Estimation of human tumor growth rate from distribution of tumor size at detection

Methods are presented for estimating the growth curve of a tumor (up to an unknown scale factor of time) from the distribution of volumes at detection on the basis of two assumptions: 1) the existence of a common growth curve and 2) the assumption that the probability of detecting a tumor in a period of time is proportional to the tumor volume. These methods can accommodate variation between individuals in speed of traversal of the growth curve. The methods are applied to volumes of tumor at detection of a large series of breast cancers. The simplest, adequate description is exponential growth with great individual-to-individual variation in tumor doubling time. The data are consistent with bounded growth (Gompertzian or logistic form) as well as exponential growth. However, there is no evidence that the bound on growth is within the range of the data. The shape of the distribution of volumes does not yield an effective lower limit on such a bound.