Population state-space modelling of patient responses in antidepressant studies
E. Marostica(1), A. Russu(1), G. De Nicolao(1), R. Gomeni(2)
(1) Department of Computer Engineering and Systems Science, University of Pavia, Pavia, Italy; (2) Pharmacometrics, GlaxoSmithKline, King of Prussia, PA, USA
Objectives: A major challenge posed by the analysis of the clinical scores used to assess the disease status in depression trials is the lack of "first principles" from which response models can be derived. The state-space framework, which is based on a set of differential (or difference) equations that describes the evolution of one or more variables characterizing the patient's health state [1], represents an appealing and more mechanistically driven approach to describe these data. In order to develop a comprehensive state-space approach, we address two main questions: (i) do state-space models give adequate descriptions of the clinical response? (ii) how should flexible dosing schedules be handled within a state-space framework?
Methods: A double-blind, randomized, placebo controlled, flexible dose depression trial was used as a benchmark for alternative state-space approaches. Discrete- and continuous-time stochastic processes (i.e. integrated random walks and integrated Wiener processes [2, 3]) were used to describe the time-course of the HAMD score, within the framework of population modelling. In particular, each individual curve was expressed as the sum of an average curve and an individual shift, both described as random processes whose statistics were specified through hyperparameters. Dose changes were modelled as impulses on the second derivative of the patient's score. According to an empirical Bayes paradigm, hyperparameters were estimated through Maximum Likelihood. Estimation and post-processing were carried out with R 2.10.0 [4].
Results: Even low-order discrete- and continuous-time state-space models were able to fit very satisfactorily the whole range of shapes observed in individual responses. Moreover, the explicit description of dose changes improved the performances in terms of residuals. The continuous-time model appears to be marginally superior to the discrete-time one.
Conclusions: The results demonstrate that state-space approaches not only provide adequate description of population responses but are also easily adapted to account for possible dose changes during the trial. Among the advantages, there is the possibility to model the presence of random perturbations that affect the patient's health state. A further step to explore is the development of an integrated response and dropout model within the state-space framework.
References:
[1] Russu A, Marostica E, De Nicolao G, Hooker AC, Poggesi I, Gomeni R, Zamuner S (2010), Integrated model for clinical response and dropout in depression trials: a state-space approach, Population Approach Group Europe (PAGE) 19th Meeting, Abstract 1852
[2] Magni P, Bellazzi R, De Nicolao G, Poggesi I, Rocchetti M (2002), Nonparametric AUC estimation in population studies with incomplete sampling: a Bayesian approach, Journal of Pharmacokinetics and Pharmacodynamics 29, pp. 445-471
[3] Neve M, De Nicolao G, Marchesi L (2007), Nonparametric identification of population models via Gaussian processes, Automatica 43, pp. 1134-1144
[4] R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2010).
