STAT40250 Survival Models

Academic Year 2022/2023

The aim of the subject is to give a grounding in survival models and their applications. The is a focus on human mortality and actuarial applications. This module covers part of the core syllabus of the Actuarial Profession's Subject CS2 [Risk Modelling and Survival Analysis]. The material covered includes the mathematics of survival models, estimation of lifetime distributions (e.g., Kaplan-Meier and Nelson-Aalen estimators), Binomial and Poisson mortality models, graduation of crude rates and goodness-of-fit of derived models, methods of projecting mortality rates and the Cox model. There is no choice of questions in the examination.

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Curricular information is subject to change

Learning Outcomes:

Learning outcomes include ability to: Define the density, distribution, survival and hazard function for random future lifetimes, and derive relationships between them. Estimate the survival function from data (e.g., using using Kaplan-Meier estimator) and using maximum likelihood estimation. Calculate exposed to risk and crude mortality rates under Binomial and Poisson models, and estimate parameters of well-known laws of mortality. Understand why graduation of crude rates is important and be able to apply several approaches to graduation and assess the results from graduations. Finally, the student will be able to apply several popular approaches to forecasting mortality rates.

Indicative Module Content:

Chapter 0: Preface

Chapter 1: Introduction to the Key Concepts, Notation & Mathematics of Survival Models

Chapter 2: Introduction to the survival statistics: censoring & estimating lifetime distributions

Chapter 3: Exposed-to-Risk, Binomial & Poisson Models

Chapter 4: Graduating Life Tables

Chapter 5: Methods to Graduating

Chapter 6: Projecting Mortality Rates

Chapter 7: Proportional Hazard models to deal with covariates

Student Effort Hours: 
Student Effort Type Hours




Autonomous Student Learning




Approaches to Teaching and Learning:
This module is delivered in the traditional manner of lectures, with students participating in weekly tutorials as they work through questions on the material presented (e.g. active/task-based learning of material delivered in lectures). However, if COVID-19 restrictions require a change to this form of delivery, or to the final assessment of a 2-hour final exam at the end of the semester, then students will be informed as soon as possible. 
Requirements, Exclusions and Recommendations
Learning Recommendations:

Basic statistical knowledge including expectation, variance and maximum likelihood.

Module Requisites and Incompatibles
Not applicable to this module.
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: End of semester exam 2 hour End of Trimester Exam No Graded No


Class Test: In-Class Test Week 6 n/a Graded No


Carry forward of passed components
Resit In Terminal Exam
Spring Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Self-assessment activities

How will my Feedback be Delivered?

Students can assess their individual learning in tutorials. The mid-term test gives an independent review of their grasp of the material.

Name Role
Dr Vasiliki Dimitrakopoulou Lecturer / Co-Lecturer
Mr Enda Carroll Tutor