A continuous-time adaptive particle filter for estimations under measurement time uncertainties with an application to a plasma-leucine mixed effects model

Abstract

BackgroundWhen mathematical modelling is applied to many different application areas, a common task is the estimation of states and parameters based on measurements. With this kind of inference making, uncertainties in the time when the measurements have been taken are often neglected, but especially in applications taken from the life sciences, this kind of errors can considerably influence the estimation results. As an example in the context of personalized medicine, the model-based assessment of the effectiveness of drugs is becoming to play an important role. Systems biology may help here by providing good pharmacokinetic and pharmacodynamic (PK/PD) models. Inference on these systems based on data gained from clinical studies with several patient groups becomes a major challenge. Particle filters are a promising approach to tackle these difficulties but are by itself not ready to handle uncertainties in measurement times.ResultsIn this article, we describe a variant of the standard particle filter (PF) algorithm which allows state and parameter estimation with the inclusion of measurement time uncertainties (MTU). The modified particle filter, which we call MTU-PF, also allows the application of an adaptive stepsize choice in the time-continuous case to avoid degeneracy problems. The modification is based on the model assumption of uncertain measurement times. While the assumption of randomness in the measurements themselves is common, the corresponding measurement times are generally taken as deterministic and exactly known. Especially in cases where the data are gained from measurements on blood or tissue samples, a relatively high uncertainty in the true measurement time seems to be a natural assumption. Our method is appropriate in cases where relatively few data are used from a relatively large number of groups or individuals, which introduce mixed effects in the model. This is a typical setting of clinical studies. We demonstrate the method on a small artificial example and apply it to a mixed effects model of plasma-leucine kinetics with data from a clinical study which included 34 patients.ConclusionsComparisons of our MTU-PF with the standard PF and with an alternative Maximum Likelihood estimation method on the small artificial example clearly show that the MTU-PF obtains better estimations. Considering the application to the data from the clinical study, the MTU-PF shows a similar performance with respect to the quality of estimated parameters compared with the standard particle filter, but besides that, the MTU algorithm shows to be less prone to degeneration than the standard particle filter.

Exact Gradients Improve Parameter Estimation in Nonlinear Mixed Effects Models with Stochastic Dynamics

“…The linear dependency of the standard deviation on q can be reasoned directly from Eqs. (17) and (18), by assuming a numerical error term in relation to each calculation of the function value that is independent of the step size. The forward finite difference gradient Δf/Δθ k can be written as…”

“…Nevertheless, some attempts to develop methods for parameter estimation in NLME models with stochastic dynamics have been successful, using for example (i) Bayesian inference (9,10), (ii) expectation maximization (EM) methods (11)(12)(13), and (iii) by expanding the traditional gradient-based estimation methods using Kalman filters (14,15). These methods have been used for several PK/PD applications (16)(17)(18)(19). This paper focuses on gradient-based methods.…”

Inference of protein-protein interaction networks from multiple heterogeneous data

“…However, with no first principles to tell deterministically yet if two given proteins interact or not, the pair-wise biological similarity based on various features and attributes can run out its predictive power, as often the signals may be too weak or noisy. Therefore, recently, many researches have been focused on integrating heterogeneous pair-wise features, e.g., genomic features, semantic similarities, in seek of better prediction accuracy [ 8 – 11 ]. It is biologically meaningful if we can disentangle the relations among various pair-wise biological similarities and PPIs, but it is still in early stage for the incomplete and noisy pair-wise similarity kernels.…”