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Biometrika 1997 84(2):349-363; doi:10.1093/biomet/84.2.349
© 1997 by Biometrika Trust
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Regression on hazard ratios and cross ratios in multivariate failure time analysis

ROSS L. PRENTICE and LI HSU

Division of Public Health Sciences, Fred Hutchinson Cancer Research Center 1124 Columbia Street, Seattle, Washington 98104, U.S.A. e-mail: rprentice{at}fhcrc.org lih{at}fhcrc.org

Cox model marginal survivor function and pairwise correlation models are specified for a multivariate failure time vector. The corresponding mean and covariance structure for the cumulative baseline hazard variates and standard baseline hazard function estimators are used to develop joint estimating equations for hazard ratio and correlation parameters, in the absence of censorship. Semiparametric models for pairwise survivor functions are required to generalise these equations to allow arbitrary right censorship. Under Clayton model bivariate distributions the resulting equations lead to joint estimators of hazard ratio and cross ratio parameters, and to inferences with useful and ready interpretation. For example, these estimates yield summary measures of pairwise dependency that have been adjusted for covariate effects on marginal hazard rates. Solutions to the proposed estimating equations are shown to be quite generally consistent and asymptotically normally distributed. Moderate sample size properties are examined in simulation studies, and illustrations are provided.

Key Words: Censoring • Cayton bivariate survival model • Correlated failure times • Covariance • Cox regression • Cross ratio • Estimating equation • Family cohort study • Genetic epidemiology • Martingale • Multivariate failure times • Regression • Time-varying covariate


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K. Bandeen-Roche and J. Ning
Nonparametric estimation of bivariate failure time associations in the presence of a competing risk
Biometrika, March 1, 2008; 95(1): 221 - 232.
[Abstract] [PDF]


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