This thesis deals with non parametric estimation methods of medical cost and of incidences of clinical events that generate it. Such statistical analysis methods already exist but they are sometimes misused due to the bias induced by the data when encountering censorship, recurence of interest events, and competitive risks. The choice of a correct statistical method of estimation is generally an issue within such a context. In a first part, we have studied the statistical methods that are usually used but none was defined at a sufficient general level to take into account all the classical situations. So, in a second time, we have developped a "multi-state" framewok of non parametric approaches allowing to estimate both the medical cost and the incidences of the events that generate it when in presence of all these situations. The properties of the estimators, in terms of bias and asymptotic behavior have been then studied. Finally, all the methods that were studied and developped have been applied to a real case: the medical and economical evaluation of the pre-treatment screening of the toxicities for the 5-fluorouracile that has been set up by the research teams of the Laboratoire d'Oncopharmacologie and INSERM U892 of the Centre Paul Papin d'Angers. This study has showed that this pre-treatment screening could lead to a significant reduction of the major and lethal toxicities which takes place during the first two cycles of the treatment that uses the 5-FU. Moreover, the supplementary cost that it induces could be significantly inferior to the cost of the toxicities that it helps to avoid, whatever type of economical study is considered.
