Dans la première partie de cette thèse, nous considérons plusieurs problèmes d'estimation de paramètre de dimension finie pour les séquences de Markov dans l'asymptotique des grands échantillons. Le comportement asymptotique des estimateurs bayésiens et les estimateurs obtenus par la méthode des moments sont décrits. Nous montrons que sous les conditions de régularité ces estimateurs sont consistants et asymptotiquement normaux et que l'estimateur bayésien est asymptotiquement efficace. Les estimateur-processus du maximum de vraisemblance un-pas et deux-pas sont étudiés. Ces estimateurs nous permettent de construire des estimateurs asymptotiquement efficaces sur la base de certainsestimateurs préliminaires, par exemple, les estimateurs obtenus par la méthode des moments ou l'estimateur deBayes et la structure de l'estimateur du maximum de vraisemblance un-pas. Nous proposons notamment des processus autorégressifs non linéaires comme exemple et nous illustrons les propriétés de ces estimateurs à l'aide de simulations numériques. Dans la deuxième partie, nous donnons les applications de processus de Markov en économie de la santé. Nous comparons les modèles de Markov homogènes et non-homogènes pour l'analyse coût-efficacité de l'utilisation depansements transparents contenant un gel de gluconate de chlorhexidine par rapport aux pansements transparents standard. Le pansement antimicrobien protège les accès vasculaire centrale et réduit le risque de bactériémies liées aux cathéters. L'impact de l'approche de modélisation sur la décision d'adopter des pansements antimicrobiens pour les patients gravement malades est discuté. / In the first part of this dissertation we consider several problems of finite-dimensional parameter estimation for Markov sequences in the asymptotics of large samples. The asymptotic behavior of the Bayesian estimators and the estimators of the method of moments are described. It is shown that under regularity conditions these estimators are consistent and asymptotically normal. We show that the Bayesian estimator is asymptotically efficient. The one-step and two-step maximum likelihood estimator-processes are studied. These estimators allow us to construct the asymptotically efficient estimators based on some preliminary estimators, say, the estimators of the method of moments or Bayes estimator and the one-step maximum likelihood estimator structure. We propose particular non-linear autoregressive processes as examples and we illustrate the properties of these estimators with the help of numerical simulations. In the second part we give theapplications of Markov processes in health economics. We compare homogeneous and non-homogeneous Markov models for cost-effectiveness analysis of routine use of transparent dressings containing a chlorhexidine gluconate gel pad versus standard transparent dressings. The antimicrobial dressing protects central vascular accesses reducing the risk of catheter-related bloodstream infections. The impact of the modeling approach on the decision of adopting antimicrobialdressings for critically-ill patients is discussed.

Introduction: Central Line-Associated Bloodstream Infections (CLABSIs) are a major cause of increased mortality, morbidity and healthcare costs in neonatal intensive care units (NICUs) patients. Despite CDC's efforts to reduce infection rates, patients often suffer consequences. The objective of this study is to perform a systematic review of strategies utilized in the neonatal population and evaluate them with the current CDC's guidelines to assess the effectiveness of bundles in preventing CLABSI in NICUs. Methods: A systematic literature search was conducted using CINAHL Plus with Text, Cochrane Database of Systematic Reviews and MEDLINE from January 2008 up to 2018. There were multiple search terms used and these included "neonate OR newborn OR infant", "CLABSI OR central line-associated bloodstream infection", "intervention OR prevention" and "bundle". The search solely focused on the outcome of infant patients. Therefore studies were excluded for the following criteria: being non-peer reviewed, being published before 2008, and being a case in which CLABSI was assessed in patients outside the NICU. See Table 4 and 5 for further information. Results: Eight articles were eligible for inclusion all of which CDC's guidelines were implemented in their strategy of intervention. The systematic review showed that adherence to care bundles decreases infection rates drastically. All eight articles reported a significant decrease in CLABSI rates following the implementation of the bundle set by CDC with two studies achieving a CLABSI rate of zero. Author's Conclusion: Implementation of care bundles showed a success in reducing CLABSI rates in the NICUs; however none of the studies endorsed a specific bundle application utilized to achieve its intended goal. Some practices adopted CDC's guidelines more than others and those showed a greater decrease in infection rate. In addition, it is evident that nurses deliver the best care when preventing an infection. Further research is needed to assess the effectiveness of a specific bundle element.