Summer Semester 2009

Perturbation Analysis of Longevity

Hal Caswell (Woods Hole Oceanographic Institution)

Start: 30 March 2009
End: 17 April 2009
Location:Max Planck Institute for Demographic Research (MPIDR), Rostock, Germany


Course description:

Longevity is one of the most fundamental demographic quantities. Summary statistics describing longevity (its expectation and variance, measures of inequality, longevity under various kinds of health conditions) are widely used to contrast mortality schedules and the environments (biological, social, historical, medical) affecting populations. This course will address perturbation analysis of longevity in its various guises. Perturbation analysis asks how some quantity will change as a result of changes in one or more underlying parameters, and so it is an essential tool for analyzing differences among populations.

The course will present the main mathematical approaches to perturbation analysis of longevity (due originally to Keyfitz, Pollard, and Vaupel) and recent extensions and generalizations that I have been working on. We will extend the classical results from age-classified to stage-classified models, including multistate models in which individuals are classified by age and other variables, such as health status. We will also go beyond the analysis of life expectancy to consider the sensitivity of the variance of longevity, of measures of inequality, and perhaps other statistics. Students will have an opportunity to apply the methods to analysis of human and biodemographic data. The course will include a computer lab.


Instruction is given in the form of four 60-minute lectures a week for three weeks, beginning 31 March 2009. There will be a 2-hour computer laboratory on one day each week. Students will be working in pairs in the computer lab. The computer lab and assignments will utilize Matlab software.

Tentative lecture schedule:

  1. Introduction. Longevity and its measurement. Discrete and continuous models. Generalizations of the basic age-classified model: stage-classification, health expectancy, time-variation. Perturbation analysis, sensitivity and elasticity, decomposition (LTRE) analysis.
  2. Keyfitz’s population entropy and the elasticity of life expectancy.
  3. Pollard’s derivative and decomposition of life expectancy differences.
  4. The Vaupel-Romo approach to temporal change in life expectancy.
  5. Markov chain approaches. Formulation of the model. Absorbing chain theory. Describing longevity: life expectancy, variance, inequality.
  6. Perturbation analysis of Markov chains: expectation of longevity.
  7. Perturbation analysis of Markov chains: Variance in longevity.
  8. Health expectancy and related quantities; perturbation analysis.
  9. Indices of inequality. Calculation from Markov chains. Perturbation analysis.
  10. Comparative studies and decomposition of temporal differences.
  11. Comparative studies and decomposition of interpopulation differences.
  12. Wrap-up.


Students should be familiar with the basics of life table analysis and matrix population models, basic calculus, and the demographic concepts of life expectancy. Expertise in Matlab software is not required, but will be helpful.


Students will be evaluated on participation in class and completion of exercises.

Recruitment of students:

How to apply:

Financial support:

There is no tuition fee for this course. Up to 4 scholarships are available, each worth up to a maximum of 2000 Euro. These scholarships can only be used to cover transportation costs to and from Rostock, Germany, as well as accommodation in Rostock. Scholarship holders will need to submit an invoice and receipts to the MPIDR. The MPIDR will reimburse actual costs if actual costs are lower than 2000 Euro. The MPIDR will reimburse 2000 Euro if actual costs are higher than 2000 Euro.

General readings:

The course will make use of readings from:

Additional reading material will be provided at the beginning of the course.

[ Home | Courselist Summer Semester 2009]