1,720,985 research outputs found
Population state-space modelling of patient responses in antidepressant studies
No full textObjectives: 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)
Tumor-growth inhibition in preclinical animal studies: steady-state analysis of biomarker-driven models
No full textObjectives: Three different models describing tumour growth inhibition (TGI) dynamics in xenografted mice are considered, two of which are biomarker-driven. The main objective is finding whether and under which conditions the tumour is eradicated or its volume tends to an asymptote. A further objective is to assess the explanatory capability of the models through their application to experimental preclinical data as well as their identifiability through simulated population data.
Methods: A comparison is carried out between the drug-driven Simeoni's TGI model [1,2] and two recent biomarker-driven TGI models, called B1-Simeoni and B2-Simeoni [3]. These two models assume that the biomarker modulation, described by a type I indirect PK-PD model, is causal for tumour growth inhibition.
To investigate the steady-state behaviours of the models, possible equilibrium values of the tumour volume have been analytically derived assuming that mice are exposed to constant plasma concentrations of a drug. For the B1- and B2-Simeoni models, the type I indirect model is used to obtain the corresponding steady-state biomarker inhibition, to be plugged into the biomarker-driven TGI model. A visual comparison between steady-state behaviours is obtained by plotting the output (equilibrium tumour volumes) against the input (constant drug concentrations).
Models are fitted to literature data [4]. Estimated parameters are used to simulate different steady-state conditions. The models are also assessed in a population context by analysing simulated TGI data. In particular, the issue of model mismatch is considered by fitting data using a model different from the one used for generating them.
Results: The stability analysis of the three models highlights two distinct behaviours. Both the standard Simeoni and B2-Simeoni models present a threshold concentration above which tumour eradication is asymptotically achieved. Conversely, in the B1-Simeoni model, the existence of a threshold drug concentration ensuring tumour eradication depends on the values of some parameters. All models explain well the experimental data.
Conclusions: The aim of this work is to further investigate two biomarker-driven TGI models, comparing their steady-state behaviours with those of the standard Simeoni model. This analysis highlights the equivalence between standard Simeoni and B2-Simeoni models, whereas achievement of tumour eradication in the B1-Simeoni model depends on the parameters values.
This work was supported by the DDMoRe project (www.ddmore.eu).
References:
[1] M. Simeoni et al. Cancer Research, 64: 1094-1101 (2004).
[2] P. Magni et al. Mathematical Biosciences, 200: 127-151 (2006).
[3] M. L. Sardu et al. PAGE 21 (2012) Abstr 2498 [www.page-meeting.org/?abstract=2498]
[4] L. Salphati et al. DMD, 38: 1436-1442 (2010)
Bayesian population modelling of Phase I dose escalation studies: Gaussian process vs parametric approaches
No full textBiomarker-driven models of tumor growth inhibition in preclinical animal studies
No full textObjectives: A biomarker - in the context of mechanism-based PK-PD modelling - is a measurement that defines quantitatively a process on the causal path between drug administration and clinical outcome [1]. The aim of this work is to investigate mathematical models that link biomarker modulation (due to the action of anticancer compounds) to tumour growth inhibition in preclinical experimental models. A major goal is the derivation of tumour growth inhibition models that are biomarker-driven rather than directly linked to drug pharmacokinetics. Being dependent on measurements which are likely to be more directly related to tumour response, this model formulation should provide more accurate predictions of the antitumor treatment effects.
Methods: To describe mathematically tumour growth we propose a biomarker-driven version of the TGI Simeoni model [2,3], herein named B-Simeoni, where the input is not represented by the drug concentration but depends on the drug-induced biomarker modulation. Different alternative formulations of the B-Simeoni model were considered. Constraints on the potency parameter were derived to ensure consistency of the outcomes of Simeoni and B-Simeoni models. This was done by equating the steady-state tumour volumes predicted following constant drug concentrations. The specific biomarker inhibition needed to maintain a certain constant tumour volume was mathematically determined. NONMEM (vers. VI) was used to analyze and simulate data sets.
Results: To assess the applicability of the modeling approach in a population context, simulated data were analyzed. Parameter estimates were fully satisfactory both on the side of data fitting and CV values. Moreover, the B-Simeoni model was tested on tumor growth inhibition data taken from the literature [4]. Also in this case, identification was successful in terms of both data fitting and CV values.
Conclusions: Building on the Simeoni TGI model, different mathematical models linking tumor growth inhibition and biomarker modulation have been proposed. The steady-state relationship that links tumor volume to drug concentration and biomarker inhibition was devised. This made it possible to express the potency parameter of the newly proposed B-Simeoni model as a function of the potency parameter of the standard Simeoni model, thus reducing unnecessary redundancy. Both experimental individual data and simulated population ones confirmed model suitability.
References:
[1] M. Danhof et al. Pharm Res, 22: 1432-7 (2005).
[2] M. Simeoni et al. Cancer Research, 64: 1094-1101 (2004).
[3] P. Magni et al. Mathematical Biosciences, 200: 127-151 (2006).
[4] L. Salphati et al. DMD, 38: 1436-1442 (2010)
Dose escalation studies in Phase I clinical trials: a comparison among Bayesian population approaches
No full textSecond order Markov modelling of HAMD responses in depression trials
No full textObjectives: 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/
First-order longitudinal population model of FEV1 data: single-trial modeling and meta-analysis
No full textObjectives: Asthma is a complex and multi-factorial disease and the underlying physiopathological mechanism is not completely known. Therefore, empirical models are usually adopted to describe the evolution of the patient's health state. The first objective of this work is to develop a parsimonious population model to describe the time course of placebo response. The clinical response is measured by the Forced Expiratory Volume in the first second (FEV1). The second objective is to perform a model-based meta-analysis, in order to assess differences among studies and to estimate the inter-trial variability.
Methods: Placebo FEV1 longitudinal data from 11 clinical trials in subjects with mild-to-moderate asthma were available. All studies lasted 12 weeks. A parametric first-order response model was developed and identified on each dataset. Based on a single-trial analysis, the proposed model was compared to the linear, polynomial, Inverse Bateman and Weibull-and-Linear models. All the models were implemented in WinBUGS 1.4.3 [1] and compared through the Deviance Information Criterion (DIC). The best model was then adopted to perform a meta-analysis on the 11 datasets together. In the meta-analysis model, each individual parameter was defined as the sum of a term relative to the subject and one relative to the study. For both the single-trial analysis and the meta-analysis, log-normal distribution was assumed for all the parameters. Graphical outputs were obtained through R 2.13.1 [2].
Results: In the single-trial analysis, the first-order parametric model here proposed yielded the best performance in terms of DIC in most cases. Good individual fittings and Visual Predictive Checks were obtained for all the 11 trials. Hence, meta-analysis was performed. The proposed model yielded good performances also when applied in a meta-analysis context. Moreover, it was found that the inter-individual variability in each study is higher than the inter-trial one (baseline: 24% vs 6%; maximal response: 148% vs 28%; time constant: 906% vs 71%).
Conclusion: A parsimonious parametric model able to describe FEV1 data from different studies in mild-to-moderate asthma was developed. The proposed model performs well both in the single-trial analysis and meta-analysis context. Moreover, the model can be extended by including clinically relevant covariates which may affect the patient's health state. A further work is to assess the model capabilities in predicting long-term outcomes from short-term trials in placebo group.
References:
[1] D.J. Lunn, A. Thomas, N. Best and D. Spiegelhalter, WinBUGS A Bayesian modelling framework: concepts, structure and extensibility, Statistics and Computing 10, 325-337, 2000
[2] R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2011). http://www.R-project.org
Joint Modeling of Efficacy, Dropout, and Tolerability in Flexible-Dose Trials: A Case Study in Depression
No full textMany difficulties may arise during the modeling of the time course of Hamilton Rating Scale for Depression (HAM D) scores in clinical trials for the evaluation of antidepressant drugs: (i) flexible designs, used to increase the chance of selecting more efficacious doses, (ii) dropout events, and (iii) adverse effects related to the experimental compound. It is crucial to take into account all these factors when designing an appropriate model of the HAM D time course and to obtain a realistic description of the dropout process. In this work, we propose an integrated approach to the modeling of a double-blind, flexible-dose, placebo-controlled, phase II depression trial that comprises response, tolerability, and dropout. We investigate three different dropout mechanisms in terms of informativeness. Goodness of fit is quantitatively assessed with respect to response (HAM D score) and dropout data. We show that dropout is a complex phenomenon that may be influenced by HAM D evolution, dose changes, and occurrence of drug-related adverse effects
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