Particle Methods for Stochastic Differential Equation Mixed Effects Models

Stochastic differential equation mixed effects models (SDEMEMs) are increasingly used in biomedical research as they are able to accurately capture changes in biological processes (e.g. the absorption of a drug) over time and across multiple subjects or individuals.

In this work, we consider the growth of tumor volumes in a group of mice. The applied SDEMEM allows for daily fluctuations in the size of the tumors, which more closely resembles what is seen in practice. It also accounts for influential differences between the mice, e.g. genetics, immune system, deficiencies etc. 

While flexible, these models are computationally expensive, which greatly complicates their parameter estimation (i.e. calibration of the model to a particular dataset). Relatively few methods exist, and many of these impose unrealistic constraints on the model, which greatly limits their potential use in practice. 

Lead by Imke Botha, the ACEMS team from QUT and UNSW introduce three novel parameter estimation methods for SDEMEMs. The introduced methods are accurate, flexible and impose very few restrictions on the model.