Quantile Regression Based on Semi-Competing Risks Data
Affiliation(s)
Department of Mathematics, National Chung Cheng University, Chia-Yi, Chinese Taipei. Department of Mathematics, Northeastern University, Boston, USA.. Institute of Statistics, National Chiao-Tung University, Hsin-Chu, Chinese Taipei.
Department of Mathematics, National Chung Cheng University, Chia-Yi, Chinese Taipei. Department of Mathematics, Northeastern University, Boston, USA.. Institute of Statistics, National Chiao-Tung University, Hsin-Chu, Chinese Taipei.
ABSTRACT
This paper considers quantile regression analysis based on
semi-competing risks data in which a non-terminal event may be dependently
censored by a terminal event. The major interest is the covariate effects on
the quantile of the non-terminal event time. Dependent censoring is handled by
assuming that the joint distribution of the two event times follows a
parametric copula model with unspecified marginal distributions. The technique
of inverse probability weighting (IPW) is adopted to adjust for the selection
bias. Large-sample properties of the proposed estimator are derived and a model
diagnostic procedure is developed to check the adequacy of the model
assumption. Simulation results show that the proposed estimator performs well.
For illustrative purposes, our method is applied to analyze the bone marrow
transplant data in [1].
Cite this paper
J. Hsieh, A. Ding, W. Wang and Y. Chi, "Quantile Regression Based on Semi-Competing Risks Data," Open Journal of Statistics, Vol. 3 No. 1, 2013, pp. 12-26. doi: 10.4236/ojs.2013.31003.
J. Hsieh, A. Ding, W. Wang and Y. Chi, "Quantile Regression Based on Semi-Competing Risks Data," Open Journal of Statistics, Vol. 3 No. 1, 2013, pp. 12-26. doi: 10.4236/ojs.2013.31003.
References
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[1] J. P. Klein and M. L. Moeschberger, “Survival Analysis: Techniques for Censored and Truncated Data,” 2nd Edition, Springer, New York, 2003. [2] J. Powell, “Least Absolute Deviations Estimation for the Censored Regression Model,” Journal of Econometrics, Vol. 25, No. 3, 1984, pp. 303-325. doi:10.1016/0304-4076(84)90004-6 [3] J. Powell, “Censored Regression Qunatiles,” Journal of Econometrics, Vol. 32, No. 1, 1986, pp. 143-155. doi:10.1016/0304-4076(86)90016-3 [4] B. Fitzenberger, “A Guide to Censored Quantile Regressions,” In: G. S. Maddala and C. R. Rao, Eds., Hand- books of Statistics, North-Holland, Amsterdam, 1997, pp. 405-437. doi:10.1016/S0169-7161(97)15017-9 [5] M. Buchinsky and J. Hahn, “A Alternative Estimator for Censored Quantile Regression,” Econometrica, Vol. 66, No. 3, 1998, pp. 653-671. doi:10.2307/2998578 [6] Z. Ying, S. H. Jung and L. J. Wei, “Survival Analysis with Median Regression Models,” Journal of the American Statistical Association, Vol. 90, No. 429, 1995, pp. 178-184. doi:10.1080/01621459.1995.10476500 [7] S. Yang, “Censored Median Regression Using Weighted Empirical Survival and Hazard Functions,” Journal of the American Statistical Association, Vol. 94, No. 445, 1999, pp. 137-145. doi:10.1080/01621459.1999.10473830 [8] S. Portnoy, “Censored Regression Quantiles,” Journal of the American Statistical Association, Vol. 98, No. 464, 2003, pp. 1001-1012. doi:10.1198/016214503000000954 [9] L. Peng and Y. Huang, “Survival Analysis Based on Quantile Regression Models,” Journal of the American Statistical Association, Vol. 103, No. 482, 2008, pp. 637- 649. doi:10.1198/016214508000000355 [10] G. Yin, D. Zeng and H. Li, “Power Transformed Linear Quantile Regression with Censored Data,” Journal of the American Statistical Association, Vol. 103, No. 483, 2008, pp. 1214-1224. doi:10.1198/016214508000000490 [11] S. Portnoy and G. Lin, “Asymptotics for Censored Regression Quantiles,” Journal of Nonparametric Statistics, Vol. 22, No. 1, 2010, pp. 115-130. doi:10.1080/10485250903105009 [12] J. P. Fine, H. Jiang and R. Chappell, “On Semi-Competing Risks Data,” Biometrika, Vol. 88, No. 4, 2001, pp. 907-919. [13] L. Peng and J. P. Fine, “Competing Risks Quantile Regression,” Journal of the American Statistical Association, Vol. 104, No. 488, 2009, pp. 1440-1453. doi:10.1198/jasa.2009.tm08228 [14] R. Li and L. Peng, “Quantile Regression for Left-Truncated Semicompeting Risks Data,” Biometrics, Vol. 67 No. 3, 2011, pp. 701-710. doi:10.1111/j.1541-0420.2010.01521.x [15] A. J. Patton, “Modeling Asymmetric Exchange Rate Dependence,” International Economic Review, Vol. 47, No. 2, 2006, pp. 527-556. doi:10.1111/j.1468-2354.2006.00387.x [16] W. Wang, “Estimating the Association Parameter for Copula Models under Dependent Censoring,” Journal of the Royal Statistical Society, Series B, Vol. 65, No. 1, 2003, pp. 257-273. doi:10.1111/1467-9868.00385 [17] L. Lakhal, L.-P. Rivest and B. Abdous, “Estimating Survival and Association in a Semicompeting Risks Model,” Biometrics, Vol. 64, No. 1, 2008, pp. 180-188. doi:10.1111/j.1541-0420.2007.00872.x [18] M. Fygenson and Y. Ritov, “Monotone Estimating Equations for Censored Data,” The Annals of Statistics, Vol. 22, No. 2, 1994, pp. 732-746. doi:10.1214/aos/1176325493 [19] L.-P. Rivest and M. Wells, “A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring,” Journal of Multivariate Analysis, Vol. 79, No. 1, 2001, pp. 138-155. doi:10.1006/jmva.2000.1959 [20] J. X. Zheng, “A Consistent Nonparametric Regression Models under Quantile Restrictions,” Econometric Theory, Vol. 14, No. 1, 1998, pp. 123-138. doi:10.1017/S0266466698141051 [21] J. L. Horowitz and V. G. Spokoiny, “An Adaptive, RateOptimal Test of Linearity for Median Regression Models,” Journal of the American Statistical Association, Vol. 97, No. 459, 2002, pp. 822-835. doi:10.1198/016214502388618627 [22] X. He and L. Zhu, “A Lack-of-Fit Test for Quantile Regression,” Journal of the American Statistical Association, Vol. 98, No. 464, 2003, pp. 1013-1022. doi:10.1198/016214503000000963 [23] D. Y. Lin and L. J. Wei and Z. Ying, “Checking the Cox Model with Cumulative Sums of Martingle-Based Residuals,” Biometrika, Vol. 80, No. 3, 1993, pp. 557-572. doi:10.1093/biomet/80.3.557 [24] R. Braekers and N. Veraverbeke, “A Copula-Graphic Estimator for the Conditional Survival Function under Dependent Censoring,” The Canadian Journal of Statistics, Vol. 33, No. 3, 2005, pp. 429-447. doi:10.1002/cjs.5540330308