Survival Analysis: Theory and Application in Finance

This chapter outlines some commonly used statistical methods for studying the occurrence and timing of events, i.e., survival analysis. It is also called duration analysis or transition analysis in econometrics. Statistical methods for survival data usually include non-parametric method, parametric method and semiparametric method. While some non-parametric estimators (e.g., the Kaplan–Meier estimator and life-table estimator) estimate survivor functions, others (e.g., the Nelson–Aalen estimator) estimate the cumulative hazard function. The commonly used non-parametric test for comparing survivor functions is the log-rank test. Parametric models such as the exponential model, Weibull model, and the generalized Gamma model, etc., are based on different assumptions of survival time. Semiparametric regression models are also called the Cox proportional hazards (PH) model, which is estimated by the method of partial likelihood and do not require the assumption of survival time. Other applications of discrete time data and the competing risks model are also introduced.