F79SU - Survival Models

Course leader(s):

• Alistair Wallis (Edinburgh, January)
• Andres Barajas Paz (Dubai, January)
• To be announced (Malaysia, January)

Syllabus

1. Estimating the Lifetime Distribution: (1.1 1 Life time distributions, survival functions, rates and forces of mortality, 1.2 2 Cohort studies, 1.3 3 Censoring, 1.4 4 Kaplan-Meier estimate of the survivor function, 1.5 5 Cox regression model, partial likelihood, estimation)

2. Markov Models (2.1 1 2-state model, 2.2 2 Multi-state Markov models, 2.3 3 Maximum likelihood estimate MLE of the force of mortality, 2.4 4 Score function and the maximum likelihood theorem, 2.5 5 Properties of the MLE of the force of mortality, 2.6 6 Likelihood and estimation in the multi-state model)

3. Binomial and Poisson Models of Mortality (3.1 1 Binomial model, 3.2 2 Two assumptions: uniform distribution of deaths, constant force of mortality, 3.3 3 Likelihood and estimation for the binomial model, 3.4 4 Actuarial estimate of qx, 3.5 5 Poisson model)

4. Graduation and Statistical tests (4.1 1 Graduation process, 4.2 2 Testing adherence to data, 4.3 3 χ2 test, standardised deviations test, sign test, change of sign test, grouping of signs test, serial correlation test)

5. Exposed to Risk (5.1 1 Calculation of exact exposed to risk., 5.2 2 Calculation of approximate exposed to risk using census data.)

6. Mortality Projection (6.1 1 Approaches to projecting mortality, 6.2 2 The Lee-Carter model, 6.3 3 The Cairns-Blake-Dowd model, 6.4 4 The P-spline model, 6.5 5 Age-period-cohort models, 6.6 6 Sources of forecast error)

Learning outcomes

By the end of the course, students should be able to do the following:

• Calculate the central exposed to risk exactly and from census data.
• perform estimation of a survival distribution using methods including the Kaplan-Meier estimator and the Cox model.
• apply appropriate Markov multi-state models for a system with multiple transfers.
• determine maximum likelihood estimators (with standard errors) in a Markov multi-state model and under the binomial and Poisson models.
• appraise the main methodologies for graduation and forecasting of observed mortality and morbidity rates.
• apply a range of appropriate statistical tests to check for adherence of a graduation to data.
• apply appropriate software tools in the computational aspects of mortality modelling, including maximum likelihood estimation, graduation of observed rates and related tests, and forecasting.
• employ communication and report writing skills for presenting results on matters relating to the modelling of mortality and morbidity data to a variety of audiences.

Further details

Curriculum explorer: Click here

SCQF Level: 9

Credits: 15