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

We model the growth dynamics for repeated measurements of tumor volumes in mice. We consider a two compartments representation corresponding to the fractions of tumor cells killed by and survived to a treatment, respectively. Dynamics are modelled with stochastic differential equations, resulting in a new state-space stochastic differential equation mixed effects model (SDEMEM) for response to treatment and regrowth. Inference for SDEMEMs is challenging due to the intractable likelihood function. We were able to estimate the model parameters, using both exact Bayesian methodology and an approximate method using the synthetic likelihoods approach. As a case study we consider data from two treatment groups and one control from a tumor xenography study, each consisting of 7-8 mice. Results from the case study and from a further simulation study shows that our models are able to reproduce the observed patterns and that Bayesian synthetic likelihoods is a reliable inference tool for SDEMEMs.