### Abstract

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant ρ and assumes that g_{ρ}(S(t\Z)) = α(t) + β′Z where g_{ρ}(s) = log(ρ^{-1}(s^{-ρ} - 1)) for ρ > 0, g_{0} (s) = log(-log s), S(t\Z) is the survival function of the time to event for an individual with q×1 covariate vector Z, β is a q×1 vector of unknown regression parameters, and α(t) is some arbitrary increasing function of t. When ρ = 0, this model is equivalent to the proportional hazards model and when ρ = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for β and exp(α(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for β is semiparametric efficient in the sense that it attains the semiparametric variance bound.

Original language | English (US) |
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Pages (from-to) | 355-391 |

Number of pages | 37 |

Journal | Lifetime Data Analysis |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1998 |

### Keywords

- Nonparametric maximum likelihood
- Proportional hazards model
- Proportional odds model
- Survival analysis

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*Lifetime Data Analysis*,

*4*(4), 355-391. https://doi.org/10.1023/A:1009634103154