Estimating and determining the effect of a therapy on tumor dynamics by means of a modified Gompertz diffusion process

A modified Gompertz diffusion process is considered to model tumor dynamics. The infinitesimal mean of this process includes non-homogeneous terms describing the effect of therapy treatments able to modify the natural growth rate of the process. Specifically, therapies with an effect on cell growth and/or cell death are assumed to modify the birth and death parameters of the process. This paper proposes a methodology to estimate the time-dependent functions representing the effect of a therapy when one of the functions is known or can be previously estimated. This is the case of therapies that are jointly applied, when experimental data are available from either an untreated control group or from groups treated with single and combined therapies. Moreover, this procedure allows us to establish the nature (or, at least, the prevalent effect) of a single therapy in vivo. To accomplish this, we suggest a criterion based on the Kullback-Leibler divergence (or relative entropy). Some simulation studies are performed and an application to real data is presented.