Annals of Statistics

Proportional hazards models with continuous marks

Yanqing Sun, Peter B. Gilbert, and Ian W. McKeague

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For time-to-event data with finitely many competing risks, the proportional hazards model has been a popular tool for relating the cause-specific outcomes to covariates [Prentice et al. Biometrics 34 (1978) 541–554]. This article studies an extension of this approach to allow a continuum of competing risks, in which the cause of failure is replaced by a continuous mark only observed at the failure time. We develop inference for the proportional hazards model in which the regression parameters depend nonparametrically on the mark and the baseline hazard depends nonparametrically on both time and mark. This work is motivated by the need to assess HIV vaccine efficacy, while taking into account the genetic divergence of infecting HIV viruses in trial participants from the HIV strain that is contained in the vaccine, and adjusting for covariate effects. Mark-specific vaccine efficacy is expressed in terms of one of the regression functions in the mark-specific proportional hazards model. The new approach is evaluated in simulations and applied to the first HIV vaccine efficacy trial.

Article information

Ann. Statist., Volume 37, Number 1 (2009), 394-426.

First available in Project Euclid: 16 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62N01: Censored data models
Secondary: 62N02: Estimation 62N03: Testing 62G20: Asymptotic properties

Competing risks distribution-free confidence bands and tests failure time data genetic data HIV vaccine trial pointwise and simultaneous confidence bands semiparametric model survival analysis


Sun, Yanqing; Gilbert, Peter B.; McKeague, Ian W. Proportional hazards models with continuous marks. Ann. Statist. 37 (2009), no. 1, 394--426. doi:10.1214/07-AOS554.

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