On estimating the growth function of tumors

Abstract The growth rate of a cancerous tumor as a function of its age is a subject of intellectual and practical importance, as it influences both the effectiveness of proposed screening programs and the strategy of treatment. Obtaining direct evidence on the growth rate is quite difficult, owing to the ethical necessity to intervene when cancer is confirmed. The reasonable assumption that there is a common growth function of age and that probability of detection of a tumor in a short time period is proportional to its size allow the growth function to be inferred from data on sizes at detection. These results can be generalized to allow for individual variation in the rate of traversal of the common growth function. An estimator for the growth function from data on size at detection is obtained. Simulations indicate that it performs reasonably. Application of this estimator to data on a large series of cases of breast cancer at U.T. M. D. Anderson Hospital indicates that the growth function in the range of sizes seen at detection, can be adequately described by exponential growth, with rather large individual-to-individual variations in growth rate.