# Matrix Approaches to Health Demography

Start: 13 March 2017
End: 24 March 2017

Location: Max Planck Institute for Demographic Research (MPIDR), Rostock, Germany

Instructor:
Hal Caswell

## Course description

This course will introduce matrix methods for the analysis of health demography. Health demography is particularly concerned with measures of longevity and healthy longevity, with the dynamics of individual transitions among health and disease states, with the projection of the future health composition of populations, and analyses accounting for causes of death. Matrix methods describe the dynamics of individuals, cohorts, and populations, in a powerful generalization of classical life table methods. We will use them to extend the usual analyses in two directions. First, we will incorporate variance and stochasticity into the analyses, going beyond the usual obsession with mean results. Second, we will use sensitivity analyses to quantify the effects of parameters on the results.

The class will introduce methods based on Markov chains, Markov chains with rewards, multistate matrix models, and matrix calculus. These methods will be compared to traditional approaches, and applied to data on prevalence of health conditions, incidence of disease and disability, population projections, and causes of death.

Although the applications will focus on human populations, all of these topics have direct (or, at least potential) applications in animal and plant demography. Biodemographers and population biologists interested in new perspectives in demographic analysis are encouraged to apply.

## Organization

The course will be a mixture of lectures, discussions, and computer exercises.

## Prerequisites

Basic demography (human, plant, or animal), including life tables, mortality and fertility schedules, and their applications. Familiarity with the basic operations of matrix algebra (matrices, vectors, multiplication, inverses, eigenvalues and eigenvectors). Fluency in Matlab or R.

## Examination

Students will be evaluated on the basis of computer exercises and class participation.

Specific readings will be provided before the beginning of the course. The following are some useful sources.

A comprehensive treatment of the "classical" methods and applications health demography:

• Siegel, J.S. 2012. The Demography and Epidemiology of Human Health and Aging. Springer-Verlag

The basic source for matrix population models is:

• Caswell, H. 2001. Matrix Population Models. 2nd edition. Sinauer Associates, Sunderland, MA.

Some of the matrix material is also covered in:

• Keyfitz, N. and H. Caswell. 2005. Applied Mathematical Demography. 3rd edition. Springer-Verlag.

Some of the methods we will explore are presented in the following papers.

• van Daalen, S. and H. Caswell. 2015. Lifetime reproduction and the second demographic transition: stochasticity and individual variation.  Demographic Research 33:561-588.
• Caswell, H.  2012. Matrix models and sensitivity analysis of populations classified by age and stage: a vec-permutation matrix approach. Theoretical Ecology 5:403-417.  DOI 10.1007/s12080-011-0132-2 (published online 2011)
• Caswell, H. 2009. Stage, age, and individual stochasticity in demography.  The Per Brinck Oikos Award Lecture 2008.  Oikos 118:1763-1782.

## Financial support

There is no tuition fee for this course. Students are expected to pay their own transportation and living costs. However, a limited number of scholarships are available on a competitive basis for outstanding candidates and for those applicants who might otherwise not be able to come.

## Recruitment of students

• Applicants should either be enrolled in a PhD program (those well on their way to completion will be favored) or have received their PhD.
• A maximum of 15 students will be admitted.
• The selection will be made by the MPIDR based on the applicants’ scientific qualifications.