Combining regression and association modelling for longitudinal data on bacterial carriage

A longitudinal data set, from the Finnish Otitis Media (FinOM) Studies, reporting carriage or non-carriage of Streptococcus pneumoniae at 2, 3, 4, 5, 6, 9, 12, 15 and 18 months of age of 329 children living in Tampere, Finland, is analysed. A logistic regression model on five time varying explanatory variables is fitted. The temporal association between presence at different ages is measured by dependence ratios and the structure of these is shown to be well described by a model indicating that roughly 10 per cent of the children are not susceptible to the bacteria, while for those that are susceptible, carriage status at a future observation age is conditionally independent of past observed statuses, given the present status. The dependence ratios between carriage at adjacent observation ages decay exponentially with age. Maximum likelihood estimates are obtained for the parameters of the full model, which is the combination of the marginal logistic regression and the association models. The parameter estimates of the full model, strengthened by non-testable Markov assumptions, are used for assessing the median duration of carriage and the acquisition rate as functions of age.