2012 - Venice - Italy

PAGE 2012: Estimation Methods
Marc Lavielle

On the use of stochastic differential mixed effects models for modeling inter occasion variability. Models and methods

M. Lavielle (1), M. Delattre (1)

(1) Inria Saclay, France

Objectives: One objective of WP6.4 of the DDMoRe project is to develop new methods for complex NLMEM. We consider here stochastic differential mixed-effects models used for describing intra-subject variability of certain PK parameters.

Methods: A commonly used model for describing intra-subject variability of PK parameters assumes that each individual parameter is piecewise-constant over time and can randomly change between occasions. This Inter Occasion Variability model does not really make sense biologically if we consider short consecutive periods, since it allows discontinuities in PK parameters. Nevertheless, we show that a SDE model is the limit of the IOV model when the length of each period tends to 0 and with an appropriate autocorrelation structure which ensures the continuity of the process.
In this model, some PK parameters are random processes described with SDEs. We propose different volatility models that respect biological constraints.
In a mixed effects context, the SAEM algorithm and the Extended Kalman Filter (EKF) can be efficiently combined for estimating the population parameters of the model. EKF can also be combined with an Importance Sampling Monte Carlo procedure for estimating the likelihood function.

Results: We investigated the properties of the proposed method through simulations. The model used for the simulations is an IV bolus model with an elimination rate process k(t) defined as a stochastic process.
First, we show that the proposed model faithfully mimics biological dynamics. Indeed, even if the elimination rate process is extremely erratic (which is biologically relevant), the random fluctuations of the concentration profile are smooth and satisfactorily describe real PK profiles.
The statistical issues are twofold: recovering the dynamics of the system and estimating the population parameters. Numerical results confirm what we would expect: i) the dynamics of the system are correctly recovered with rich data. On the other hand, it becomes extremely difficult to distinguish the random fluctuations of the dynamical system from the residual error when the data is sparse, ii) the accuracy of the population parameters estimate depends on the number of subjects.

Conclusions: We have shown that stochastic differential mixed-effects models can satisfactorily model the inter occasion variability of PK parameters. The use of the Extended Kalman Filter allowed us to efficiently develop several extensions of methods used for NLMEM.

Acknowledgements: The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreement n° 115156, resources of which are composed of financial contributions from the European Union's Seventh Framework Programme (FP7/2007-2013) and EFPIA companies' kind contribution. The DDMoRe project is also financially supported by contributions from Academic and SME partners.

References:
[1] C. W. Tornøe, R.V. Overgaard, H. Agersø, H. A. Nielsen, H. Madsen, E. N. Jonsson, "Stochastic Differential Equations in NONMEM: Implementation, Application,and Comparison with Ordinary Differential Equations", Pharmaceutical Research, Vol. 22, No. 8, 2005.
[2] S. Mortensen, S. Klim, B. Dammann, N. Kristensen, H. Madsen, R. Overgaard, "A Matlab framework for estimation of NLME models using stochastic differential equations", Journal of Pharmacokinetics and Pharmacodynamics  vol:34, pages: 623-642, 2007.
[3] S. Ditlevsen, A. De Gaetano, "Mixed Effects in Stochastic Differential Equation Models", REVSTAT - Statistical Journal, Vol. 3, No. 2, 137-153, 2005.




Reference: PAGE 21 (2012) Abstr 2372 [www.page-meeting.org/?abstract=2372]
Poster: Estimation Methods
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