Stochastic differential equation mixed effects models for tumor growth and response to treatment

This paper aim at modeling the growth dynamics underlying the repeated measurements of tumor volumes in mice obtained from a tumor xenography study. We consider a two compartments representation corresponding to the fractions of tumor cells that have been killed by the treatment and survived it, respectively. Growth and elimination dynamics are modeled with stochastic differential equations. This results in a new biologically plausible stochastic differential equation mixed effects model (SDEMEM) for response to treatment and regrowth. Inference for SDEMEMs is notoriously challenging due to the intractable likelihood function. Methods for exact and approximate Bayesian inference for the model parameters are discussed. As a case study we consider experimental data from two treatment groups and one control, each consisting of 7-8 mice. We were able to estimate the model parameters, using both an exact Bayesian method (pseudo marginal approach, using sequential Monte Carlo) and an approximate method using the synthetic likelihoods approach. We believe this is the first application of synthetic likelihoods to SDEMEMs. Consistently for both methods, our model is able to identify a specific treatment to be the most effective in delaying tumor growth.