A review on estimation of stochastic differential equations for pharmacokinetic/pharmacodynamic models

Abstract

This paper is a survey of existing estimation methods for pharmacokinetic/pharmacodynamic (PK/PD) models based on stochastic differential equations (SDEs). Most parametric estimation methods proposed for SDEs require high frequency data and are often poorly suited for PK/PD data which are usually sparse. Moreover, PK/PD experiments generally include not a single individual but a group of subjects, leading to a population estimation approach. This review concentrates on estimation methods which have been applied to PK/PD data, for SDEs observed with and without measurement noise, with a standard or a population approach. Besides, the adopted methodologies highly differ depending on the existence or not of an explicit transition density of the SDE solution.

Stochastic Modelling of Solution Particle Movement: An Individual Case of Coupled Concentration Gradient Dependent and Independent Movements of Efavirenz

“…The work has allowed for a proposition on the possibility to study the two movements in the 24 h dosing period that aid the process of diffusion by considering stochastic differential equations [5] [10]. It describes the movement of an interacting particle.…”

“…It has been noted that there is an increasing need to extend the deterministic models which are currently favoured to models including a stochastic component in modelling pharmacological processes [5].…”

“…This enables us to study the relationship between transport and self forms of diffusion. Stochastic coupled models have been applied on combined PK/PD processes [5]. In addition, in this case the coupling is in modelling the relationship of the two separate diffusional movements.…”

Parametric inference for stochastic differential equations with random effects in the drift coefficient

“…Statistical estimation of parameters in the diffusion processes has been studied for a long time; Feigin [8] provided a useful historical overview of the early studies and introduced a general asymptotic theory of maximum likelihood estimation for continuous diffusion processes. In the recent years, the stochastic differential equations with random effects have been considered in various works [9] Tornøe et al (2005) [10] Ditlevsen and De Gaetano (2005)) and have been the subject of various applications such as pharmacokinetic/pharmacodynamics, neuronal modeling and modeling of electrical circuits (Delattre and Lavelle 2013 [11], Klim, Søren [12],Christoffer [10] ,Donnet and Samson 2013 [13], Picchini et al 2010 [14], kampowsky and et al (1992)) [15].The problem of estimating parameters in SDE models is not straightforward, except in a simple cases. A natural approach would be likelihood inference, but the transition densities of the process are rarely known, and thus it is usually not possible to write the likelihood function explicitly.…”

Computational Modeling Under Uncertainty: Challenges and Opportunities

“…Furthermore, the profiles of those "other regulatory layers" are in most cases not available during modeling. A second explanation for uncertainty is the stochastic nature of some biological processes as shown in intra-cellular chemical reactions, gene expression (Magklara and Lomvardas, 2013) and pharmacokinetics (Donnet and Samson, 2013) among others. In both explanations, we need to clearly face uncertainty during the modeling, in the parameters of the model and in the biological processes when investigating model behaviors.…”