Estimation of time‐dependent association for bivariate failure times in the presence of a competing risk

This article targets the estimation of a time-dependent association measure for bivariate failure times, the conditional cause-specific hazards ratio (CCSHR), which is a generalization of the conditional hazards ratio (CHR) to accommodate competing risks data. We model the CCSHR as a parametric regression function of time and event causes and leave all other aspects of the joint distribution of the failure times unspecified. We develop a pseudo-likelihood estimation procedure for model fitting and inference and establish the asymptotic properties of the estimators. We assess the finite-sample properties of the proposed estimators against the estimators obtained from a moment-based estimating equation approach. Data from the Cache County study on dementia are used to illustrate the proposed methodology.

[1]  R. Prentice,et al.  Dependence Estimation Over a Finite Bivariate Failure Time Region , 2000, Lifetime data analysis.

[2]  Kenneth P. Burnham,et al.  Handbook of Statistics, Vol. 12: Environmental Statistics. , 1995 .

[3]  H C Hendrie,et al.  Epidemiology of dementia and Alzheimer's disease. , 1998, The American journal of geriatric psychiatry : official journal of the American Association for Geriatric Psychiatry.

[4]  Ross L. Prentice,et al.  On assessing the strength of dependency between failure time variates , 1996 .

[5]  K. Bandeen-Roche,et al.  A Diagnostic for Association in Bivariate Survival Models , 2005, Lifetime data analysis.

[6]  D. Oakes,et al.  Semiparametric inference in a model for association in bivanate survival data , 1986 .

[7]  P. Albert,et al.  Modeling Familial Association of Ages at Onset of Disease in the Presence of Competing Risk , 2010, Biometrics.

[8]  Jason P. Fine,et al.  Nonparametric estimation of cause-specific cross hazard ratio with bivariate competing risks data , 2008 .

[9]  J. Robins,et al.  Time-dependent cross ratio estimation for bivariate failure times. , 2011, Biometrika.

[10]  Martin T. Wells,et al.  Estimation of Kendall's tau under censoring , 2000 .

[11]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[12]  D. Oakes.  A Model for Association in Bivariate Survival Data , 1982 .

[13]  Karen Bandeen-Roche,et al.  Non-parametric estimation of bivariate failure time associations in the presence of a competing risk. , 2008, Biometrika.

[14]  T. Louis,et al.  Inferences on the association parameter in copula models for bivariate survival data. , 1995, Biometrics.

[15]  A. Manatunga,et al.  Diagnostic Plots for Assessing the Frailty Distribution in Multivariate Survival Data , 2001, Lifetime data analysis.

[16]  Mei-Jie Zhang,et al.  A Class of Goodness of Fit Tests for a Copula Based on Bivariate Right‐Censored Data , 2005, Biometrical journal. Biometrische Zeitschrift.

[17]  Jianwen Cai,et al.  Covariance and survivor function estimation using censored multivariate failure time data , 1992 .

[18]  Kaare Christensen,et al.  Longevity studies in GenomEUtwin. , 2003, Twin research : the official journal of the International Society for Twin Studies.

[19]  K. Welsh-Bohmer,et al.  APOE-ε4 count predicts age when prevalence of AD increases, then declines , 1999, Neurology.

[20]  Bin Nan,et al.  Piecewise Constant Cross-Ratio Estimation for Association of Age at a Marker Event and Age at Menopause , 2006 .

[21]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .

[22]  P. Hartge,et al.  The risk of cancer associated with specific mutations of BRCA1 and BRCA2 among Ashkenazi Jews. , 1997, The New England journal of medicine.

[23]  Luc Martens,et al.  The Signal Tandmobiel (r) Project: a longitudinal intervention oral health promotion study in Flanders (Belgium) baseline and first year results. , 2000 .

[24]  D. Oakes,et al.  Bivariate survival models induced by frailties , 1989 .

[25]  D. Clayton,et al.  Multivariate generalizations of the proportional hazards model , 1985 .

[26]  Christian Genest,et al.  Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données , 1986 .

[27]  Xiaohong Chen,et al.  A MODEL SELECTION TEST FOR BIVARIATE FAILURE-TIME DATA , 2007, Econometric Theory.

[28]  Karen Bandeen-Roche,et al.  Modelling multivariate failure time associations in the presence of a competing risk , 2002 .