Lifetime Data Analysis

, Volume 4, Issue 4, pp 355–391

Semiparametric Efficient Estimation in the Generalized Odds-Rate Class of Regression Models for Right-Censored Time-to-Event Data

  • Daniel O. Scharfstein
  • Anastasios A. Tsiatis
  • Peter B. Gilbert
Article

DOI: 10.1023/A:1009634103154

Cite this article as:
Scharfstein, D.O., Tsiatis, A.A. & Gilbert, P.B. Lifetime Data Anal (1998) 4: 355. doi:10.1023/A:1009634103154

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

gρ(S(t|Z)) = α(t) + β′Z

where gρ(s) = log(ρ-1(s-ρ) for ρ > 0, g0(s) = log(- log s), S(t|Z) is the survival function of the time to event for an individual with qx1 covariate vector Z, β is a qx1 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.

Nonparametric maximum likelihoodproportional hazards modelproportional odds modelsurvival analysis

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Daniel O. Scharfstein
    • 1
  • Anastasios A. Tsiatis
    • 2
  • Peter B. Gilbert
    • 1
  1. 1.Department of BiostatisticsJohns Hopkins School of Hygiene and Public HealthBaltimore
  2. 2.Department of StatisticsNorth Carolina State UniversityRaleigh