Filter inference: A scalable nonlinear mixed effects inference approach for snapshot time series data

Abstract

Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We extend earlier work by Hasenauer et al (2011) to introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference is a new variant of approximate Bayesian computation, with dominant computational costs that do not increase with the number of measured individuals, making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms, such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.

Competing Interest Statement

KW and ACW are employees and shareholders of F. Hoffmann-La Roche Ltd.

Footnotes

* https://github.com/DavAug/filter-inference