Modelling longitudinal counts data with application to recurrent epileptic seizure events.

Abstract

The objectives of this thesis is to explore different approaches of modelling clustered correlated data in the form of repeated or longitudinal counts data leading to a replicated Poisson process. The specific application is from repeated epileptic seizure time to events data. Two main classes of models will be considered in this thesis. These are the marginal and subject or cluster specific effects models. Under the marginal class of models the generalized estimating equations approach due to Liang and Zeger (1986) is first considered. These models are concerned with population averaged effects as opposed to subject-specific effects which include random subject-specific effects such that multiple or repeated outcomes within a subject or cluster are assumed to be independent conditional on the subject−specific effects. Finally we consider a distinct class of marginal models which include three common variants namely the approach due to Anderson and Gill (1982), Wei et al (1989) and Prentice et al. (1981)