Prof R.B. Geskus
Academisch Medisch Centrum Amsterdam
CONTENT: In the end we all die. More interesting than the death event itself is the time component: at what age does one die and what characteristics make some individuals die earlier than others? Survival analysis, or time-to-event analysis, provides the set of tools that help answer the question of which factors influence the time until the occurrence of some event, which is not restricted to be death. The main quantities of interest are the rate (hazard) and the risk (cumulative incidence, survival function).
In time-to-event analysis, the time component typically makes the event information in the data to be incomplete. We discuss the different types of incomplete information: right, left and interval censored data and left truncated data. The analysis of such data requires the use of special estimation methods. An important assumption, which is often ignored, is that the reason for incompleteness is unrelated to the event process.
With right censored and/or left truncated data, estimation is often based on the hazard. Examples are the Kaplan-Meier estimator of the survival function, the log-rank test to compare the time-to-event distributions between groups and the Cox proportional hazards model to quantify the effect of covariables on the time-to-event distribution. In principle, time-varying covariables are easily included in regression models that are based on the hazard. We also discuss two approaches that model effects on another quantity than the hazard: the proportional odds model and the accelerated failure time model. We explain how results form a hazard-based model can be used to quantify, or predict, on the scale of the risk.
In the last part of the course, we extend the classical setting of a single event type. A competing risks model considers a collection of mutually exclusive potential event types: in the end we all die, but not all from the same cause. We explain when a competing risks analysis is the appropriate approach. The important quantities are defined and we introduce their estimators. A further extension is the multi-state model, which additionally allows for intermediate events: in the end we all die, but not all for the same reason nor with the same life histories. Under the frequently assumed Markov property, a multi-state model can be seen as a sequence of competing risks models.
LEARNING OUTCOMES: During the course, the student will learn the tools to quantify the rate and risk with partially observed information on the event time. He/she will understand in which situations these tools can be used. In the regression setting, most attention is given to the Cox proportional hazards model. The student will learn to interpret its results and to critically evaluate validy of its underlying assumptions. He/she will be able to consider alternative approaches. Finally, the student will understand when extensions to the competing risks and multi-state setting may be of interest and will be able to perform some basic analyses.
INSTRUCTIONAL METHODS: Classes consist of a combination of lectures, exercises and computer practicals. Examples are given to explain the theoretical concepts. Several exercises are inspired by the teacher's own practice. Furthermore, all concepts are practiced by means of an existing data set, using the R statistical program.
Contact person: Rossella Miglio