MA216-7-SP-CO:
Survival Analysis
2019/20
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Monday 13 January 2020
Friday 20 March 2020
15
01 October 2019
Requisites for this module
(none)
(none)
(none)
(none)
MA319
DIP G30009 Statistics,
MSC G30012 Statistics,
DIP N32309 Actuarial Science,
MSC N32312 Actuarial Science
Calculations in clinical trials, pensions and life and health insurance require reliable estimates of transition intensities/survival rates. This Survival Analysis module covers the estimation of these intensities. This module covers the related units of CS2 (Risk Modelling and Survival Analysis, Core Principles), Institute and Faculty of Actuaries CS2 syllabus.
The aims of this module are:
1. to critically outline the distinctive characteristics of non-parametric estimation procedures for the lifetime distribution;
2. to critically analyse and derive maximum likelihood estimators for the transition intensities;
3. to examine in detail the Binomial and Poisson models of mortality and compare with the Markov models;
4. to analytically describe the estimation procedure for transition intensities depending on age;
5. to critically analyse and carry out tests for the consistency of crude estimates with a standard table or a set of graduated estimates;
6. to describe in detail the process of graduation and the advantages and disadvantages of the various methods.
On completion of this module, students should be able to:
• explain the concept of survival models (4.1)
• describe estimation procedures for lifetime distributions (4.2)
• estimate transition intensities dependent on age (exact or census) (4.4)
• understand graduation and graduation tests (4.5)
• understand mortality projection (4.6)
Syllabus
1. Concepts of actuarial modelling [CS2-4.1]:
* Describe why and how models are used, their benefits and limitations.
* Explain the concept of survival models.
* Describe the model of lifetime or failure time from age x as a random variable.
* State the consistency condition between the random variable representing lifetimes from different ages.
* Define the distribution and density functions of the random future lifetime, the survival function, the force of mortality or hazard rate, and derive relationships between them.
* State the Gompertz and Makeham laws of mortality.
* Compute life tables.
* Define the expected value and variance of the complete and curtate future lifetime and derive expressions for them.
* Define the curtate future lifetime from age x and state its probability function.
2. Exact or approximate estimations of transition intensities [CS2-4.4]:
* Describe the principle of correspondence and explain its fundamental importance in the estimation procedure.
* Specify the data needed for the exact calculation of a central exposed to risk (waiting time) depending on age and sex, and calculate a central exposed to risk.
* Explain how to obtain estimates of transition probabilities, including in the single decrement model and the actuarial estimate based on the simple adjustment to the central exposed to risk.
* Explain the assumptions underlying the census approximation of waiting times.
* Explain the concept of rate interval.
3. Explain the concept of survival models [CS2-4.2]:
* Recognise the characteristics of survival data, e.g. censoring and truncation
* Describe the various ways in which lifetime data might be censored
* Describe the Kaplan-Meier (or product limit) estimate of the survival function and the Nelson-Aalen estimate of the cumulative hazard rate; compute it from typical data and estimate its variance
* Determine the proper method to be used in analysing time-to-event data (e.g. parametric, semi-parametric or non-parametric method)
* Describe the Cox proportional hazard model, derive the partial likelihood estimate, and state its asymptotic distribution
* Perform survival analysis using a computer statistical software package, and interpret computer outputs
4. Method of graduation and statistical tests [CS2-4.5]:
* Describe and apply statistical tests of the comparison of crude estimates with a standard mortality table testing for:
a. the overall fit
b. the presence of consistent bias
c. the presence of individual age where the fit is poor
d. the consistency of the 'shape' of the crude estimates and the standard table
* For each test describe:
a. the formulation of the hypothesis
b. the test statistic
c. the distribution of the test statistic using approximations where appropriate
d. the application of the test statistic
e. how tests should be amended to compare crude and graduated sets of estimates
f. how tests should be amended to allow for the presence of duplicate policies
* Describe the reasons for graduating crude estimates of transition intensities or probabilities and state the desirable properties of a set of graduated estimates
5. Mortality projection [CS2-4.6]:
* Describe the approaches to the forecasting of future mortality rates based on extrapolation, explanation and expectation, and their advantages and disadvantages.
* Describe the Lee-Carter, age-period-cohort, and p-spline regression models for forecasting mortality
* Use an appropriate computer package to apply the Lee-Carter, age-period-cohort, and p-spline regression models to a suitable mortality dataset.
* List the main sources of error in mortality forecasts.
The module consists of 30 lectures, 5 classes, 5 labs, in the spring term. In the summer term 3 revision lectures are given. A project is undertaken in groups.
This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Group Research Proposal |
|
25% |
| Coursework |
Group Assignment |
|
75% |
| Exam |
Main exam: 24hr during Summer (Main Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Prof Hongsheng Dai, email: hdaia@essex.ac.uk.
Dr Hongsheng Dai (hdaia@essex.ac.uk), Jackie Wong (jw19203@essex.ac.uk), Dr Yanchun Bao (ybaoa@essex.ac.uk)
Dr Hongsheng Dai (hdaia@essex.ac.uk)
No
No
No
Dr Dimitrina Dimitrova
Cass Business School, City, University of London
Senior Lecturer
Available via Moodle
Of 229 hours, 89 (38.9%) hours available to students:
140 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
Disclaimer: The University makes every effort to ensure that this information on its Module Directory is accurate and up-to-date. Exceptionally it can
be necessary to make changes, for example to programmes, modules, facilities or fees. Examples of such reasons might include a change of law or regulatory requirements,
industrial action, lack of demand, departure of key personnel, change in government policy, or withdrawal/reduction of funding. Changes to modules may for example consist
of variations to the content and method of delivery or assessment of modules and other services, to discontinue modules and other services and to merge or combine modules.
The University will endeavour to keep such changes to a minimum, and will also keep students informed appropriately by updating our programme specifications and module directory.
The full Procedures, Rules and Regulations of the University governing how it operates are set out in the Charter, Statutes and Ordinances and in the University Regulations, Policy and Procedures.