**Pathway** |
Population Health |

**Category** |
Statistics module, requires Statistics Modules II |

**Credits** |
10 credits |

This course aims to describe the theory and to develop the practical skills required for the analysis of medical studies leading to the observation of survival times or multiple failure times. By the end of the course students should be able to carry out sophisticated analyses of this type, should be aware of the variety of statistical models and methods now available, and understand the nature and importance of the underlying model assumptions.

In many medical applications interest lies in times to or between events. Examples include time from diagnosis of cancer to death, or times between epileptic seizures. This advanced course begins with a review of standard approaches to the analysis of possibly censored survival data. Survival models and estimation procedures are reviewed, and emphasis is placed on the underlying assumptions, how these might be evaluated through diagnostic methods and how robust the primary conclusions might be to their violation.

The course closes with a description of models and methods for the treatment of multivariate survival data, such as repeated failures, the lifetimes of family members or competing risks. Stratified models, marginal models and frailty models are discussed.

### Topics covered will include

- Survival data. Censoring. Survival, hazard and cumulative hazard functions. Kaplan-Meier plots. Parametric models and likelihood construction. Cox’s proportional hazards model, partial likelihood, Nelson-Aalen estimators. Survival time prediction
- Diagnostic methods. Schoenfeld and other residuals. Testing the proportional hazards assumption. Detecting changes in covariate effects
- Frailty models and effects. Identifiability and estimation. Competing risks. Marginal models for clustered survival data

### On successful completion students will be able to

- Apply a range of appropriate statistical techniques to survival and event history data using statistical software
- Accurately interpret the output of statistical analyses using survival models fitted using standard software
- Construct and manipulate likelihood functions from parametric models for censored data
- Identify when particular models are appropriate through the application of diagnostic checks and model building strategies

#### Bibliography

- P. Hougaard, Analysis of Multivariate Survival Data. Springer, 2000
- T.M. Therneau and P.M. Grambsch, Modelling Survival Data: Extending the Cox Model. Springer, 2000
- T.H. Fleming, and D.P. Harrington, Counting processes and survival analysis. Wiley, 1991