The Koziol-Green and Generalized Koziol-Green Model with Covariates under Dependent Censoring

Abstract

The study of non-negative response variables is crucial and takes several forms in a wide variety of areas of modern scientific investigations. One of these is lifetime or survival time studies, where the response variable is expressed as the time until certain event of interest (time-to-event endpoint). In engineering for example, researchers are often interested in studying the time until the break down of a machine component. Another example is in the social sciences, where interest lies in the duration of strikes, duration of unemployment or the duration of marriages in societies. In medical settings, survival times emerge from investigations that focus on the time until recurrence of cancer tumors, the time to recovery after a surgical operation or the life span of some biological units, among others. Nonetheless, there are also cases in survival time studies where the term ”time” may not represent the literal time. For instance, in quality control or reliability in manufacturing, this could be the amount of force needed to render a part unusable. While in economics, it could also be the amount payed by an insurance company in case of damage. In various fields of survival time studies, researchers are often confronted with the distinguishable and unifying phenomenon of censoring. This surfaces as a consequence of the fact that, for some study units, the exact survival time is known, whereas for others only a partial information is available. Censoring in general occurs for various reasons. Depending on the underlying reason for censoring, we can broadly distinguish between three types of censoring, namely Type I, Type II and Random censoring schemes. Type I censoring occurs when the censoring time is fixed a priori. While in type II censoring, the censoring time is determined by a fixed number of exact survival times to be observed. In both these types of censoring however, the censoring mechanism is controlled by the investigator. In a laboratory experiment for example, a researcher who wants to investigate the lifespan of a number of fluorescent tubes may put them on a test in order to record their times to failure. Some tubes may take a long time to burn out and it may not be feasible for the experimenter to wait that long. Therefore, he/she may decide to end the experiment at a prescribed time (i.e. fixed censoring time). In such situation, the exact lifetime of some tubes may not be observed and this leads to Type I censoring. On the other hand, the investigator may not have a prior knowledge of the appropriate fixed censoring time and may chose to wait until a prespecified proportion of the tubes burns out. The exact lifetime of some tubes may not be observed in this second scenario as well, in which case we have type II censoring. Obviously, the censoring mechanisms in these scenarios are under the control of the investigator. ...