Bayesian inference for stochastic differential equation mixed effects models of a tumor xenography study

We model the growth dynamics of 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 new state-space stochastic differential equation mixed effects models (SDEMEM) for response to treatment and regrowth. We considered Bayesian inference for model parameters, using both exact methodology based on sequential Monte Carlo and an approximate one using synthetic likelihoods. A case study considers data from a tumor xenography study with two treatment groups and one control, each containing 5-8 mice. Results from the case study and from a simulation study show that our models are able to reproduce the observed growth patterns and that Bayesian synthetic likelihoods perform similarly to exact Bayesian inference. This opens up possibilities to study SDEMEMs that are not restricted to state-space models. With the small sample sizes as in the case study, prior information is needed to identify all model parameters, while in simulations with a larger sample of 17 mice per group unidentifiability is no longer an issue.