Modellering van Niet-Normale Longitudinale Data in Continue Tijd, Gebaseerd op de Likelihoodfunctie

Abstract

We shall begin from the general fact that most of the methods proposed in the literature to analyse non-normal longitudinal data make the assumption that the observations are equally-spaced in time. Very often, the authors of such papers mention that extension to continuous time is not a problem, although without explicitly explaining how to do so. However, such a generalization usually turns out to be theoretically difficult, if not impossible, the original model making a large use of the discrete structure of time. A second worrying limitation is the wide use of marginal models when irregularly sampled longitudinal data have to be analyzed, few flexible conditional model being available. This is not a problem in observational population studies, such as epidemiology, where marginal tools exist and are well adapted to answer the usual type of questions attached to such settings. However, when the data generating mechanism is the central question of the study, when the way that the observations evolve over time is of interest, such as in clinical trials or biological experiments, conditional models are desired. For all these reasons, building conditional models for non-normal longitudinal data turns out to be both an interesting and challenging problem to be considered. An extra motivating problem was to concentrate on likelihood based approaches to enable different models to be compared, either directly through their likelihood functions, which indicate how probable they each make the observed data, or by more sophisticated model selection procedures, such as the AIC, which penalizes for the complexity of the competing models. Note that this is not possible with most of the marginal models in the literature, because they essentially rely on some kind of score equations, the generalized estimating equations, which, most often, cannot be integrated back to obtain a likelihood function. ....