| Summary: | This thesis focusses on the cumulative hazard function as a tool for modelling time-to-event data, as opposed to the more common hazard or survival functions. By focussing on and providing a detailed discussion of the properties of these functions a new framework is explored for building complex models from, the relatively simple, cumulative hazards. Parametric families are thoroughly explored in this thesis by detailing types of parameters for time-to-event models. The discussion leads to the proposal of combination parametric families, which aim to provide flexible behaviour of the cumulative hazard function. A common issue in the analysis of time-to-event data is the presence of informative censoring. This thesis explores new models which are useful for dealing with this issue.
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