Proportional hazards models with continuous marks. (English) Zbl 1155.62075

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

Ann. Stat. 37, No. 1, 394-426 (2009).

Summary: 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 [R. L. Prentice et al., Biometrics 34, 541–554 (1978; Zbl 0392.62088)]. 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.

MSC:

62N03	Testing in survival analysis and censored data
62N01	Censored data models
62P10	Applications of statistics to biology and medical sciences; meta analysis
62N02	Estimation in survival analysis and censored data
62G20	Asymptotic properties of nonparametric inference
62G10	Nonparametric hypothesis testing
60F05	Central limit and other weak theorems

Keywords:

competing risks; distribution-free confidence bands; failure time data; genetic data; HIV vaccine trial; pointwise and simultaneous confidence bands; semiparametric model

Citations:

Zbl 0392.62088

Software:

timereg

References:

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