B.Sc. (Hons.) in Statistics, University College of Wales, Aberystwyth, 1981

Ph.D. in Statistical Science, University of Birmingham, UK, 1991

Thesis: Competing Risk Survival Analysis with Industrial Applications

**Synopsis**: Some results in competing risk survival analysis are presented. In particular, a general expression for the non-parametric likelihood is derived, involving the cause specific hazard function. Unlike earlier forms, it can be correctly applied when there are tied lifetimes of different failure types. This likelihood function is shown to be a special case of the likelihood for a multiple group logistic model. The case of ties of different types in the data is also explored via a cause conditional hazard function, and the corresponding likelihood function is derived.

This approach, which uses an application of the E-M algorithm, gives a new perspective on the special case of when the largest survival time is a censoring, and in particular why some probability estimates do not sum to unity in this case. Extensions of competing risk models to those which include covariates are presented, including the novel use of logistic regression to adjust a non-specific hazard model to reflect competing risk aspects of survival depending on fail type. The cause conditional hazard is also generalized to the covariate arena.

Industrial life testing data sets are analysed to illustrate some of the results.