Additive intensity models for discrete time recurrent event data

The thesis considers the Aalen additive regression model for recurrent event data. The model itself, estimation of the cumulative regression functions, testing procedures, checking goodness of fit and inclusion of dynamic covariates in the model are reviewed. A disadvantage of this model is that estimates of the conditional probabilities are not constrained to lie between zero and one, therefore a model with logistic intensity is considered. Results under the logistic model are shown to be qualitatively similar to those under the additive model. The additive model is extended to incorporate the possibility of spatial or spatio-temporal clustering, possibly caused by unobserved environmental factors or infectivity. Various tests for the presence of clustering are described and implemented. The issue of frailty modelling and its connection to dynamic modelling is presented and examined. We show that frailty and dynamic models are almost indistinguishable in terms of residual summary plots. A graphical procedure based on the property that the covariance between martingale residuals at time to and t > to is independent of t is proposed and supplemented by a formal test statistic to investigate the adequacy of the fitted models. The results can be used to compare models and to check the validity of the model being tested. Also we investigate properties under various types of model misspecification. All our works are illustrated using two sets of data measuring daily prevalence and incidence of infant diarrhoea in Salvador, Brazil. Significant clustering is identified in the data. We investigate risk factors for diarrhoea and there is strong evidence of dynamic effects being important, implying heterogeneity between individuals not explained by measured socio- economic and environmental factors.EThOS - Electronic Theses Online ServiceGBUnited Kingdo