Conferencias
Patrick Borges
Universidade Federal do Espírito Santo, Brazil
Certain well-studied stochastic processes are available for representing the dynamics of tumor growth. In the simplest case, the tumor growth can be assumed to obey the postulates of a linear birth-and-death process with two absorbing states. The lower barrier corresponds to extinction of the process, whereas the upper barrier, N , is interpreted, depending on the application, either as the size of a detectable tumor or as the tumor size responsible for death of the organism. It takes a random time for resistant tumor cells to increase their numbers up to a value of N . In this paper we proposed a cure rate survival model based on the following premises: the kinetics of tumor growth after treatment is deterministic and described by a generalized growth function; the initial number, n, and the threshold number, N , of tumor cells are r.v.'s with their ratio, K = n/N , obeying a exponentiated Kumaraswamy distribution. This model provides a realistic interpretation of the biological mechanism of the event of interest, as it models a variety of tumor growth patterns. Parameter estimation of the proposed model is then discussed through the maximum likelihood estimation procedure. Finally, we illustrate the usefulness of the model by applying it to real dataset.
