Modelling of Dependent Competing Risks and Semi-Competing Risks by Means of First Passage Times of Gamma Processes
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In this thesis we model both dependent competing risks and semi-competing risks by means of first passage times in a gamma process. In both cases, we consider a terminal event, such as death of a person or component failure, and a non-terminal event like for instance disease recurrence or preventive maintenance of a component. We let the time to the terminal event equal the first passage time to a fixed level c in a gamma process. The time to the non-terminal event is represented by the first passage time to a stochastic level S. We have assumed that S is independent of the gamma process so that we have random signs censoring. In the competing risks case, a similar model based on Wiener processes has been considered before. For semi-competing risks this is a new modelling approach, as semi-competing risks data have mostly been analysed through copula models in the past. We conduct simulation studies that show that the parameters in the gamma process model can be estimated satisfactorily for both competing and semi-competing risks data. The model is also applied to real datasets and seems to be able to fit the data well, at least for certain chosen distributions of the random level S. It is particularly interesting to note that our results for semi-competing risks are consistent with earlier published results.