Lecturer: S. J. Richards
- To understand the use of mathematical models of mortality,
illness and other life history events in the study of processes of
- To be able to estimate the parameters in these models, mainly by
- To apply methods of smoothing observed rates of mortality and to
test the goodness-of-fit of the models.
- Estimation for lifetime distributions: Kaplan-Meier estimate of
the survival function, estimation for the Cox model for proportional
- 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.
- Tests of consistency of crude estimates of rates of mortality
and their graduated values.
At the end of studying this module, students should be able to:
- Estimate a survival function using the Kaplan-Meier method.
- Find the partial likelihood function in the Cox model.
- Use the partial likelihood to estimate the parameters (with
standard errors) in the Cox model.
- Write down an appropriate Markov multi-state model for a system
with multiple transfers.
- Obtain the Kolmogorov forward equations in a Markov multi-state model.
- Derive the likelihood function in a Markov multi-state model
- Use the likelihood function to estimate the parameters (with
standard errors) in a Markov multi-state model with data.
- Obtain the likelihood function in the 2-state model with states
Alive and Dead under the binomial or Poisson models.
- Use any of three assumptions (uniform distribution of
deaths, constant force of mortality, Balducci assumption) to
reduce the binomial likelihood to a function of a single parameter,
and estimate the parameter.
- To apply the test, the standardised deviations test,
the sign test, the change of sign test, the grouping of signs test,
the serial correlation test to testing the adherence of a graduation
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, all tutorial material and
copies of past examination papers.
The modules F73ZF2 and F73ZH3 are examined synoptically in
a single three hour written examination paper.
If you have any problems or
questions regarding the module, you are encouraged to contact the
lecturer by email at ????@ma.hw.ac.uk.
information and course materials are available at
- Introduction, Notation and Revision:
- life time distributions, survival functions, rates and forces of
- Estimating the Lifetime Distribution:
- cohort studies
- Kaplan-Meier estimate of the survivor function
- Cox regression model, partial likelihood, estimation
- Markov Models: Theory:
- computation of
- 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
- three assumptions: uniform distribution of deaths, Balducci,
constant force of mortality
- likelihood and estimation for the binomial model
- actuarial estimate of
- Poisson model
- Graduation and Statistical tests:
- graduation process
- testing adherence to data
- test, standardised deviations test, sign test, change
of sign test, grouping of signs test, serial correlation test
- This module is linked and examined with F73ZH3, Survival Models