Regression problems with partially informative or dependent censoring

Abstract

At first sight some research areas in medicine, engineering, insurance, social sciences, . . . do not have anything in common. However, in each of these areas, researchers are interested in positive variables, which in most cases are expressed as a time until a certain event. In medicine, for example, the time until survival of a patient or the progression of a disease is recorded while in engineering, this is the time until breakdown of a machine. In social sciences this variable can be the duration of unemployment and in insurance, this is usually the amount paid by the insurer in case of damage. For various reasons, the collected data in these situations may be incomplete. One of the sources of incompleteness is censoring. This happens, for example, when a researcher does not have the time to wait until all the observations show the event of interest. In engineering, it is not always possible to wait until all the machines have broken down and in medicine, it is unethical for a doctor to wait until all the patients under study have died. We call this type of censoring, right censoring. Such a data set consists of two parts: on one hand, we have observations which have shown the event of interest at a certain time (uncensored observations) and on the other hand, there are observations which have not yet shown this event (censored observations). For the latter group we only know a lower bound for the time until the event of interest. In a medical study where we are looking for the time until the progression of a type of cancer, some of the patients in this data set are censored because the study was stopped before their cancer progressed. ... In this thesis we investigate two different censoring models and each time find an estimator for the distribution function of the time until the event of interest in the presence of covariates. ...