Regression modeling on stratified data with the lasso

We consider the estimation of regression models on strata defined using a categorical covariate, in order to identify interactions between this categorical covariate and the other predictors. A basic approach requires the choice of a reference stratum. We show that the performance of a penalized version of this approach depends on this arbitrary choice. We propose a refined approach that bypasses this arbitrary choice, at almost no additional computational cost. Regarding model selection consistency, our proposal mimics the strategy based on an optimal and covariate-specific choice for the reference stratum. Results from an empirical study confirm that our proposal generally outperforms the basic approach in the identification and description of the interactions. An illustration on gene expression data is provided.Comment: 23 pages, 5 figure

Penalized Poisson model for network meta-analysis of individual patient time-to-event data

Network meta-analysis (NMA) allows the combination of direct and indirect evidence from a set of randomized clinical trials. Performing NMA using individual patient data (IPD) is considered as a gold standard approach as it provides several advantages over NMA based on aggregate data. For example, it allows to perform advanced modelling of covariates or covariate-treatment interactions. An important issue in IPD NMA is the selection of influential parameters among terms that account for inconsistency, covariates, covariate-by-treatment interactions or non-proportionality of treatments effect for time to event data. This issue has not been deeply studied in the literature yet and in particular not for time-to-event data. A major difficulty is to jointly account for between-trial heterogeneity which could have a major influence on the selection process. The use of penalized generalized mixed effect model is a solution, but existing implementations have several shortcomings and an important computational cost that precludes their use for complex IPD NMA. In this article, we propose a penalized Poisson regression model to perform IPD NMA of time-to-event data. It is based only on fixed effect parameters which improve its computational cost over the use of random effects. It could be easily implemented using existing penalized regression package. Computer code is shared for implementation. The methods were applied on simulated data to illustrate the importance to take into account between trial heterogeneity during the selection procedure. Finally, it was applied to an IPD NMA of overall survival of chemotherapy and radiotherapy in nasopharyngeal carcinoma

Statistical Model Selection by penalized likelihood method for the study of complex data

Cette thèse est principalement consacrée au développement de méthodes de sélection de modèles par maximum de vraisemblance pénalisée dans le cadre de données complexes. Un premier travail porte sur la sélection des modèles linéaires généralisés dans le cadre de données stratifiées, caractérisées par la mesure d’observations ainsi que de covariables au sein de différents groupes (ou strates). Le but de l’analyse est alors de déterminer quelles covariables influencent de façon globale (quelque soit la strate) les observations mais aussi d’évaluer l’hétérogénéité de cet effet à travers les strates.Nous nous intéressons par la suite à la sélection des modèles non linéaires à effets mixtes utilisés dans l’analyse de données longitudinales comme celles rencontrées en pharmacocinétique de population. Dans un premier travail, nous décrivons un algorithme de type SAEM au sein duquel la pénalité est prise en compte lors de l’étape M en résolvant un problème de régression pénalisé à chaque itération. Dans un second travail, en s’inspirant des algorithmes de type gradient proximaux, nous simplifions l’étape M de l’algorithme SAEM pénalisé précédemment décrit en ne réalisant qu’une itération gradient proximale à chaque itération. Cet algorithme, baptisé Stochastic Approximation Proximal Gradient algorithm (SAPG), correspond à un algorithme gradient proximal dans lequel le gradient de la vraisemblance est approché par une technique d’approximation stochastique.Pour finir, nous présentons deux travaux de modélisation statistique, réalisés au cours de cette thèse.This thesis is mainly devoted to the development of penalized maximum likelihood methods for the study of complex data.A first work deals with the selection of generalized linear models in the framework of stratified data, characterized by the measurement of observations as well as covariates within different groups (or strata). The purpose of the analysis is then to determine which covariates influence in a global way (whatever the stratum) the observations but also to evaluate the heterogeneity of this effect across the strata.Secondly, we are interested in the selection of nonlinear mixed effects models used in the analysis of longitudinal data. In a first work, we describe a SAEM-type algorithm in which the penalty is taken into account during step M by solving a penalized regression problem at each iteration. In a second work, inspired by proximal gradient algorithms, we simplify the M step of the penalized SAEM algorithm previously described by performing only one proximal gradient iteration at each iteration. This algorithm, called Stochastic Approximation Proximal Gradient Algorithm (SAPG), corresponds to a proximal gradient algorithm in which the gradient of the likelihood is approximated by a stochastic approximation technique.Finally, we present two statistical modeling works realized during this thesis

Données pharmacologiques utiles pour une bonne utilisation des anticoagulants oraux directs

Les anticoagulants oraux directs offrent une alternative aux médicaments antivitamines K dans la prévention et le traitement des événements thromboemboliques. Contrairement à ces derniers, ils inhibent de façon directe et spécifique certains facteurs de la coagulation (Xa, IIa). Leurs propriétés pharmacologiques permettent une administration à dose fixe et sans suivi biologique pour la majorité des patients. Néanmoins, leur pharmacocinétique dépendante de transporteurs membranaires (glycoprotéine P [P-gp]) et des cytochromes P450 (CYP3A4) les exposent à des interactions médicamenteuses non négligeables. Une adaptation posologique peut alors s’avérer nécessaire tout comme dans certaines situations cliniques, comme l’insuffisance rénale ou hépatique. Cependant certaines questions restent ouvertes, en particulier sur le maniement optimal de ces médicaments dans certaines populations, qui cumulent plusieurs sources de variabilité

Stochastic Proximal Gradient Algorithms for Penalized Mixed Models

International audienceMotivated by penalized likelihood maximization in complex models, we study optimization problems where neither the function to optimize nor its gradient have an explicit expression, but its gradient can be approximated by a Monte Carlo technique. We propose a new algorithm based on a stochastic approximation of the Proximal-Gradient (PG) algorithm. This new algorithm, named Stochastic Approximation PG (SAPG) is the combination of a stochastic gradient descent step which-roughly speaking-computes a smoothed approximation of the past gradient along the iterations, and a proximal step. The choice of the step size and the Monte Carlo batch size for the stochastic gradient descent step in SAPG are discussed. Our convergence results cover the cases of biased and unbiased Monte Carlo approximations. While the convergence analysis of the Monte Carlo-PG is already addressed in the literature (see Atchadé et al. [2016]), the convergence analysis of SAPG is new. The two algorithms are compared on a linear mixed effect model as a toy example. A more challenging application is proposed on non-linear mixed effect models in high dimension with a pharmacokinetic data set including genomic covariates. To our best knowledge, our work provides the first convergence result of a numerical method designed to solve penalized Maximum Likelihood in a non-linear mixed effect model

A SAEM Algorithm for Fused Lasso Penalized NonLinear Mixed Effect Models: Application to Group Comparison in Pharmacokinetics

International audienceNonlinear mixed effect models are classical tools to analyze nonlinear longitudinal data in many fields such as population pharmacokinetics. Groups of observations are usually compared by introducing the group affiliations as binary covariates with a reference group that is stated among the groups. This approach is relatively limited as it allows only the comparison of the reference group to the others. The proposed method compares groups using a penalized likelihood approach. Groups are described by the same structural model but with parameters that are group specific. The likelihood is penalized with a fused lasso penalty that induces sparsity in the differences between groups for both fixed effects and variances of random effects. A penalized Stochastic Approximation EM algorithm is proposed that is coupled to Alternating Direction Method Multipliers to solve the maximization step. An extensive simulation study illustrates the performance of this algorithm when comparing more than two groups. Then the approach is applied to real data from two pharmacokinetic drug–drug interaction trials