  We consider a non homogeneous Gompertz diffusion process whose parameters are
modified by generally time-dependent exogenous factors included in the
infinitesimal moments. The proposed model is able to describe tumor dynamics
under the effect of anti-proliferative and/or cell death-induced therapies. We
assume that such therapies can modify also the infinitesimal variance of the
diffusion process. An estimation procedure, based on a control group and two
treated groups, is proposed to infer the model by estimating the constant
parameters and the time-dependent terms. Moreover, several concatenated
hypothesis tests are considered in order to confirm or reject the need to
include time-dependent functions in the infinitesimal moments. Simulations are
provided to evaluate the efficiency of the suggested procedures and to validate
the testing hypothesis. Finally, an application to real data is considered.
