F79SU Survival Models

Prof George StreftarisDr Andres Barajas Paz

Course co-ordinator(s): Prof George Streftaris (Edinburgh), Dr Wai Meng Kwok (Malaysia), Dr Andres Barajas Paz (Dubai).

Aims:

  • To understand the use of mathematical models of mortality, illness and other life history events in the study of processes of actuarial interest.
  • To be able to estimate the parameters in these models, mainly by maximum likelihood.
  • To apply methods of smoothing observed rates of mortality and to test the goodness-of-fit of the models.

Summary:

  • Estimation for lifetime distributions: Kaplan-Meier estimate of the survival function, estimation for the Cox model for proportional hazards.
  • Statistical models for transfers between multiple states (e.g., alive, ill, dead), the multi-state Markov model, relationship between probabilities of transfer and transition intensities, estimation for the parameters in these models. The binomial and Poisson models of mortality.
  • Methods of projecting future mortality rates to allow for improving longevity.
  • Methods of graduation: parametric and standard table. Tests of consistency of crude estimates of rates of mortality and their graduated values.
  • Computing facilities, especially R, will be used extensively and this work will be assessed by practical assignments.

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisite course(s): F78PA Probability and Statistics A & F78PB Probability and Statistics B .

Location: Edinburgh, Malaysia.

Semester: 2.

Syllabus:

  • Introduction, Notation and Revision:
    • life time distributions, survival functions, rates and forces of mortality
  • Estimating the Lifetime Distribution:
    • cohort studies
    • censoring
    • Kaplan-Meier estimate of the survivor function
    • Cox regression model, partial likelihood, estimation
  • Markov Models: Theory:
    • computation of tpx
    • multi-state Markov models
    • Kolmogorov forward equations
  • Markov models: Data and Estimation:
    • 2-state model
    • maximum likelihood estimate (MLE) of the force of mortality
    • score function and the maximum likelihood theorem
    • properties of the MLE of the force of mortality
    • likelihood and estimation in the multi-state model
  • Binomial and Poisson Models of Mortality
    • binomial model
    • two assumptions: uniform distribution of deaths, constant force of mortality
    • likelihood and estimation for the binomial model
    • actuarial estimate of qx
    • Poisson model
  • Graduation and Statistical tests:
    • graduation process
    • testing adherence to data
    • χ2 test, standardised deviations test, sign test, change of sign test, grouping of signs test, serial correlation test
  • Exposed to Risk
    • Calculation of exact exposed to risk.
    • Calculation of approximate exposed to risk using census data.
  • Mortality Projection
    • Approaches to projecting mortality
    • The Lee-Carter model
    • The Cairns-Blake-Dowd model
    • The P-spline model
    • Age-period-cohort models
    • Sources of forecast error
  • The course F79SU is synoptic with F79SP Stochastic Processes.

Reading list:

The course book is: I D Currie, Survival Models. The book is essential reading and is available from the department. It contains outline copies of the lecture material and all tutorial material. Copies of past examination papers and illustrative R code will be available through the course web site.

Supplementary reading is provided in Macdonald, A.S.,
Richards, S.J &  Currie, I.D. (2018). Modelling Mortality with Actuarial 
Applications. Cambridge University Press.

SCQF Level: 9.

Credits: 15.

Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.

Canvas: further information and course materials are available on Canvas