This module introduces some of the fundamental ideas and issues of lifetime and time-to-event data analysis, as used in actuarial practice, biomedical research and demography.
Pre-requisites: MATH2011 OR ECON2006
Aims and Objectives
Having successfully completed this module you will be able to:
- Describe and apply models of mortality and similar events which are specified as continuous-time discrete-state Markov processes
- 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
- analyse and interpret data, and especially to adopt a critical approach to numerical data
- 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
- 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 morality.
- 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
Learning and Teaching
Teaching and learning methods
Lectures, problem classes, office hours, computer laboratories.
|Total study time||150|
Resources & Reading list
Reading List. A suggested reading list for each part, and starting references for each assessment, will be made available on Blackboard
D. Collett (2003). Modelling survival data in medical research.. Chapman and Hall/CRC..
A. Hinde (1998). Demographic methods. Arnold.
This is how we’ll formally assess what you have learned in this module.
|Data analysis project||20%|
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Repeat type: Internal & External