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

Journal article, 2013

ABSTRACT: BACKGROUND: When mathematical modelling is applied to many different application areas, a common task is the estimationof states and parameters based on measurements. With this kind of inference making, uncertainties in the timewhen the measurements have been taken are often neglected, but especially in applications taken from the lifesciences, this kind of errors can considerably influence the estimation results. As an example in the context ofpersonalized medicine, the model-based assessment of the effectiveness of drugs is becoming to play animportant 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 patientgroups becomes a major challenge. Particle filters are a promising approach to tackle these difficulties but areby itself not ready to handle uncertainties in measurement times. RESULTS: In this article, we describe a variant of the standard particle filter (PF) algorithm which allows state andparameter estimation with the inclusion of measurement time uncertainties (MTU). The modified particlefilter, which we call MTU-PF, also allows the application of an adaptive stepsize choice in the time-continuouscase to avoid degeneracy problems. The modification is based on the model assumption of uncertainmeasurement times. While the assumption of randomness in the measurements themselves is common, thecorresponding measurement times are generally taken as deterministic and exactly known. Especially in caseswhere the data are gained from measurements on blood or tissue samples, a relatively high uncertainty in thetrue measurement time seems to be a natural assumption. Our method is appropriate in cases where relativelyfew data are used from a relatively large number of groups or individuals, which introduce mixed effects in themodel. This is a typical setting of clinical studies. We demonstrate the method on a small artificial exampleand apply it to a mixed effects model of plasma-leucine kinetics with data from a clinical study which included34 patients. CONCLUSIONS: MTU-PF with the standard PF and with an alternative Maximum Likelihood estimationmethod on the small artificial example clearly show that the MTU-PF obtains better estimations. Consideringthe application to the data from the clinical study, the MTU-PF shows a similar performance with respect tothe quality of estimated parameters compared with the standard particle filter, but besides that, the MTUalgorithm shows to be less prone to degeneration than the standard particle filter. KEYWORDS: particle filter, sequential.