Survival Models

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Understand the theory underlying survival models and their estimation and of how to use R to fit models, including the Kaplan-Meier estimate of the survival function, parametric models and the Cox regression model
• Understand models for human mortality, including how to compute and interpret the life table in a variety of contexts and models for forecasting mortality
• Solve problems, and especially to apply ideas learnt in one context to other contexts
• Understand the key features of lifetime data, including censoring, and of probability models for lifetime data: survival function, hazard and force of mortality
• Understand the need to graduate crude data on mortality rates and an understanding of how to compare crude mortality rates against a standard of graduated set of rates
• Describe and apply models of mortality and similar events which are specified as continuous-time discrete-state Markov processes
• Analyse and interpret data, and especially to adopt a critical approach to numerical data

• Introduction to concepts of modelling, survival data and survival models; censoring; survival and hazard functions.
• Estimating the survivor function non-parametrically (Kaplan-Meier and Nelson-Aalen estimators); parametric survival models; estimation using maximum likelihood.
• Regression models for survival data; proportional hazards; the Cox regression model; accelerated failure time models.
• Introduction to continuous-time, discrete-state Markov models; two-state and multiple-state models; Kolmogorov equations; estimating the parameters of multiple-state models.
• Models for human mortality; the life table: theory and applications.
• Comparison of models of mortality: Binomial, Poisson and multiple-state models. Estimation and inference using maximum likelihood and other methods.
• Exposure to risk; the principle of correspondence; estimating the exposed-to-risk with aggregate data.
• Comparison of mortality experiences; mortality rates and standardised mortality ratios; statistical tests appropriate for the comparison.
• Graduation of mortality data; reasons for graduation; methods of graduation; tests of adherence to data and smoothness of a graduation.
• Models for forecasting human mortality
• Using R to analyse lifetime and survival data

Lectures, problem classes, computer laboratories

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.