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Biological processes measured repeatedly among a series of individuals are standardly analyzed by mixed models. These biological processes can be adequately modeled by parametric Stochastic Differential Equations (SDEs). We focus on the parametric maximum likelihood estimation of this mixed-effects model defined by SDE. As the likelihood is not explicit, we… (More)

We consider a linear mixed-effects model where Yk,j = αk+βktj+εk,j is the observed value for individual k at time tj , k = 1, . . . , N , j = 1, . . . , J . The random effects αk, βk are independent identically distributed random variables with unknown densities fα and fβ and are independent of the noise. We develop nonparametric estimators of these two… (More)

- Adeline Samson, Marc Lavielle, France Mentré
- Computational Statistics & Data Analysis
- 2006

The reduction of viral load is frequently used as a primary endpoint in HIV clinical trials. Non-linear mixed-effects models are thus proposed to model this decrease of the viral load after initiation of treatment and to evaluate the intraand inter-patient variability. However, left censoring due to quantification limits in the viral load measurement is an… (More)

- Xavière Panhard, Adeline Samson
- Biostatistics
- 2009

This article focuses on parameter estimation of multilevel nonlinear mixed-effects models (MNLMEMs). These models are used to analyze data presenting multiple hierarchical levels of grouping (cluster data, clinical trials with several observation periods, ...). The variability of the individual parameters of the regression function is thus decomposed as a… (More)

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the… (More)

Parametric incomplete data models defined by ordinary differential equations (ODEs) are widely used in biostatistics to describe biological processes accurately. Their parameters are estimated on approximate models, whose regression functions are evaluated by a numerical integration method. Accurate and efficient estimations of these parameters are critical… (More)

- Julien J Stirnemann, Adeline Samson, Jean-Pierre Bernard, Jean-Christophe Thalabard
- Human reproduction
- 2013

STUDY QUESTION
When, within the female cycle, does conception occur in spontaneously fertile cycles?
SUMMARY ANSWER
This study provides reference values of day-specific probabilities of date of conception in ongoing pregnancies. The maximum probability of being within a 5-day fertile window was reached on Day 12 following the last menstrual period (LMP).… (More)

- Sylvie Retout, Emmanuelle Comets, Adeline Samson, France Mentré
- Statistics in medicine
- 2007

We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the… (More)

This chapter is concerned with continuous time processes, which are often modeled as a system of ordinary differential equations (ODEs). These models assume that the observed dynamics are driven exclusively by internal, deterministic mechanisms. However, real biological systems will always be exposed to influences that are not completely understood or not… (More)

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularisation in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is the estimation of the SDE parameters. We use the main advantage of a one-dimensional observation to obtain an easy way to… (More)