AMS 588: Failure and Survival Data Analysis

This course introduces both parametric and non-parametric statistical models for analysis of the failure and survival data – a critical topic in quantitative finance, econometrics, and biostatistics. Different censoring mechanisms will be discussed. The course will mainly cover Kaplan-Meier estimator for characterizing the distribution of the failure and survival data, non-parametric log-rank test for comparing multiple groups, and the accelerated failure time model and Cox regression model uncovering various predictor/explanatory variables to survival/failure. Applications to finance, economics and biomedicine will be illustrated. Topics include basic life table construction, estimation of selected hazards models, and discussion of various problems associated with hazards models analysis.

Required Textbook: Survival Analysis: Techniques for Censored and Truncated Data by John P. Klein and Melvin L. Moeschberger, 2nd edition, 2003, Springer

Supplementary Textbook: Survival Analysis Using The SAS^® System: A Practical Guide by Paul D. Allison, 2nd edition, 2010, SAS Institute

Learning Outcomes

1. Demonstrate skills of working with common problems related to failure data in finance, econometrics, and biostatistics.
   • Understand basic settings for problems in failure and survival data;
   • Be able to recognize problems related to failure and survival data;
   • Analysis of time to event data.
2. Demonstrate skills with statistical inference for failure and survival data.
   • Kaplan-Meier estimator for characterizing the distribution of time-to-event data;
   • Non-parametric logrank test for comparing multiple groups;
   • Accelerated failure time models: exponential, Weibull, log-normal and Gamma;
   • Cox regression model.
3. Understand mathematical properties of methods used in survival analysis of failure data.
   • Conditional expectation and variance;
   • Central limit theorem and delta methods;
   • Partial likelihood construction.
4. Demonstrate skills with proficient usage of standard statistical software tools for failure and survival data analysis.
   • Understanding of the assumptions, derivation, interpretation of results from survival statistical analysis;
   • Proficient in SAS^® procedures: LIFETEST, LIFEREG and PHREG.