## Abstract

We consider the problem of modelling the failure-time distribution, where failure is due to two distinct causes. One approach is to adopt a two-component mixture model where the components correspond to the two different causes of failure. However, routine application of this approach with typical parametric forms for the component densities proves to be inadequate in modelling the time to a re-replacement operation or death after the initial replacement of the aortic valve in the heart by a prosthesis, such as a xenograft valve. Hence we consider modifications to the usual mixture model approach to handle situations where there exists a strong dependency between the failure times of the distinct causes. With these modifications, a suitable model is able to be provided for the distribution of the time to a re-replacement operation conditional on the age of the patient at the time of the initial replacement operation. The estimate so obtained by the probability that a patient of a given age will undergo a re-replacement operation provides a useful guide to heart surgeons on the type of valve to be used in view of the patient's age.

Original language | English |
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Pages (from-to) | 753-767 |

Number of pages | 15 |

Journal | Environmetrics |

Volume | 10 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Nov 1999 |

Externally published | Yes |

## Keywords

- Competing risks
- Constrained mixture models
- EM algorithm
- Model
- Proportional hazards