Semiparametric Estimation of the Survival Function in the Presence of Covariates

Abstract

The main interest of survival analysis is to estimate the distribution function of the survival time based on observations of a random sample. In this thesis, a semiparametric estimator is used not only to estimate the survival probability, but also to consider the influence of explanatory variables within the estimation. Therefore, the weighted maximum likelihood estimator of the conditional survival function is derived and a corresponding pointwise likelihood ratio confidence band is developed. Subsequently, the established estimator is compared to a similar estimator which was proposed by Iglesias-Pérez and de Ũna-Álvarez (2008). Since the idea of this paper arose in cooperation with an automotive company, the focus is on the application of this model in context of the automotive industry. A method to select covariates which seem to have the most impact on the failure behavior is derived, using the proposed estimate. Furthermore, the strength of the impact is identified and a profile of the effect is established.