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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)
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 intra-and inter-patient variability. However, left censoring due to quantification limits in the viral load measurement is an(More)
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)
Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics(More)
Consider an autoregressive model with measurement error: we observe Z i = X i + ε i , where X i is a stationary solution of the autoregressive equation X i = f θ 0 (X i−1) + ξ i. The regression function f θ 0 is known up to a finite dimensional parameter θ 0. The distributions of X 0 and ξ 1 are unknown whereas the distribution of ε 0 is completely known.(More)
The paper considers a process Zt = (Xt, Yt) where Xt is the position of a particle and Yt its velocity, driven by a hypoelliptic bi-dimensional stochastic differential equation. Under adequate conditions, the process is stationary and geometrically β-mixing. In this context, we propose an adaptive non-parametric kernel estimator of the stationary density p(More)
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-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(More)
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)