Our method of analysis

In the treatment of cancer, one often observes an initial reduction in the amount of tumor, followed by growth as the fraction of the tumor initially fully or partially resistant to the therapy grows in size. Although to the clinician this appears as one continuum, in fact what one observes clinically is the result of two process that are occurring simultaneously – regression of the fraction of tumor that is sensitive to the therapy being administered which is gradually dying and growth of the fraction of tumor that is either fully or partially resistant to the administered therapy.

At any point during treatment, the quantity of tumor that is observed is the sum of these two fractions, whose quantity is changing over time, with gradual decrease in the quantity that is drug sensitive and incremental increases in the fraction that is resistant to the treatment. Both processes are exponential in their behavior and in the majority of cases occur at a constant rate. As these processes usually occur at constant rates, using data collected as the therapy is administered one is able to estimate the rate of regression of the fraction that is sensitive to the therapy being administered – a rate we have designated d for decay rate - and likewise estimate the rate of growth of the fully or partially resistant fraction – a rate we refer to as g for growth rate. Because the fraction that is sensitive to the therapy being administered will disappear it is not surprising that the rate at which disappearance occurs has little if any impact on the overall survival of the patient. However, the rate at which the resistant fraction is growing has been shown time and again across many different tumor types and all types of therapies (chemotherapy, targeted therapy, and immunotherapy) to correlate strongly with overall survival.

In the care of individuals with a diagnosis of cancer our method of analysis has two important attributes:

1. the rate of tumor growth (g) correlates strongly with overall survival and can be used to estimate a tumor’s doubling time;
2. because the mathematical equations used to estimate the rates of growth (g) and regression (d) include time as a variable, the intervals of assessment become irrelevant, an attribute that makes our approach ideal for real world analyses, given the often wide differences in intervals of assessment.