arXiv subjects

Marc Lavielle

Publications and source records attributed to Marc Lavielle.

7 recordsLinked to original sources

arXiv2026

Evaluation of the npde performance for the evaluation of joint model with longitudinal and TTE data: an application in metastatic hormono-resistant prostate cancer

Introduction: Joint models are increasingly used in clinical trials. An important part of model building is to properly assess the descriptive and predictive ability of these models. Normalised prediction discrepancies (npd) and normalised prediction distribution errors (npde) have been developed to evaluate graphically and statistically non-linear mixed effect models for continuous responses. In this work, we propose to use a combined test to evaluate joint models. Methods: Prediction discrepancies (pd) are defined as the quantile of the observation within its predictive distribution and obtained by Monte-Carlo simulations. The pd for unobserved (censored) event times are imputed in a uniform distribution based on the model prediction of the probability of censoring, using a similar method as the one developed to handle data under the lower quantification limit (LOQ). We propose to combine the p-values of the tests on longitudinal data and on time-to-event (TTE) data, adjusted with a Bonferroni correction. We performed simulation studies based on a joint model characterising the relationship between prostate specific antigen biomarker (PSA) and survival in prostate cancer patients to evaluate the type I error and power of npd/npde to detect different types of model misspecifications. Results: For all types of misspecifications, the type I error of the combined test was found to be close to the expected 5%. The power of the combined test to detect model misspecifications increased with the difference from the true model and as expected, with sample size. Graphically the power increase can be related to larger differences in the shape of the survival function or PSA evolution. Conclusions: npd can be readily extended for event data by imputing the pd for censored event under the model. The test showed an adequate type I error, and was quite sensitive to alternative models tested.

stat.ME↗

arXiv2019

On the Global Convergence of (Fast) Incremental Expectation Maximization Methods

The EM algorithm is one of the most popular algorithm for inference in latent data models. The original formulation of the EM algorithm does not scale to large data set, because the whole data set is required at each iteration of the algorithm. To alleviate this problem, Neal and Hinton have proposed an incremental version of the EM (iEM) in which at each iteration the conditional expectation of the latent data (E-step) is updated only for a mini-batch of observations. Another approach has been proposed by Cappé and Moulines in which the E-step is replaced by a stochastic approximation step, closely related to stochastic gradient. In this paper, we analyze incremental and stochastic version of the EM algorithm as well as the variance reduced-version of Chen et. al. in a common unifying framework. We also introduce a new version incremental version, inspired by the SAGA algorithm by Defazio et. al. We establish non-asymptotic convergence bounds for global convergence. Numerical applications are presented in this article to illustrate our findings.

stat.ML↗

arXiv2019

f-SAEM: A fast Stochastic Approximation of the EM algorithm for nonlinear mixed effects models

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to perform such sampling, but this method is known to converge slowly for medium dimensional problems, or when the joint structure of the distributions to sample is spatially heterogeneous. The main contribution consists of an independent Metropolis-Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the incomplete data model. Such approximation is shown to be equivalent to linearizing the structural model in the case of continuous data. Numerical experiments based on simulated and real data illustrate the performance of the proposed methods. For fitting nonlinear mixed effects models, the suggested MH algorithm is efficiently combined with a stochastic approximation version of the EM algorithm for maximum likelihood estimation of the global parameters.

stat.ME↗

arXiv2019

Efficient Metropolis-Hastings Sampling for Nonlinear Mixed Effects Models

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge slowly for medium dimension problems, or when the joint structure of the distributions to sample is complex. We propose a Metropolis Hastings (MH) algorithm based on a multidimensional Gaussian proposal that takes into account the joint conditional distribution of the random effects and does not require any tuning, in contrast with more sophisticated samplers such as the Metropolis Adjusted Langevin Algorithm or the No-U-Turn Sampler that involve costly tuning runs or intensive computation. Indeed, this distribution is automatically obtained thanks to a Laplace approximation of the original model. We show that such approximation is equivalent to linearizing the model in the case of continuous data. Numerical experiments based on real data highlight the very good performances of the proposed method for continuous data model.

stat.AP↗

arXiv2019

Logistic Regression with Missing Covariates -- Parameter Estimation, Model Selection and Prediction within a Joint-Modeling Framework

Logistic regression is a common classification method in supervised learning. Surprisingly, there are very few solutions for performing logistic regression with missing values in the covariates. We suggest a complete approach based on a stochastic approximation version of the EM algorithm to do statistical inference with missing values including the estimation of the parameters and their variance, derivation of confidence intervals and a model selection procedure. We also tackle the problem of prediction for new observations (on a test set) with missing covariate data. The methodology is computationally efficient, and its good coverage and variable selection properties are demonstrated in a simulation study where we contrast its performances to other methods. For instance, the popular approach of multiple imputation by chained equations can lead to estimates that exhibit meaningfully greater biases than the proposed approach. We then illustrate the method on a dataset of severely traumatized patients from Paris hospitals to predict the occurrence of hemorrhagic shock, a leading cause of early preventable death in severe trauma cases. The aim is to consolidate the current red flag procedure, a binary alert identifying patients with a high risk of severe hemorrhage. The methodology is implemented in the R package misaem.

stat.ME↗

arXiv2010

Random threshold for linear model selection, revisited

In [Lavielle and Ludena 07], a random thresholding metho d is intro duced to select the significant, or non null, mean terms among a collection of independent random variables, and applied to the problem of recovering the significant coefficients in non ordered model selection. We intro duce a simple modification which removes the dep endency of the proposed estimator on a window parameter while maintaining its asymptotic properties. A simulation study suggests that both procedures compare favorably to standard thresholding approaches, such as multiple testing or model-based clustering, in terms of the binary classification risk. An application of the method to the problem of activation detection on functional magnetic resonance imaging (fMRI) data is discussed.

stat.ME↗

arXiv2010

Selection of a Model of Cerebral Activity for fMRI Group Data Analysis

This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome certain limitations of standard voxel-based testing methods, as implemented in the Statistical Parametric Mapping (SPM) software, we introduce a Bayesian model selection approach to this problem, meaning that the most probable model of cerebral activity given the data is selected from a pre-defined collection of possible models. Based on a parcellation of the brain volume into functionally homogeneous regions, each model corresponds to a partition of the regions into those involved in the task under study and those inactive. This allows to incorporate prior information, and avoids the dependence of the SPM-like approach on an arbitrary threshold, called the cluster- forming threshold, to define active regions. By controlling a Bayesian risk, our approach balances false positive and false negative risk control. Furthermore, it is based on a generative model that accounts for the spatial uncertainty on the localization of individual effects, due to spatial normalization errors. On both simulated and real fMRI datasets, we show that this new paradigm corrects several biases of the SPM-like approach, which either swells or misses the different active regions, depending on the choice of a cluster-forming threshold.

stat.AP↗