Amélioration de la performance des analyses de survie dans le cadre des essais de prévention et application à la maladie d'Alzheimer

Amélioration de la performance des analyses de survie dans le cadre des essais de prévention et application à la maladie d'Alzheimer. En l'absence de traitement curatif de la maladie d'Alzheimer, les efforts se portent actuellement sur la prévention. A ce jour, tous les essais publiés, qui avaient comme objectif de prévenir la démence de type Alzheimer, ont échoué. Le plan d'analyse statistique de ces essais proposait de traiter ces données de survie par le classique test du logrank. Les traitements préventifs supposent une imprégnation au long cours avant d'en percevoir l'effet, ce qui est contradictoire avec l'hypothèse des risques proportionnels, sous laquelle le test du logrank est reconnu être le plus puissant. Il est donc envisageable de trouver des tests plus puissants permettant de capter un effet tardif (tests du logrank et Kaplan-Meier pondérés). Des outils théoriques pour comparer ces tests sont introduits tels que la consistance et l'efficacité asymptotique. Si l'existence de l'effet tardif est connue a priori, une méthodologie est proposée afin de choisir la bonne pondération. Si la forme de l'effet n'est pas connue a priori, une nouvelle statistique de type "Maximum" est introduite. Enfin, cette méthodologie est appliquée aux données réelles GuidAge.No effective curative treatment currently exists for Alzheimer disease, making its prevention a priority. To date, the rare published articles in the field of prevention trials for dementia, which measured dementia incidence as their primary outcome, have been negative. The statistical analysis of these trials relies on the logrank test. This test is known to be optimal under the proportional hazards model, thus it may be inadequate for prevention clinical trials, which may require a certain period of exposure to an intervention before an effect can be detected. The proportional hazards condition of optimality is unrealistic in this setting. In order to solve this problem, we suggest using more efficient tests to detect a late effect (weighted logrank and Kaplan-Meier tests). Theoretical tools are introduced to compare these tests such as consistency and asymptotic efficiency. If the existence of this late effect is known a priori, a methodology is proposed for choosing the best weight. Finally, if the form of the effect isn't known a priori, a new statistic of type "Maximum" tests is introduced. Finally, we apply this methodology to real data from the GuidAge trial

Data maturity and follow-up in time-to-event analyses

NHMR

S-estimation in linear models with structured covariance matrices

We provide a unified approach to S-estimation in balanced linear models with structured covariance matrices. Of main interest are S-estimators for linear mixed effects models, but our approach also includes S-estimators in several other standard multivariate models, such as multiple regression, multivariate regression, and multivariate location and scatter. We provide sufficient conditions for the existence of S-functionals and S-estimators, establish asymptotic properties such as consistency and asymptotic normality, and derive their robustness prop-erties in terms of breakdown point and influence function. All the results are obtained for general identifiable covariance structures and are established under mild conditions on the distribution of the observations, which goes far beyond models with elliptically contoured densities. Some of our results are new and others are more general than existing ones in the literature. In this way this manuscript completes and improves results on S-estimation in a wide variety of multivariate models. We illustrate our results by means of a simulation study and an application to data from a trial on the treatment of lead-exposed children

Efficient approximations of the fisher matrix in neural networks using kronecker product singular value decomposition

We design four novel approximations of the Fisher Information Matrix (FIM) that plays a central role in natural gradient descent methods for neural networks. The newly proposed approximations are aimed at improving Martens and Grosse’s Kronecker-factored block diagonal (KFAC) one. They rely on a direct minimization problem, the solution of which can be computed via the Kronecker product singular value decomposition technique. Experimental results on the three standard deep auto-encoder benchmarks showed that they provide more accurate approximations to the FIM. Furthermore, they outperform KFAC and state-of-the-art first-order methods in terms of optimization speed

Optimal transport for data integration

International audienceStatistical matching methods consist in integrating two or more data sources, related to the same target population, which share a subset of covariates while each data source has its own distinct subset of variables. The aim is to derive a unique synthetic data set in which all the variables, coming from the different sources, are jointly available. A method based on an application of optimal transport theory has been proposed by Garès and Omer (2020), in the case where the distinct variables in the different data sources are categorical. Joint distribution of shared and distinct variables is transported within the data sources. Although the method demonstrated good performance, the proposed approach also transports the distribution of shared and distinct variables and estimate a function to predict the missing variables. The performances are assessed through a Monte Carlo simulation study.Les méthodes d'appariement statistique consistent à intégrer deux ou plusieurs sources de données, relatives à une même population cible. Ces sources partagent un sousensemble de covariables tout en disposant d'autres sous-ensembles de variables distincts. Le but est de construire un ensemble unique de données synthétique dans lequel toutes les variables des différentes sources sont disponibles conjointement. Une méthode basée sur une application du transport optimal a été proposée dans Garès and Omer (2020), dans le cas où les variables distinctes des différentes sources de données sont catégorielles. La distribution jointe des variables partagées et distinctes est transportée dans un jeu de données. L'approche proposée ici utilise également le transport optimal pour la distribution des variables partagées et distinctes, mais intègre de plus l'estimation d'une fonction pour prédire les variables distinctes dans l'autre source. Les performances de la méthode sont évaluées via une étude par simulation de Monte Carlo

Regularized optimal transport of covariates and outcomes in data recoding

When databases are constructed from heterogeneous sources, it is not unusual that different encodings are used for the same outcome. In such case, it is necessary to recode the outcome variable before merging two databases. The method proposed for the recoding is an application of optimal transportation where we search for a bijective mapping between the distributions of such variable in two databases. In this article, we build upon the work by Garès et al. [9], where they transport the distributions of categorical outcomes assuming that they are distributed equally in the two databases. Here, we extend the scope of the model to treat all the situations where the covariates explain the outcomes similarly in the two databases. In particular, we do not require that the outcomes be distributed equally. For this, we propose a model where joint distributions of outcomes and covariates are transported. We also propose to enrich the model by relaxing the constraints on marginal distributions and adding an L1 regularization term. The performances of the models are evaluated in a simulation study, and they are applied to a real dataset

Optimal transport for data integration

International audienceStatistical matching methods consist in integrating two or more data sources, related to the same target population, which share a subset of covariates while each data source has its own distinct subset of variables. The aim is to derive a unique synthetic data set in which all the variables, coming from the different sources, are jointly available. A method based on an application of optimal transport theory has been proposed by Garès and Omer (2020), in the case where the distinct variables in the different data sources are categorical. Joint distribution of shared and distinct variables is transported within the data sources. Although the method demonstrated good performance, the proposed approach also transports the distribution of shared and distinct variables and estimate a function to predict the missing variables. The performances are assessed through a Monte Carlo simulation study.Les méthodes d'appariement statistique consistent à intégrer deux ou plusieurs sources de données, relatives à une même population cible. Ces sources partagent un sousensemble de covariables tout en disposant d'autres sous-ensembles de variables distincts. Le but est de construire un ensemble unique de données synthétique dans lequel toutes les variables des différentes sources sont disponibles conjointement. Une méthode basée sur une application du transport optimal a été proposée dans Garès and Omer (2020), dans le cas où les variables distinctes des différentes sources de données sont catégorielles. La distribution jointe des variables partagées et distinctes est transportée dans un jeu de données. L'approche proposée ici utilise également le transport optimal pour la distribution des variables partagées et distinctes, mais intègre de plus l'estimation d'une fonction pour prédire les variables distinctes dans l'autre source. Les performances de la méthode sont évaluées via une étude par simulation de Monte Carlo

Closed-form variance estimators for weighted and stratified dose-response function estimators using generalized propensity score

Propensity score methods are widely used in observational studies for evaluating marginal treatment effects. The generalized propensity score (GPS) is an extension of the propensity score framework, historically developed in the case of binary exposures, for use with quantitative or continuous exposures. In this paper, we proposed variance esti-mators for treatment effect estimators on continuous outcomes. Dose-response functions (DRF) were estimated through weighting on the inverse of the GPS, or using stratification. Variance estimators were evaluated using Monte Carlo simulations. Despite the use of stabilized weights, the variability of the weighted estimator of the DRF was particularly high, and none of the variance estimators (a bootstrap-based estimator, a closed-form estimator especially developped to take into account the estimation step of the GPS, and a sandwich estimator) were able to adequately capture this variability, resulting in coverages below to the nominal value, particularly when the proportion of the variation in the quantitative exposure explained by the covariates was 1 large. The stratified estimator was more stable, and variance estima-tors (a bootstrap-based estimator, a pooled linearized estimator, and a pooled model-based estimator) more efficient at capturing the empirical variability of the parameters of the DRF. The pooled variance estimators tended to overestimate the variance, whereas the bootstrap estimator, which intrinsically takes into account the estimation step of the GPS, resulted in correct variance estimations and coverage rates. These methods were applied to a real data set with the aim of assessing the effect of maternal body mass index on newborn birth weight

Optimal transport for data integration

International audienceStatistical matching methods consist in integrating two or more data sources, related to the same target population, which share a subset of covariates while each data source has its own distinct subset of variables. The aim is to derive a unique synthetic data set in which all the variables, coming from the different sources, are jointly available. A method based on an application of optimal transport theory has been proposed by Garès and Omer (2020), in the case where the distinct variables in the different data sources are categorical. Joint distribution of shared and distinct variables is transported within the data sources. Although the method demonstrated good performance, the proposed approach also transports the distribution of shared and distinct variables and estimate a function to predict the missing variables. The performances are assessed through a Monte Carlo simulation study.Les méthodes d'appariement statistique consistent à intégrer deux ou plusieurs sources de données, relatives à une même population cible. Ces sources partagent un sousensemble de covariables tout en disposant d'autres sous-ensembles de variables distincts. Le but est de construire un ensemble unique de données synthétique dans lequel toutes les variables des différentes sources sont disponibles conjointement. Une méthode basée sur une application du transport optimal a été proposée dans Garès and Omer (2020), dans le cas où les variables distinctes des différentes sources de données sont catégorielles. La distribution jointe des variables partagées et distinctes est transportée dans un jeu de données. L'approche proposée ici utilise également le transport optimal pour la distribution des variables partagées et distinctes, mais intègre de plus l'estimation d'une fonction pour prédire les variables distinctes dans l'autre source. Les performances de la méthode sont évaluées via une étude par simulation de Monte Carlo

Variance estimators for weighted and stratified linear dose–response function estimators using generalized propensity score

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