Survival Analysis

Survival analysis or failure time data analysis means the statistical analysis of data, where the response of interest is the time from a well-defined time origin to the occurrence of some given event (end-point). In biomedicine the key example is the time from randomization to a given treatment for some patients until death occurs leading to the observation of survival times for these patients. The objective may be to compare different treatment effects on the survival time possibly correcting for information available on each patient such as age and disease progression indicators. This leaves us with a statistical regression analysis problem. Standard methods will, however, often be inappropriate because survival times are frequently incompletely observed with the most common example being right censoring. The event time T is said to be right censored if it is only known that T is larger than an observed right censoring time. This may be because the patient is still alive at the point in time where the study is closed and the data are to be analyzed, or because the subject is lost for follow-up due to other reasons. 

The course gives an introduction to concepts and methods in survival and event history analysis and tools for establishing their theoretical properties using counting process and martingale techniques. The exercises are mostly theoretical, but some involve programming in R where properties of the methods are investigated. Topics include counting processes, intensities, filtrations and martingales; the nonparametric Nelson-Aalen and Kaplan-Meier estimators; the log-rank test; hazard regression models including parametric models and the semiparametric Cox proportional hazards model; competing risk; statistical computing in R.