Objectives: Longitudinal models describing the time course of the clinical endpoint in psychiatric trials are usually empirical. Moreover, conditional on the individual parameters the response model does not structurally account for random fluctuations on the disease. The first attempt to include these aspects, presented in [1] resorting to stochastic difference and differential equations, did not give a completely satisfactory description of inter-individual variability. We propose an extension of the previous work through a more sophisticated continuous-time dynamic model based on second order Markov processes [2]. The proposed model aims to describe appropriately the clinical response and handle flexible dosing schemes. Methods: A Phase II, double-blind, randomized, placebo-controlled, flexible-dose depression trial was analyzed. We modelled the individual time series of HAMD scores within the framework of population modelling. The typical curve was modelled as an integrated Wiener process [3] whereas a second order Markov model was adopted to describe the individual shifts with respect to the population curve. Two Markov models were analyzed having either (i) two coincident poles or (ii) two distinct poles in the transfer function. Dose changes were accounted for by varying the trend of the response profile. Models statistics were specified through hyperparameters. A unique hyperparameter for the measurement error was considered in order to simultaneously identify the model on the four subpopulations (placebo and drug: non-escalating and escalating subjects). Software R 2.10.0 [4] was adopted according to the empirical Bayes paradigm. Results: Both models were able to capture the shapes of individual responses. Moreover, good predictive performances in terms of VPCs were obtained. According to the Bayesian Information Criterion, the second order Markov model with two coincident poles in the transfer function should be preferred. Conclusions: The results demonstrate the feasibility and effectiveness of second order Markov processes as an innovative modelling approach for longitudinal data, when mechanistic knowledge is poor or absent. We showed that the proposed models yield good individual fittings as well as a good estimate of the population response and an appropriate representation of the inter-individual variability. Interestingly, both models are able to easily handle dose changes and account for random perturbations with greater flexibility than previous approaches [1]. References: [1] Marostica E, Russu A, De Nicolao G, Gomeni R (2011), Population state-space modelling of patient responses in antidepressant studies, Population Approach Group Europe (PAGE) 20th Meeting, Abstract 2133. [2] Mortensen SB (2010), Markov and mixed models with applications, PhD Thesis, Technical University of Denmark (DTU), Kgs. Lyngby. [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). http://www.r-project.org/.

Second order Markov modelling of HAMD responses in depression trials

MAROSTICA, ELEONORA;RUSSU, ALBERTO;DE NICOLAO, GIUSEPPE
2012-01-01

Abstract

Objectives: Longitudinal models describing the time course of the clinical endpoint in psychiatric trials are usually empirical. Moreover, conditional on the individual parameters the response model does not structurally account for random fluctuations on the disease. The first attempt to include these aspects, presented in [1] resorting to stochastic difference and differential equations, did not give a completely satisfactory description of inter-individual variability. We propose an extension of the previous work through a more sophisticated continuous-time dynamic model based on second order Markov processes [2]. The proposed model aims to describe appropriately the clinical response and handle flexible dosing schemes. Methods: A Phase II, double-blind, randomized, placebo-controlled, flexible-dose depression trial was analyzed. We modelled the individual time series of HAMD scores within the framework of population modelling. The typical curve was modelled as an integrated Wiener process [3] whereas a second order Markov model was adopted to describe the individual shifts with respect to the population curve. Two Markov models were analyzed having either (i) two coincident poles or (ii) two distinct poles in the transfer function. Dose changes were accounted for by varying the trend of the response profile. Models statistics were specified through hyperparameters. A unique hyperparameter for the measurement error was considered in order to simultaneously identify the model on the four subpopulations (placebo and drug: non-escalating and escalating subjects). Software R 2.10.0 [4] was adopted according to the empirical Bayes paradigm. Results: Both models were able to capture the shapes of individual responses. Moreover, good predictive performances in terms of VPCs were obtained. According to the Bayesian Information Criterion, the second order Markov model with two coincident poles in the transfer function should be preferred. Conclusions: The results demonstrate the feasibility and effectiveness of second order Markov processes as an innovative modelling approach for longitudinal data, when mechanistic knowledge is poor or absent. We showed that the proposed models yield good individual fittings as well as a good estimate of the population response and an appropriate representation of the inter-individual variability. Interestingly, both models are able to easily handle dose changes and account for random perturbations with greater flexibility than previous approaches [1]. References: [1] Marostica E, Russu A, De Nicolao G, Gomeni R (2011), Population state-space modelling of patient responses in antidepressant studies, Population Approach Group Europe (PAGE) 20th Meeting, Abstract 2133. [2] Mortensen SB (2010), Markov and mixed models with applications, PhD Thesis, Technical University of Denmark (DTU), Kgs. Lyngby. [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). http://www.r-project.org/.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/1029989
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