Statistical analysis of seasonality in sudden infant death syndrome
SIDS deaths exhibit a seasonal pattern with a winter peak, and the cause of this seasonality is unknown. The seasonal pattern is not symmetrical and it has been thought that the relatively flat winter peak may be due to the existence of more than one underlying population, where each population corresponds to a different cause of seasonality. In this thesis, mixtures of von Mises distributions have been fitted using maximum likelihood estimation to determine whether there is heterogeneity in the UK SIDS data. Various computational problems arise with the fitting procedures and attempts to tackle these for the SIDS data are discussed. A bootstrap likelihood ratio method is used to assess the number of components in the mixture, and its properties are investigated by simulation. Changes in the seasonal pattern since the 'back to sleep' campaign are also examined as any differences might give clues as to what caused the fall in 1992, and what the reasons for the remaining deaths might be. The von Mises distributions are compared with cosinor analysis and skewed regression models to determine the most appropriate method for modelling the seasonality in the data. Mixtures of Weibull and Gamma distributions are used to model the age distribution in SIDS. The motivation for this was to determine whether there are two or more groups of babies whose age-at-death distributions are different and to examine any changes since the 'back to sleep' campaign. Generalised linear models have previously been used to determine whether month of birth is an independent risk factor in addition to month of death and age at death. In this thesis, mixtures of these generalised linear models have been fitted using the EM algorithm to determine whether there are different groups of babies with different risks. Childhood type 1 diabetes mellitus is another condition which exhibits a seasonal pattern in diagnosis. The thesis concludes by considering analysis of these data using the mixture modelling approach.