### Abstract

We develop tests of the proportional hazards assumption, with respect to a continuous covariate, in the presence of unobserved heterogeneity with unknown distribution at the individual observation level. The proposed tests are specially powerful against ordered alternatives useful for modeling non-proportional hazards situations. By contrast to the case when the heterogeneity distribution is known up to finite dimensional parameters, the null hypothesis for the current problem is similar to a test for absence of covariate dependence. However, the two testing problems differ in the nature of relevant alternative hypotheses. We develop tests for both the problems against ordered alternatives. Small sample performance and an application to real data highlight the usefulness of the framework and methodology .

Original language | English |
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Place of Publication | St. Andrews |

Publisher | University of St. Andrews |

Publication status | Published - 2009 |

### Publication series

Name | Discussion Paper Series |
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### Keywords

- two-sample tests
- increasing hazard ratio
- trend tests
- partial orders
- mixed proportional hazards model
- time varying coefficients

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## Cite this

Bhattacharjee, A. (2009).

*Testing for proportional hazards with unrestricted univariate unobserved heterogeneity*. (Discussion Paper Series). University of St. Andrews .