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

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.Birth weight has long been acknowledged as an important measure of neonatal health [1]. In addition to providing insights into prenatal development, this variable is known to be associated with a wide range of important cognitive, behavioural and health outcomes in infancy, childhood and adulthood. While there is widespread agreement that birth weight shows seasonal fluctuations [2,3], there is a lack of between-location agreement about features such as: (a) the timing (or phase) of maximum weight, and (b) the presence of a single peak (unimodal, 12 month periodicity) or two peaks (bimodal, 6 and 12 month periodicities). With respect to the phase of peak birth weight, some populations had regular, sine wave-like 12 month periodicities, with peak birth weight in spring [4], while other studies found no a