradigm of evolutionary cancer therapy based on the “antifragility” of the drug dose-response function. Antifragility is the word originally coined to describe the opposite of fragility. Systems or organisms can be described as antifragile if they derive a benefit from systemic variability, volatility, randomness, or disorder. In this work, we quantify the evolutionary and ecological benefit (or harm) derived from increasing dose volatility in treatment scheduling. Nonlinear sigmoidal dose-response curves are ubiquitous in medicine and have both convex and concave regions. Despite the ubiquity of dose response assays in biological sciences, these curves are typically used to measure differential response in first-order effects (mean value of drug dose delivered), while second-order effects (variance of drug dose) are generally ignored. Analysis of the convexity of dose response curves provides a direct prediction of response to continuous treatment (“even” schedules with zero volatility) in comparison to high-dose/low-dose treatment (“uneven” schedules with high volatility). For example, if the dose response function is antifragile (concave) near a dose of ‘x’, continuous administration of x may have a less efficacious response compared to a regimen that switches equally between 120% of x and 80% of x, even though both regimens use the same total drug. Mathematical analysis of dose response curves in vitro for a H3122 ALK-positive non-small cell lung cancer (NSCLC) cell line predicts that evolved-resistance cell lines can be more effectively treated using volatile treatment scheduling regimens, while treatment-naïve cell lines are most effectively treated by continuous treatment. However, selection pressure due to treatment selects for resistant phenotypes over time. We construct a mathematical model of gradual resistance, parameterized to data, and predict time-dependent antifragility in continuous (8 weeks), volatile (8 weeks) ALK inhibition in vivo. The key insight is that dose-response concavity (“anti-fragility”) increases in proportion to the amount of resistance in the tumor population. Antifragility provides a time-dependent metric which 1) predicts the emergence of resistance and 2) determines the optimal subsequent dosing strategy. Previous work indicates that resistance to ALK inhibitors occurs gradually, through the acquisition of multiple cooperating genetic and epigenetic adaptive changes. This observation led us to hypothesize that there is a critical point in the evolution of ALK-positive tumors where it is optimal to switch from continuous treatment to volatile dosing to optimally control the onset of gradual resistance. This hypothesis is also tested in vivo, comparing continuous and volatile treatment schedules of ALK inhibitors to a switching schedule of continuous-volatile (4 weeks each). We end by discussing the implications for adaptive therapy. Citation Format: Jeffrey West, Bina Desai, Maximilian Strobl, Luke Pierik, Richard Miles, Cole Armagost, Mark Robertson-Tessi, Andriy Marusyk, Alexander R. A. Anderson. Antifragile therapy [abstract]. In: Proceedings of the AACR Special Conference on the Evolutionary Dynamics in Carcinogenesis and Response to Therapy; 2022 Mar 14-17. Philadelphia (PA): AACR; Cancer Res 2022;82(10 Suppl):Abstract nr B025.