We start this chapter by introducing some basic elements for the analysis of censored survival data. Then we focus on right censored data and develop two types of regression models. The first one concerns the so-called accelerated failure time models (AFT), which are parametric models where a function of a parameter depends linearly on the covariables. The second one is a semiparametric model, where the covariables enter in a multiplicative form in the expression of the hazard rate function.

The main statistical tool for analysing these regression models is the maximum likelihood methodology and, in spite we recall some essential results about the ML theory, we refer to the chapter “Logistic Regression” for a more detailed presentation.