Recently, the US Food and Drug Administration announced an initiative to reform the decades-old maximum-tolerable dose paradigm called Project Optimus. The initiative notes that dose selection schemes designed for cytotoxic therapies may not apply for targeted therapies with exposure-response curves that often plateau below maximum tolerable patient toxicity levels. We introduce a novel framework for guiding treatment scheduling based on the convexity (or its converse, concavity) of exposure-response curves. This framework is flexible and broadly applicable across a wide range of targeted therapies, but we provide analysis of response curves in vitro for a H3122 ALK-positive non-small cell lung cancer (NSCLC) cell line. Evolved-resistance lines are generally more concave, while treatment-naïve lines are more convex. Quantifying dose response curvature (e.g. a convex or concave shape) provides a direct prediction of continuous treatment, compared with high-dose / low-dose treatment. For example, if the exposure-response function is concave near a dose of ‘x’, continuous (daily) administration of x may be less effective response compared to a regimen that switches equally between 120% of x and 80% of x (every other day), even though both regimens use the same total drug. We hypothesized the existence of a critical point in the time-evolution of ALK-positive tumors where it is optimal to switch from continuous treatment to high-dose / low-dose to mitigate the onset of gradual resistance. Resistance to ALK inhibitors in vivo occurs gradually, as tumors acquire cooperating genetic and epigenetic adaptive changes. In this work, we construct a mathematical modeling framework of gradual resistance, parameterized to data, and predict time-dependent curvature in continuous (8 weeks), volatile (8 weeks) ALK inhibition in vivo. our key insight is that curvature increases in proportion to the amount of resistance in the tumor population. The framework provides a time-dependent metric which 1) predicts the emergence of resistance and 2) determines the optimal subsequent dosing strategy. We test our key hypothesis in vivo, comparing continuous and volatile treatment schedules of ALK inhibitors to a switching schedule of continuous-volatile (4 weeks each).