Book Chapter

Modulation models for seasonal incidence tables

Eilers, P. H. C., Gampe, J., Marx, B. D., Rau, R.

In: del Castillo, J., Espinal, A., Puig, P. (Eds.): Proceedings of the 22nd International Workshop on Statistical Modelling, Barcelona, July 2-6, 2007, 239-244 (2007)
Barcelona: Institut d´Estadistica de Catalunya, IDESCAT.

ISBN 978-84-690-5943-2


We model monthly disease counts on an age time grid using two-dimensional varying coefficient Poisson regression. Since the marginal profile of counts show a very strong and varying annual cyclical behavior over time, sine and cosine regressors model periodicity, but their coefficients are allowed flexibility by assuming smoothness over the age and time plane. The two-dimensional varying coefficient surfaces are estimated using a gridded tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of AIC. The seasonal effects are summarized with two-dimensional amplitude and phase image plots. A motivating and illustrative example is provided using data on monthly deaths due to respiratory diseases, for US females during 1959 - 1999 and for ages 44 - 96.