Inferring the effect of therapies on tumor growth by using diffusion processes

Modeling the effect of therapies in cancer animal models remains a challenge. This point may be addressed by considering a diffusion process that models the tumor growth and a modified process that includes, in its infinitesimal mean, a time function modeling the effect of the therapy. In the case of a Gompertz diffusion process, where a control group and one or more treated groups are examined, a methodology to estimate this function has been proposed by Albano et al. (2011). This method has been applied to infer the effect of cisplatin and doxorubicin+cyclophosphamide on breast cancer xenografts. Although this methodology can be extended to other diffusion processes, it has an important restriction: it is necessary that a known diffusion process adequately fits the control group. Here, we propose the use of a stochastic process for a hypothetical control group, in such a way that both the control and the treated groups can be modeled by modified processes of the former. Thus, the comparison between models would allow estimating the real effect of the therapy. The new methodology has been validated by inferring the effects in breast cancer models, and we have checked the robustness of the procedure against the choice of stochastic model for the hypothetical control group. Finally, we have also applied the methodology to infer the effect of a therapeutic peptide and ovariectomy on the growth of a breast cancer xenograft, and its efficiency in modeling the effect of different treatments in the absence of control group data is shown.