Life tables for specific causes of death can be computed easily from the records that are made available by NCHS's Multiple Cause of Death Data. If we work at the monthly level of aggregation, relatively strong seasonal effects become visible. It is of interest to develop models that catch the overall trend with age and time, the seasonal pattern within a year, and the variation of the strength of that pattern over age and time.

I will present two modulation models. The first model describes the seasonal pattern by a sine and a cosine wave with a one-year period. They each are multiplied by a smooth surface over age and time, the modulation. Changes in phase and amplitude of the seasonality can be deduced from the modulation surfaces. Differences between gender and type of disease can be studied this way.

The second model borrows the idea of the modulation surface, but assumes an arbitrary seasonal pattern within a year, called the carrier wave, which is estimated from the data.

Trends and modulation surfaces are modeled by two-dimensional P-splines: tensor products of B-splines, combined with differences penalties on their coefficients, to tune smoothness. Large tables (500 months by 100 age categories) are analyzed. To speed up the computations, the fast algorithms from GLAM (generalized linear array models) turn out to be very useful.

The models are illustrated with data on US deaths from cerebrovascular and respiratory diseases.

This is joint work with Brian Marx (LSU), Jutta Gampe and Roland Rau (MPIDR).

Keywords: Modulation; P-splines; Generalized linear models; Smoothing

Biography: Paul Eilers started his career as an electronic engineer, but he gradually moved into statistics. Presently he is Professor of Genetical Statistics, but he has worked in the social sciences, in medical statistics, and in environmental monitoring and research. He has a special interest in smoothing, statistical computation, and chemometrics.