An ensemble model based on early predictors to forecast COVID-19 health care demand in France

Short-term forecasting of the COVID-19 pandemic is required to facilitate the planning of COVID-19 health care demand in hospitals. Here, we evaluate the performance of 12 individual models and 19 predictors to anticipate French COVID-19-related health care needs from September 7, 2020, to March 6, 2021. We then build an ensemble model by combining the individual forecasts and retrospectively test this model from March 7, 2021, to July 6, 2021. We find that the inclusion of early predictors (epidemiological, mobility, and meteorological predictors) can halve the rms error for 14-d–ahead forecasts, with epidemiological and mobility predictors contributing the most to the improvement. On average, the ensemble model is the best or second-best model, depending on the evaluation metric. Our approach facilitates the comparison and benchmarking of competing models through their integration in a coherent analytical framework, ensuring that avenues for future improvements can be identified.

SAMBA: A novel method for fast automatic model building in nonlinear mixed-effects models

The success of correctly identifying all the components of a nonlinear mixed-effects model is far from straightforward: it is a question of finding the best structural model, determining the type of relationship between covariates and individual parameters, detecting possible correlations between random effects, or also modeling residual errors. We present the Stochastic Approximation for Model Building Algorithm (SAMBA) procedure and show how this algorithm can be used to speed up this process of model building by identifying at each step how best to improve some of the model components. The principle of this algorithm basically consists in "learning something" about the "best model," even when a "poor model" is used to fit the data. A comparison study of the SAMBA procedure with Stepwise Covariate Modeling (SCM) and COnditional Sampling use for Stepwise Approach (COSSAC) show similar performances on several real data examples but with a much reduced computing time. This algorithm is now implemented in Monolix and in the R package Rsmlx.

Reciprocal association between voting and the epidemic spread of COVID-19: observational and dynamic modeling study

BACKGROUND

Whether voting is a risk factor for epidemic spread is unknown. Reciprocally, whether an epidemic can deter citizens from voting has not been often studied. We aimed to investigate such relationships for France during the coronavirus disease 19 (COVID-19) epidemic.

METHODS

We performed an observational study and dynamic modelling using a sigmoidal mixed effects model. All hospitals with COVID-19 patients were included (18 March 2020-17 April 2020). Abstention rate of a concomitant national election was collected.

RESULTS

Mean abstention rate in 2020 among departments was 52.5% ± 6.4% and had increased by a mean of 18.8% as compared with the 2014 election. There was a high degree of similarity of abstention between the two elections among the departments (P < 0.001). Among departments with a high outbreak intensity, those with a higher participation were not affected by significantly higher COVID-19 admissions after the elections. The sigmoidal model fitted the data from the different departments with a high degree of consistency. The covariate analysis showed that a significant association between participation and number of admitted patients was observed for both elections (2020: β = -5.36, P < 1e-9 and 2014: β = -3.15, P < 1e-6) contradicting a direct specific causation of the 2020 election. Participation was not associated with the position of the inflexion point suggesting no effect in the speed of spread.

CONCLUSIONS

Our results suggest that the surrounding intensity of the COVID-19 epidemic in France did not have any local impact on participation to a national election. The level of participation had no impact on the spread of the pandemic.

Predicting the propagation of COVID-19 at an international scale: extension of an SIR model

OBJECTIVES

Several epidemiological models have been published to forecast the spread of the COVID-19 pandemic, yet many of them have proven inaccurate for reasons that remain to be fully determined. We aimed to develop a novel model and implement it in a freely accessible web application.

DESIGN

We built an SIR-type compartmental model with two additional compartments: D (deceased patients); L (individuals who will die but who will not infect anybody due to social or medical isolation) and integration of a time-dependent transmission rate and a periodical weekly component linked to the way in which cases and deaths are reported.

RESULTS

The model was implemented in a web application (as of 2 June 2020). It was shown to be able to accurately capture the changes in the dynamics of the pandemic for 20 countries whatever the type of pandemic spread or containment measures: for instance, the model explains 97% of the variance of US data (daily cases) and predicts the number of deaths at a 2-week horizon with an error of 1%.

CONCLUSIONS

In early performance evaluation, our model showed a high level of accuracy between prediction and observed data. Such a tool might be used by the global community to follow the spread of the pandemic.

SPIX: A new software package to reveal chemical reactions at trace amounts in very complex mixtures from high‐resolution mass spectra dataset

Rationale

High‐resolution mass spectrometry based non‐targeted screening has a huge potential for applications in environmental sciences, engineering and regulation. However, it produces large datasets for which full appropriate processing is a real challenge; the development of processing software is the last building‐block to enable large‐scale use of this approach.

Methods

A new software application, SPIX, has been developed to extract relevant information from high‐resolution mass spectral datasets. Dealing with intrinsic sample variability and reducing operator subjectivity, it opens up opportunities and promising prospects in many areas of analytical chemistry. SPIX is freely available at: http://spix.webpopix.org.

Results

Two features of the software are presented in the field of environmental analysis. An example illustrates how SPIX reveals photodegradation reactions in wastewater by fitting kinetic models to significant changes in ion abundance over time. A second example shows the ability of SPIX to detect photoproducts at trace amounts in river water, through comparison of datasets from samples taken before and after irradiation.

Conclusions

SPIX has shown its ability to reveal relevant modifications between two series of large datasets, allowing, for instance, the study of the consequences of a given event on a complex substrate. Most of all – and it is to our knowledge the only software currently available allowing this – it can reveal and monitor any kind of reaction in all types of mixture.

A mathematical approach to deal with nanoparticle polydispersity in surface enhanced Raman spectroscopy to quantify antineoplastic agents

Antineoplastic agents are, for most of them, highly toxic drugs prepared at hospital following individualized prescription. To protect patients and healthcare workers, it is important to develop analytical tools able to identify and quantify such drugs on a wide concentration range. In this context, surface enhanced Raman spectroscopy (SERS) has been tested as a specific and sensitive technique. Despite the standardization of the nanoparticle synthesis, a polydispersity of nanoparticles in the suspension and a lack of reproducibility persist. This study focuses on the development of a new mathematical approach to deal with this nanoparticle polydispersity and its consequences on SERS signal variability through the feasibility of 5-fluorouracil (5FU) quantification using silver nanoparticles (AgNPs) and a handled Raman spectrophotometer. Variability has been maximized by synthetizing six different batches of AgNPs for an average size of 24.9 nm determined by transmission electron microscopy, with residual standard deviation of 17.0%. Regarding low performances of the standard multivariate data processing, an alternative approach based on the nearest neighbors were developed to quantify 5FU. By this approach, the predictive performance of the 5FU concentration was significantly improved. The mean absolute relative error (MARE) decreased from 16.8% with the traditional approach based on PLS regression to 6.30% with the nearest neighbors approach (p-value < 0.001). This study highlights the importance of developing mathematics adapted to SERS analysis which could be a step to overcome the spectral variability in SERS and thus participate in the development of this technique as an analytical tool in quality control to quantify molecules with good performances, particularly in the pharmaceutical field.

Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data

Motivation

Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, most existing methods to infer stochastic gene expression models from single-cell data dedicate little attention to the reconstruction of mother–daughter inheritance dynamics.

Results

Starting from a transcription and translation model of gene expression, we propose a stochastic model for the evolution of gene expression dynamics in a population of dividing cells. Based on this model, we develop a method for the direct quantification of inheritance and variability of kinetic gene expression parameters from single-cell gene expression and lineage data. We demonstrate that our approach provides unbiased estimates of mother–daughter inheritance parameters, whereas indirect approaches using lineage information only in the post-processing of individual-cell parameters underestimate inheritance. Finally, we show on yeast osmotic shock response data that daughter cell parameters are largely determined by the mother, thus confirming the relevance of our method for the correct assessment of the onset of gene expression variability and the study of the transmission of regulatory factors.

Availability and implementation

Software code is available at https://github.com/almarguet/IdentificationWithARME. Lineage tree data is available upon request.

Supplementary information

Supplementary material is available at Bioinformatics online.

Mathematical model to predict B-type natriuretic peptide levels in haemodialysis patients

AIM

Clinical interpretation of B-type natriuretic peptide (BNP) levels in haemodialysis (HD) patients for fluid management remains elusive.

METHODS

We conducted a retrospective observational monocentric study. We built a mathematical model to predict BNP levels, using multiple linear regressions. Fifteen clinical/biological characteristics associated with BNP variation were selected. A first cohort of 150 prevalent HD (from September 2015 to March 2016) was used to build several models. The best model proposed was internally validated in an independent cohort of 75 incidents HD (from March 2016 to December 2017).

RESULTS

In cohort 1, mean BNP level was 630 ± 717 ng/mL. Cardiac disease (CD - stable coronary artery disease and/or atrial fibrillation) was present in 45% of patients. The final model includes age, systolic blood pressure, albumin, CD, normo-hydrated weight (NHW) and the fluid overload (FO) assessed by bio-impedancemetry. The correlation between the measured and the predicted log-BNP was 0.567 and 0.543 in cohorts 1 and 2, respectively. Age (β = 3.175e^-2 , P < 0.001), CD (β = 5.243e^-1 , P < 0.001) and FO (β = 1.227e^-1 , P < 0.001) contribute most significantly to the BNP level, respectively, but within a certain range. We observed a logistic relationship between BNP and age between 30 and 60 years, after which this relationship was lost. BNP level was inversely correlated with NHW independently of CD. Finally, our model allows us to predict the BNP level according to the FO.

CONCLUSION

We developed a mathematical model capable of predicting the BNP level in HD. Our results show the complex contribution of age, CD and FO on BNP level.

Pharmacometrics models with hidden Markovian dynamics

The aim of this paper is to provide an overview of pharmacometric models that involve some latent process with Markovian dynamics. Such models include hidden Markov models which may be useful for describing the dynamics of a disease state that jumps from one state to another at discrete times. On the contrary, diffusion models are continuous-time and continuous-state Markov models that are relevant for modelling non observed phenomena that fluctuate continuously and randomly over time. We show that an extension of these models to mixed effects models is straightforward in a population context. We then show how the forward-backward algorithm used for inference in hidden Markov models and the extended Kalman filter used for inference in diffusion models can be combined with standard inference algorithms in mixed effects models for estimating the parameters of the model. The use of these models is illustrated with two applications: a hidden Markov model for describing the epileptic activity of a large number of patients and a stochastic differential equation based model for describing the pharmacokinetics of theophyllin.

What do we mean by identifiability in mixed effects models?

We discuss the question of model identifiability within the context of nonlinear mixed effects models. Although there has been extensive research in the area of fixed effects models, much less attention has been paid to random effects models. In this context we distinguish between theoretical identifiability, in which different parameter values lead to non-identical probability distributions, structural identifiability which concerns the algebraic properties of the structural model, and practical identifiability, whereby the model may be theoretically identifiable but the design of the experiment may make parameter estimation difficult and imprecise. We explore a number of pharmacokinetic models which are known to be non-identifiable at an individual level but can become identifiable at the population level if a number of specific assumptions on the probabilistic model hold. Essentially if the probabilistic models are different, even though the structural models are non-identifiable, then they will lead to different likelihoods. The findings are supported through simulations.

Prediction of Response to Temozolomide in Low-Grade Glioma Patients Based on Tumor Size Dynamics and Genetic Characteristics

Both molecular profiling of tumors and longitudinal tumor size data modeling are relevant strategies to predict cancer patients' response to treatment. Herein we propose a model of tumor growth inhibition integrating a tumor's genetic characteristics (p53 mutation and 1p/19q codeletion) that successfully describes the time course of tumor size in patients with low-grade gliomas treated with first-line temozolomide chemotherapy. The model captures potential tumor progression under chemotherapy by accounting for the emergence of tissue resistance to treatment following prolonged exposure to temozolomide. Using information on individual tumors' genetic characteristics, in addition to early tumor size measurements, the model was able to predict the duration and magnitude of response, especially in those patients in whom repeated assessment of tumor response was obtained during the first 3 months of treatment. Combining longitudinal tumor size quantitative modeling with a tumor''s genetic characterization appears as a promising strategy to personalize treatments in patients with low-grade gliomas.

MatVPC: A User-Friendly MATLAB-Based Tool for the Simulation and Evaluation of Systems Pharmacology Models

Quantitative systems pharmacology (QSP) models are progressively entering the arena of contemporary pharmacology. The efficient implementation and evaluation of complex QSP models necessitates the development of flexible computational tools that are built into QSP mainstream software. To this end, we present MatVPC, a versatile MATLAB-based tool that accommodates QSP models of any complexity level. MatVPC executes Monte Carlo simulations as well as automatic construction of visual predictive checks (VPCs) and quantified VPCs (QVPCs).

Pharmacometrics Markup Language (PharmML): Opening New Perspectives for Model Exchange in Drug Development

The lack of a common exchange format for mathematical models in pharmacometrics has been a long-standing problem. Such a format has the potential to increase productivity and analysis quality, simplify the handling of complex workflows, ensure reproducibility of research, and facilitate the reuse of existing model resources. Pharmacometrics Markup Language (PharmML), currently under development by the Drug Disease Model Resources (DDMoRe) consortium, is intended to become an exchange standard in pharmacometrics by providing means to encode models, trial designs, and modeling steps.

The recruitment of p47(phox) and Rac2G12V at the phagosome is transient and phosphatidylserine dependent

BACKGROUND INFORMATION

During phagocytosis, neutrophils internalise pathogens in a phagosome and produce reactive oxygen species (ROS) by the NADPH oxidase to kill the pathogen. The cytosolic NADPH oxidase subunits p40(phox), p47(phox), p67(phox) and Rac2 translocate to the phagosomal membrane to participate in enzyme activation. The kinetics of this recruitment and the underlying signalling pathways are only partially understood. Anionic phospholipids, phosphatidylserine (PS) and phosphoinositides (PPI) provide an important attachment site for numerous proteins, including several oxidase subunits.

RESULTS

We investigated the kinetics of p47(phox) and Rac2 phagosomal membrane recruitment. Both subunits are known to interact with anionic phospholipids; we therefore addressed the role of PS in this recruitment. Phagosomal accumulation of p47(phox) and Rac2 tagged with fluorescent proteins was analysed by videomicroscopy. We used the C2 domain of lactadherin (lactC2) that interacts strongly and specifically with PS to monitor intracellular PS localisation and to decrease PS accessibility. During phagocytosis of opsonised zymosan, p47(phox) and constitutively active Rac2G12V briefly translocated to the phagosomal membrane, whereas ROS production continued for a longer period. However, in the presence of lactC2, Rac2G12V recruitment was inhibited and the kinetics of p47(phox) recruitment and detachment were delayed. A reduced phagosomal ROS production was also observed during the first 7 min following the phagosome closure.

CONCLUSIONS

These results suggest that p47(phox) and Rac2 accumulate only transiently at the phagosome at the onset of NADPH activity and detach from the phagosome before the end of ROS production. Furthermore, lactC2, by masking PS, interfered with the phagosomal recruitment of p47(phox) and Rac2 and disturbed NADPH oxidase activity. Thus, PS appears as a modulator of NADPH oxidase activation.

Analysis of exposure-response of CI-945 in patients with epilepsy: application of novel mixed hidden Markov modeling methodology

We propose to describe exposure-response relationship of an antiepileptic agent, using mixed hidden Markov modeling methodology, to reveal additional insights in the mode of the drug action which the novel approach offers. Daily seizure frequency data from six clinical studies including patients who received gabapentin were available for the analysis. In the model, seizure frequencies are governed by underlying unobserved disease activity states. Individual neighbouring states are dependent, like in reality and they exhibit their own dynamics with patients transitioning between low and high disease states, according to a set of transition probabilities. Our methodology enables estimation of unobserved disease dynamics and daily seizure frequencies in all disease states. Additional modes of drug action are achievable: gabapentin may influence both daily seizure frequencies and disease state dynamics. Gabapentin significantly reduced seizure frequencies in both disease activity states; however it did not significatively affect disease dynamics. Mixed hidden Markov modeling is able to mimic dynamics of seizure frequencies very well. It offers novel insights into understanding disease dynamics in epilepsy and gabapentin mode of action.

Maximum likelihood estimation of long-term HIV dynamic models and antiviral response

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.

Implementation and evaluation of the SAEM algorithm for longitudinal ordered categorical data with an illustration in pharmacokinetics-pharmacodynamics

Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable.

A comprehensive hepatitis C viral kinetic model explaining cure

We propose a model that characterizes and links the complexity and diversity of clinically observed hepatitis C viral kinetics to sustained virologic response (SVR)-the primary clinical end point of hepatitis C treatment, defined as an undetectable viral load at 24 weeks after completion of treatment)-in patients with chronic hepatitis C (CHC) who have received treatment with peginterferon alpha-2a +/- ribavirin. The new attributes of our hepatitis C viral kinetic model are (i) the implementation of a cure/viral eradication boundary, (ii) employment of all hepatitis C virus (HCV) RNA measurements, including those below the lower limit of quantification (LLOQ), and (iii) implementation of a population modeling approach. The model demonstrated excellent positive (99.3%) and negative (97.1%) predictive values for SVR as well as high sensitivity (96.6%) and specificity (99.4%). The proposed viral kinetic model provides a framework for mechanistic exploration of treatment outcome and permits evaluation of alternative CHC treatment options with the ultimate aim of developing and testing hypotheses for personalizing treatments in this disease.

Statistical aspects of environmental risk assessment of GM plants for effects on non-target organisms

Previous European guidance for environmental risk assessment of genetically modified plants emphasized the concepts of statistical power but provided no explicit requirements for the provision of statistical power analyses. Similarly, whilst the need for good experimental designs was stressed, no minimum guidelines were set for replication or sample sizes. Furthermore, although substantial equivalence was stressed as central to risk assessment, no means of quantification of this concept was given. This paper suggests several ways in which existing guidance might be revised to address these problems. One approach explored is the ;bioequivalence' test, which has the advantage that the error of most concern to the consumer may be set relatively easily. Also, since the burden of proof is placed on the experimenter, the test promotes high-quality, well-replicated experiments with sufficient statistical power. Other recommendations cover the specification of effect sizes, the choice of appropriate comparators, the use of positive controls, meta-analyses, multivariate analysis and diversity indices. Specific guidance is suggested for experimental designs of field trials and their statistical analyses. A checklist for experimental design is proposed to accompany all environmental risk assessments.

Performance in population models for count data, part II: a new SAEM algorithm

Analysis of count data from clinical trials using mixed effect analysis has recently become widely used. However, algorithms available for the parameter estimation, including LAPLACE and Gaussian quadrature (GQ), are associated with certain limitations, including bias in parameter estimates and the long analysis runtime. The stochastic approximation expectation maximization (SAEM) algorithm has proven to be a very efficient and powerful tool in the analysis of continuous data. The aim of this study was to implement and investigate the performance of a new SAEM algorithm for application to count data. A new SAEM algorithm was implemented in MATLAB for estimation of both, parameters and the Fisher information matrix. Stochastic Monte Carlo simulations followed by re-estimation were performed according to scenarios used in previous studies (part I) to investigate properties of alternative algorithms (Plan et al., 2008, Abstr 1372 [ http://wwwpage-meetingorg/?abstract=1372 ]). A single scenario was used to explore six probability distribution models. For parameter estimation, the relative bias was less than 0.92% and 4.13% for fixed and random effects, for all models studied including ones accounting for over- or under-dispersion. Empirical and estimated relative standard errors were similar, with distance between them being <1.7% for all explored scenarios. The longest CPU time was 95 s for parameter estimation and 56 s for SE estimation. The SAEM algorithm was extended for analysis of count data. It provides accurate estimates of both, parameters and standard errors. The estimation is significantly faster compared to LAPLACE and GQ. The algorithm is implemented in Monolix 3.1, (beta-version available in July 2009).

Modelling the influence of MDR1 polymorphism on digoxin pharmacokinetic parameters

OBJECTIVES

Digoxin is a well-known probe for the activity of P-glycoprotein. The objective of this work was to apply different methods for covariate selection in non-linear mixed-effect models to study the relationship between the pharmacokinetic parameters of digoxin and the genotype for two major exons located on the multi-drug-resistance 1 (MDR1) gene coding for P-glycoprotein.

METHODS

Thirty-two healthy volunteers were recruited in three pharmacokinetic drug interaction studies. The data after a single oral administration of digoxin alone were pooled. All subjects were genotyped for the MDR1 C3435T and G2677T/A genotypes. The concentration-time profile of digoxin was established using 12-16 blood samples taken between 15 min and 72 h after administration. We modelled the pharmacokinetics of digoxin using non-linear mixed-effect models. Parameter estimation was performed using the stochastic approximation EM method (SAEM). We used three methods to select the covariate model: selection from a full model using Wald tests, forward inclusion using the log-likelihood ratio test and model selection using the Bayesian Information Criterion.

RESULTS

The three covariate inclusion methods led to the same final model. Carriers of two T alleles for the C3435T polymorphism in exon 26 of MDR1 had a lower apparent volume of distribution than carriers of a C allele. The only other covariate effect was a shorter absorption time-lag in women.

CONCLUSION

The apparent volume of distribution of digoxin is lower in TT subjects, probably reflecting differences in bioavailability. Non-linear mixed-effect models can be useful for detecting the influence of covariates on pharmacokinetic parameters.

Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the MONOLIX software

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.

The SAEM algorithm for group comparison tests in longitudinal data analysis based on non-linear mixed-effects model

Non-linear mixed-effects models (NLMEMs) are used to improve information gathering from longitudinal studies and are applied to treatment evaluation in disease-evolution studies, such as human immunodeficiency virus (HIV) infection. The estimation of parameters and the statistical tests are critical issues in NLMEMs since the likelihood and the Fisher information matrix have no closed form. An alternative method to numerical integrations, in which convergence is slow, and to methods based on linearization, in which asymptotic convergence has not been proved, is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. For the Wald test and the likelihood ratio test, we propose estimating the Fisher information matrix by stochastic approximation and the likelihood by importance sampling. We evaluate these SAEM-based tests in a simulation study in the context of HIV viral load decrease after initiation of an antiretroviral treatment. The results from this simulation illustrate the theoretical convergence properties of SAEM. We also propose a method based on the SAEM algorithm to compute the minimum sample size required to perform a Wald test of a given power for a covariate effect in NLMEMs. Lastly, we illustrate these tests on the evaluation of the effect of ritonavir on the indinavir pharmacokinetics in HIV patients and compare the results with those obtained using the adaptative Gaussian quadrature method implemented in the SAS procedure NLMIXED.

Genetic analysis of growth curves using the SAEM algorithm

The analysis of nonlinear function-valued characters is very important in genetic studies, especially for growth traits of agricultural and laboratory species. Inference in nonlinear mixed effects models is, however, quite complex and is usually based on likelihood approximations or Bayesian methods. The aim of this paper was to present an efficient stochastic EM procedure, namely the SAEM algorithm, which is much faster to converge than the classical Monte Carlo EM algorithm and Bayesian estimation procedures, does not require specification of prior distributions and is quite robust to the choice of starting values. The key idea is to recycle the simulated values from one iteration to the next in the EM algorithm, which considerably accelerates the convergence. A simulation study is presented which confirms the advantages of this estimation procedure in the case of a genetic analysis. The SAEM algorithm was applied to real data sets on growth measurements in beef cattle and in chickens. The proposed estimation procedure, as the classical Monte Carlo EM algorithm, provides significance tests on the parameters and likelihood based model comparison criteria to compare the nonlinear models with other longitudinal methods.

Are fMRI event-related response constant in time? A model selection answer

An accurate estimation of the hemodynamic response function (HRF) in functional magnetic resonance imaging (fMRI) is crucial for a precise spatial and temporal estimate of the underlying neuronal processes. Recent works have proposed non-parametric estimation of the HRF under the hypotheses of linearity and stationarity in time. Biological literature suggests, however, that response magnitude may vary with attention or ongoing activity. We therefore test a more flexible model that allows for the variation of the magnitude of the HRF with time in a maximum likelihood framework. Under this model, the magnitude of the HRF evoked by a single event may vary across occurrences of the same type of event. This model is tested against a simpler model with a fixed magnitude using information theory. We develop a standard EM algorithm to identify the event magnitudes and the HRF. We test this hypothesis on a series of 32 regions (4 ROIS on eight subjects) of interest and find that the more flexible model is better than the usual model in most cases. The important implications for the analysis of fMRI time series for event-related neuroimaging experiments are discussed.

A statistical approach for array CGH data analysis

Background

Microarray-CGH experiments are used to detect and map chromosomal imbalances, by hybridizing targets of genomic DNA from a test and a reference sample to sequences immobilized on a slide. These probes are genomic DNA sequences (BACs) that are mapped on the genome. The signal has a spatial coherence that can be handled by specific statistical tools. Segmentation methods seem to be a natural framework for this purpose. A CGH profile can be viewed as a succession of segments that represent homogeneous regions in the genome whose BACs share the same relative copy number on average. We model a CGH profile by a random Gaussian process whose distribution parameters are affected by abrupt changes at unknown coordinates. Two major problems arise : to determine which parameters are affected by the abrupt changes (the mean and the variance, or the mean only), and the selection of the number of segments in the profile.

Results

We demonstrate that existing methods for estimating the number of segments are not well adapted in the case of array CGH data, and we propose an adaptive criterion that detects previously mapped chromosomal aberrations. The performances of this method are discussed based on simulations and publicly available data sets. Then we discuss the choice of modeling for array CGH data and show that the model with a homogeneous variance is adapted to this context.

Conclusions

Array CGH data analysis is an emerging field that needs appropriate statistical tools. Process segmentation and model selection provide a theoretical framework that allows precise biological interpretations. Adaptive methods for model selection give promising results concerning the estimation of the number of altered regions on the genome.