Raising the bar during early immunotherapy for cancer: simple mathematical models may help distinguish temporary vs. ultimate progression

Background: The apparent success of immunotherapy depends on the duration of follow up, sometimes with little evidence of efficacy during the first 4 to 8 months and often some degree of “pseudoprogression”. Differentiating transient pseudoprogression from true progression that would require a change in therapy can be challenging. The present study uses mathematical modeling and simulation to account for the unique kinetics and delayed clinical effects of immunotherapy and suggests improved approaches to predict efficacy and patient response from imaging studies. Methods: A mathematical model of tumor cell-immunocyte interaction is exercised to simulate a large number of individual patients and to derive surrogate endpoints for success or failure from the ratio of tumor diameter at 2, 4, 6, 8, 10, or 12 months follow up to initial tumor diameter. The simplified predator-prey model includes 4 lumped parameters: net tumor growth rate, g; immune cell killing efficiency, k; immune cell signaling, ; and immune cell half-life decay, μ. Differential equations, dT/dt = gT – kL and dL/dt = LT – μL, for numbers of tumor cells, T, (the prey) and immunocytes, L, (the predators) are solved numerically as functions of time, t , with ranges of g, k, , and initial conditions estimated from clinically available data. Tumor diameters, d, are proportional to the cube root of T + L. Apparent progression is defined when the time-varying diameter ratio, d/d0, exceeds a pre-defined, adjustable threshold. True progression is defined as d/d0 \u3e 1 at 24 months follow up or T/T0 \u3e 10 at any time. Results: Depending on initial conditions, the model equations predict either simple or complex dynamics, including cyclic increases in tumor cell numbers prior to a population crash to zero, apparent cure with late recurrence, and better long-term outcome with initially smaller lymphocyte numbers. Simulations of 4000 such complex cases show that d/d0 \u3e 1.0 at 2 to 6 months is a poor predictor of true progression, and often signals pseudoprogression. However, raising the bar or threshold for defining progressive disease from d/d0 \u3e 1.0 to d/d0 \u3e 2.0 during the first 6 months of immunotherapy and lowering the bar to d/d0 \u3e 0.5 after 6 months can eliminate most instances of pseudoprogression and lead to better over-all outcomes. Conclusions: Mathematical models can account for the complex dynamics of immune-tumor cell interactions that make accurate clinical decisions to continue or discontinue treatment difficult. The present model and approach can be adapted and calibrated to data for different types and stages of cancer and help to optimize treatment success