Two methods are given for the joint estimation of parameters in models for competing risks in survival analysis. In both cases Cox's proportional hazards regression model is fitted using a data duplication method. In principle either method can be used for any number of different failure types, assuming independent risks. Advantages of the augmented data approach are that it limits over-parametrisation and it runs immediately on existing software. The methods are used to reanalyse data from two well-known published studies, providing new insights.