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

Research output: Contribution to journalArticle

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 - 1)) for ρ > 0, g0 (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 languageEnglish (US)
Pages (from-to)355-391
Number of pages37
JournalLifetime Data Analysis
Volume4
Issue number4
DOIs
StatePublished - 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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