Quantile association for bivariate survival data.

Bivariate survival data arise frequently in familial association studies of chronic disease onset, as well as in clinical trials and observational studies with multiple time to event endpoints. The association between two event times is often scientifically important. In this article, we examine the association via a novel quantile association measure, which describes the dynamic association as a function of the quantile levels. The quantile association measure is free of marginal distributions, allowing direct evaluation of the underlying association pattern at different locations of the event times. We propose a nonparametric estimator for quantile association, as well as a semiparametric estimator that is superior in smoothness and efficiency. The proposed methods possess desirable asymptotic properties including uniform consistency and root-n convergence. They demonstrate satisfactory numerical performances under a range of dependence structures. An application of our methods suggests interesting association patterns between time to myocardial infarction and time to stroke in an atherosclerosis study.

[1]  Jianwen Cai,et al.  Quantile Regression Models with Multivariate Failure Time Data , 2005, Biometrics.

[2]  Dorota M. Dabrowska,et al.  Kaplan-Meier Estimate on the Plane , 1988 .

[3]  D. Oakes,et al.  On consistency of Kendall's tau under censoring , 2008 .

[4]  Zhiliang Ying,et al.  Linear regression analysis of censored survival data based on rank tests , 1990 .

[5]  Stephen Portnoy,et al.  Censored Regression Quantiles , 2003 .

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

[7]  Achim Zeileis,et al.  Econometrics in R: Past, Present, and Future , 2008 .

[8]  Holger Dette,et al.  A note on bootstrap approximations for the empirical copula process , 2010 .

[9]  Mingyao Li,et al.  Joint Regression Analysis of Correlated Data Using Gaussian Copulas , 2009, Biometrics.

[10]  Limin Peng,et al.  ANALYSIS OF DEPENDENTLY CENSORED DATA BASED ON QUANTILE REGRESSION. , 2014, Statistica Sinica.

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

[12]  Jun Yan,et al.  Functional Association Models for Multivariate Survival Processes , 2005 .

[13]  Lan Wang,et al.  Locally Weighted Censored Quantile Regression , 2009 .

[14]  Thomas A. Louis,et al.  Time-Dependent Association Measures for Bivariate Survival Distributions , 1992 .

[15]  Limin Peng,et al.  Quantile regression adjusting for dependent censoring from semicompeting risks , 2015, Journal of the Royal Statistical Society. Series B, Statistical methodology.

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

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

[18]  Martin T. Wells,et al.  Model Selection and Semiparametric Inference for Bivariate Failure-Time Data , 2000 .

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

[20]  Klaus Nordhausen,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition by Trevor Hastie, Robert Tibshirani, Jerome Friedman , 2009 .

[21]  Yu Cheng,et al.  Quantile Association Regression Models , 2014 .

[22]  David Beaudoin,et al.  IPCW Estimator for Kendall's Tau under Bivariate Censoring , 2009 .

[23]  Joseph G Ibrahim,et al.  Gamma frailty transformation models for multivariate survival times. , 2009, Biometrika.

[24]  R. Koenker.  Censored Quantile Regression Redux , 2008 .

[25]  Z. Ying,et al.  Rank-based inference for the accelerated failure time model , 2003 .

[26]  Jing Ning,et al.  Estimation of time‐dependent association for bivariate failure times in the presence of a competing risk , 2014, Biometrics.

[27]  Zhiliang Ying,et al.  A simple nonparametric estimator of the bivariate survival function under univariate censoring , 1993 .

[28]  Limin Peng,et al.  Survival Analysis With Quantile Regression Models , 2008 .

[29]  J. Wellner,et al.  Inefficient estimators of the bivariate survival function for three models , 1995 .

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

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

[32]  J. Shih,et al.  A goodness-of-fit test for association in a bivariate survival model , 1998 .

[33]  D. Cox.  Regression Models and Life-Tables , 1972 .

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

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

[36]  Yijian Huang,et al.  QUANTILE CALCULUS AND CENSORED REGRESSION. , 2010, Annals of statistics.

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

[38]  Delhi Paiva,et al.  Copula-based regression models: A survey , 2009 .