Tumor growth velocities inferred from survival analysis: Linking microscopic tumor dynamics to cancer prognosis

Harold de Vladar

Laboratorio de Estructura Molecular, Instituto de Estudios Avanzados, Apartado Postal 17606, Parque Central, Caracas 1015-A, Venezuela

Microscopic tumors play an important role in the prognosis of cancer. They are the ultimate cause for cancer recidivism and drug resistance, and a target for immunological sculpting. However, the detection of several-cell-size tumors is very complicated and not viable for routine tests. In this work we develop a mathematical model based on the Gompertz equation and a statistical technique that permits the estimation of the distribution of growth rates of tumors from empirical survival curves. The model considers that a treatment of constant intensity or dose of radio or chemotherapy has been administered to the patient, a feature not previously included in other survival models. Resampling the survival curves and employing our model we are able to determine the distribution of the growth rate of microscopic tumors for a given cohort. The results give plausible explanations of cancer recidivism, some aspects of drug resistance, and they also explain the shapes of the survival curves. We also discuss our findings in terms of drug selection for cancer treatments.