Phase-type inference on competing risks models with covariates, using MCMC methods

The aim with this Master's thesis has been to develop a method of fitting a Phase-type model to a competing risks data set with covariates, and to approximate an underlying model such that important functionals and quantities can be estimated. To do this, the method proposed by Bladt et al. of fitting a Phase-type model to survival data, has been generalized to the competing risks setting, and this generalized method has been further extended to include covariates.The part of the theory which involves extending the method by Bladt et al. to competing risks was mainly produced in the Master's project in the fall of 2014, and is presented in the theory part. The method is a MCMC algorithm which updates the Phase-type parameters in a Gibbs-sampler.The results for the model without covariates show that the model is able to produce estimates for the sub-distribution functions, sub-density functions and cause-specific hazard rates in a satisfying way.Before developing the new method in the theory part, three existing competing risks regression models have been presented. This is the Fine \& Gray model, Cox regression and the model developed by Scheike and Zhang. These three models have also been used for comparison with the Phase-type model in the presentation of the results.New theory has been developed in the sense that covariates have been introduced in the existing model. This has been done by using covariate regression in the absorbing intensities of the Phase-type model.The results show that the model is suitable for a variety of different data sets and underlying distributions. The method manages to produce good estimates for the sub-distribution functions, sub-density functions, the covariate regression coefficients, and in many cases also for the cause-specific hazard rates. The estimates of the covariate regression coefficients are similar to the Cox regression coefficients