Quantitative ergodicity for some switched dynamical systems

We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology

Qualitative properties of certain piecewise deterministic Markov processes

We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Working under the general assumption that the process stays in a compact set, we detail a possible construction of the process and characterize its support, in terms of the solutions set of a differential inclusion. We establish results on the long time behaviour of the process, in relation to a certain set of accessible points, which is shown to be strongly linked to the support of invariant measures. Under H\"ormander-type bracket conditions, we prove that there exists a unique invariant measure and that the processes converges to equilibrium in total variation. Finally we give examples where the bracket condition does not hold, and where there may be one or many invariant measures, depending on the jump rates between the flows.Comment: v4: more details and a fix for the constructive proof of the bracket conditio

G-computation and doubly robust standardisation for continuous-time data: A comparison with inverse probability weighting.

In time-to-event settings, g-computation and doubly robust estimators are based on discrete-time data. However, many biological processes are evolving continuously over time. In this paper, we extend the g-computation and the doubly robust standardisation procedures to a continuous-time context. We compare their performance to the well-known inverse-probability-weighting estimator for the estimation of the hazard ratio and restricted mean survival times difference, using a simulation study. Under a correct model specification, all methods are unbiased, but g-computation and the doubly robust standardisation are more efficient than inverse-probability-weighting. We also analyse two real-world datasets to illustrate the practical implementation of these approaches. We have updated the R package RISCA to facilitate the use of these methods and their dissemination

Symptoms of Infarction in Women: Is There a Real Difference Compared to Men? A Systematic Review of the Literature with Meta-Analysis

(1) Context: The management of acute coronary syndrome (ACS) is based on a rapid diagnosis. The aim of this study was to focus on the ACS symptoms differences according to gender, in order to contribute to the improvement of knowledge regarding the clinical presentation in women. (2) Methods: We searched for relevant literature in two electronic databases, and analyzed the symptom presentation for patients with suspected ACS. Fifteen prospective studies were included, with a total sample size of 10,730. (3) Results: During a suspected ACS, women present more dyspnea, arm pain, nausea and vomiting, fatigue, palpitations and pain at the shoulder than men, with RR (95%CI) of 1.13 [1.10; 1.17], 1.30 [1.05; 1.59], 1,40 [1.26; 1.56], 1.08 [1.01; 1.16], 1.67 [1.49; 1.86], 1.78 [1.02; 3.13], respectively. They are older by (95%CI) 4.15 [2.28; 6.03] years compared to men. The results are consistent in the analysis of the ACS confirmed subgroup. (4) Conclusions: We have shown that there is a gender-based symptomatic difference and a female presentation for ACS. The "typical" or "atypical" semiology of ACS symptoms should no longer be used

Conception of an easy to use application allowing to perform adjusted statistical analysis for the valorization of observational data from cohorts of chronic disease : application to the DIVAT cohort

En recherche médicale, les cohortes permettent de mieux comprendre l'évolution d'une pathologie et d'améliorer la prise en charge des patients. La mise en évidence de liens de causalité entre certains facteurs de risque et l'évolution de l'état de santé des patients est possible grâce à des études étiologiques. L'analyse de cohortes permet aussi d'identifier des marqueurs pronostiques de l'évolution d'un état de santé. Cependant, les facteurs de confusion constituent souvent une source de biais importante dans l'interprétation des résultats des études étiologiques ou pronostiques. Dans ce manuscrit, nous présentons deux travaux de recherche en Biostatistique dans la thématique des scores de propension. Dans le premier travail, nous comparons les performances de différents modèles permettant d'évaluer la causalité d'une exposition sur l'incidence d'un événement en présence de données censurées à droite. Dans le second travail, nous proposons un estimateur de courbes ROC dépendantes du temps standardisées et pondérées permettant d'estimer la capacité prédictive d'un marqueur en prenant en compte les facteurs de confusion potentiels.En cohérence avec l'objectif de fournir des outils statistiques adaptés, nous présentons également dans ce manuscrit une application nommée Plug-Stat®. En lien direct avec la base de données, elle permet de réaliser des analyses statistiques adaptées à la pathologie afin de faciliter la recherche épidémiologique et de mieux valoriser les données de cohortes observationnelles.In medical research, cohorts help to better understandthe evolution of a pathology and improve the care ofpatients. Causal associations between risk factors andoutcomes are regularly studied through etiological studies. Cohorts analysis also allow the identification of new markers for the prediction of the patient evolution.However, confounding factors are often source of bias in the interpretation of the results of etiologic or prognostic studies.In this manuscript, we presented two research works in Biostatistics, the common topic being propensity scores.In the first work, we compared the performances of different models allowing to evaluate the causality of an exposure on an outcome in the presence of rightc ensored data. In the second work, we proposed anestimator of standardized and weighted time-dependentROC curves. This estimator provides a measure of theprognostic capacities of a marker by taking into accountthe possible confounding factors. Consistent with our objective to provide adapted statistical tools, we also present in this manuscript an application, so-calledPlug-Stat®. Directly linked with the database, it allows toperform statistical analyses adapted to the pathology in order to facilitate epidemiological studies and improve the valorization of data from observational cohorts

On the stability of planar randomly switched systems

International audienceConsider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2. Assuming that there exists lambda in (0, 1) such that (1 − λ)A0 + λA1 has a positive eigenvalue, we establish that the norm of Xt may converge to 0 or infinity, depending on the the jump rate of the process I. An application to product of random matrices is studied. This paper can be viewed as a probabilistic counterpart of the paper "A note on stability conditions for planar switched systems" by Balde, Boscain and Mason

G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

International audienceAbstract In clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes

Comparisons of the performance of different statistical tests for time-to-event analysis with confounding factors: practical illustrations in kidney transplantation

International audienceConfounding factors are commonly encountered in observational studies. Several confounder-adjusted tests to compare survival between differently exposed subjects were proposed. However, only few studies have compared their performances regarding type I error rates, and no study exists evaluating their type II error rates. In this paper, we performed a comparative simulation study based on two different applications in kidney transplantation research. Our results showed that the propensity score-based inverse probability weighting (IPW) log-rank test proposed by Xie and Liu (2005) can be recommended as a first descriptive approach as it provides adjusted survival curves and has acceptable type I and II error rates. Even better performance was observed for the Wald test of the parameter corresponding to the exposure variable in a multivariable-adjusted Cox model. This last result is of primary interest regarding the exponentially increasing use of propensity score-based methods in the literature