Open Access Research article

The impact of nonlinear exposure-risk relationships on seasonal time-series data: modelling Danish neonatal birth anthropometric data

John McGrath12*, Adrian Barnett3, Darryl Eyles1, Thomas Burne1, Carsten B Pedersen4 and Preben Bo Mortensen4

Author Affiliations

1 Queensland Centre for Mental Health Research, The Park Centre for Mental Health, Wacol, Q4076, Australia

2 Department of Psychiatry, University of Queensland, St Lucia, Q4076 Australia

3 School of Population Health, University of Queensland, Herston, Q4006, Australia

4 National Centre for Register-based Research, Taasingegade 1, University of Aarhus 8000 Aarhus C, Denmark

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BMC Medical Research Methodology 2007, 7:45  doi:10.1186/1471-2288-7-45

Published: 15 October 2007



Birth weight and length have seasonal fluctuations. Previous analyses of birth weight by latitude effects identified seemingly contradictory results, showing both 6 and 12 monthly periodicities in weight. The aims of this paper are twofold: (a) to explore seasonal patterns in a large, Danish Medical Birth Register, and (b) to explore models based on seasonal exposures and a non-linear exposure-risk relationship.


Birth weight and birth lengths on over 1.5 million Danish singleton, live births were examined for seasonality. We modelled seasonal patterns based on linear, U- and J-shaped exposure-risk relationships. We then added an extra layer of complexity by modelling weighted population-based exposure patterns.


The Danish data showed clear seasonal fluctuations for both birth weight and birth length. A bimodal model best fits the data, however the amplitude of the 6 and 12 month peaks changed over time. In the modelling exercises, U- and J-shaped exposure-risk relationships generate time series with both 6 and 12 month periodicities. Changing the weightings of the population exposure risks result in unexpected properties. A J-shaped exposure-risk relationship with a diminishing population exposure over time fitted the observed seasonal pattern in the Danish birth weight data.


In keeping with many other studies, Danish birth anthropometric data show complex and shifting seasonal patterns. We speculate that annual periodicities with non-linear exposure-risk models may underlie these findings. Understanding the nature of seasonal fluctuations can help generate candidate exposures.