Heterogeneity in additive and multiplicative event history models

• Main Author: Mohammadi, Mahdi
• Published: University of Newcastle Upon Tyne 2009
• Subjects: 511.8
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.556138

Heterogeneity in survival and recurrent event data is often due to unknown, unmeasured, or immeasurable factors. Subjects may experience heterogeneous failure times or event rates due to different levels of vulnerability to the event of interest. The more prone the subjects, the shorter the survival times and the higher the event rates. Furthermore, the presence of cured subjects who are not susceptible to the event contributes to the heterogeneity. Frailty and cure models can take into account the unexplained variation due to heterogeneity and cured fractions. This research explores the ideas of these models for failure and recurrent event data. The models are checked by simulation studies and they are applied to three data sets wherever applicable. For survival data, we investigate by simulation the results of a frailty mixture model which includes frailty and cure models. Even for a small size (e.g. 100), this model fits well to the data from either frailty or cure models. We also explore misspecification of the Cox and frailty model theoretically and by simulation when data are generated from the cure model. Although the regression parameters are underestimated under the misspecified Cox model, the frailty model fits well to simulated data with a cured fraction. Furthermore, regression parameters are underestimated under a misspecified cure model when the frailty model holds. In the case of a high rate of administrative censoring (80%), the bias is small in all misspecified models. The Aalen and Cox frailty models for failure times are compared in terms of frailty parameter estimates. Under both the Cox and Aalen frailty models, the frailty variance is underestimated. However, the frailty variance is estimated to be smaller under the Aalen frailty model because this model, as opposed to the Cox frailty model, allows for time-dependent regression parameters which can explain part of the random processes. We include a time-constant frailty term into the Aalen intensity model to construct an individual time-constant frailty model (ITCF) for recurrent event data and suggest a dynamic procedure to estimate the parameters. Estimated frailty and regression parameters are unbiased in the simulation study. Although a misspecified Aalen model ignores heterogeneity, unbiased regression parameters are obtained. However, the intensity and residuals are not estimated appropriately. Several models for clustered recurrent event data are suggested. Models can be used to estimate the correlation between subjects within the clusters and heterogeneity between them. One of the models can also consider cured fractions at the cluster and individual levels. This model can make a difference to the significant results when a cluster is event-free or the rate of event-free subjects is considerably different at various levels of a covariate. A time-dependent frailty model is also explored. This model assumes that at each time there is a frailty term with variance ξ, but there is correlation between different times. The correlation between frailties at time u and v is assumed to be p |u-v|. We use an approximation for small values of ξ to estimate the parameters. Simulation studies confirm that results are good and the bias is ignorable for both frailty and regression parameters. This model includes the ITCF model when p = 1 and a misspecified ITCF model underestimates the ξ. When p is not close to 1 (e.g. 0.8), the two models can be differentiated by composite likelihood. Three data sets are used throughout the thesis. The first (leukaemia) has single event survival times whereas the second (patient controlled analgesia) and third (Blue bay diarrhoea) have recurrent events. Clustering is present in the third dataset.