### 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.

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 | Scottish Institute for Research in Economics |

Publication status | Published - 2009 |

### Publication series

Name | SIRE Discussion Papers |
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### Keywords

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

## Fingerprint Dive into the research topics of 'Testing for proportional hazards with unrestricted univariate unobserved heterogeneity'. Together they form a unique fingerprint.

## Cite this

Bhattacharjee, A. (2009).

*Testing for proportional hazards with unrestricted univariate unobserved heterogeneity*. (SIRE Discussion Papers ). Scottish Institute for Research in Economics.