Nina H. Fefferman, Jyotsna S. Jagai, Elena N. Naumova
_{Tufts University School of Medicine
Family Medicine and Community Health
136 Harrison Avenue, Boston, MA 02111 USA
e-mail: nina.fefferman@tufts.edu}

Abstract 
In epidemiology, techniques which examine periodicity in times series data can be used to understand weekly, biannual or seasonal patterns of disease.  However, a simple understanding of periodicity  is not sufficient to examine the possible influence of variation in incubation period, distributed sources of infection, and infection due to environmental factors, especially if these influences affect the rate of disease on various spatio-temporal scales.  Wavelet analysis provides the ability to consider influences on various spatio-temporal scales.  In order to examine the  feasibility of using wavelets to assess dependencies over different spatio-temporal scales in a time series of disease incidence, we abstracted 10 years of daily records of ambient temperature and precipitation in addition to daily disease incidence data for Massachusetts for two enterically transmitted diseases.  We eliminated periodic fluctuation in both seasonal and weekly case reporting using various techniques (Fourier transformation and “loess” smoothing) on each time series of disease data.   These different methods were employed in order to examine the possible effect of removed periodicities on the variance of the data.  We then performed a wavelet decomposition to examine the residuals from these  analyses on a variety of temporal scales and examined the resulting correlations to the environmental data. 

Keywords:  wavelet decomposition, time series, Fourier decomposition, loess smoothing, environmental epidemiology

In: McRoberts, R. et al. (eds).  Proceedings of the joint meeting of The 6th International Symposium On Spatial Accuracy Assessment In Natural Resources and Environmental Sciences and The 15th Annual Conference of The International Environmetrics Society, June 28 – July 1 2004, Portland, Maine, USA.