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

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 introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and 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.Author summary: Nonlinear mixed effects (NLME) models are widely used to model differences between individuals in a population. In pharmacology, for example, they are used to model the treatment response variability across patients, and in cell biology they are used to model the cell-to-cell variability in cell signalling pathways. However, NLME models introduce parameters, which typically need to be estimated from data. This estimation becomes computationally intractable when the number of measured individuals—be they patients or cells—is too large. But, the more individuals are measured in a population, the better the variability can be understood. This is especially true when individuals are measured only once. Such snapshot measurements are particularly common in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. In clinical pharmacology, datasets consisting of many snapshot measurements are less common but are easier and cheaper to obtain than detailed time series measurements across patients. Our approach can be used to estimate the parameters of NLME models from snapshot time series data with thousands of measured individuals.