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

TL;DR

This paper explores Bayesian methods for fitting stochastic differential equation mixed effects models to tumor growth data, demonstrating the robustness of Bayesian synthetic likelihoods and comparing them to exact inference methods.

Contribution

It introduces and compares exact and approximate Bayesian inference techniques for SDEMEMs in tumor studies, highlighting BSL's effectiveness with small sample sizes.

Findings

BSL is robust for inference in SDEMEMs.

SDEMEM can reproduce tumor growth patterns.

Small sample sizes require strong priors for parameter identification.

Abstract

We consider Bayesian inference for stochastic differential equation mixed effects models (SDEMEMs) exemplifying tumor response to treatment and regrowth in mice. We produce an extensive study on how a SDEMEM can be fitted using both exact inference based on pseudo-marginal MCMC and approximate inference via Bayesian synthetic likelihoods (BSL). We investigate a two-compartments SDEMEM, these corresponding to the fractions of tumor cells killed by and survived to a treatment, respectively. Case study data considers a tumor xenography study with two treatment groups and one control, each containing 5-8 mice. Results from the case study and from simulations indicate that the SDEMEM is able to reproduce the observed growth patterns and that BSL is a robust tool for inference in SDEMEMs. Finally, we compare the fit of the SDEMEM to a similar ordinary differential equation model. Due to small sample sizes, strong prior information is needed to identify all model parameters in the SDEMEM and it cannot be determined which of the two models is the better in terms of predicting tumor growth curves. In a simulation study we find that with a sample of 17 mice per group BSL is able to identify all model parameters and distinguish treatment groups.