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CPS1810 Jin-Jian Hsieh et al.
method, the coverage probability of the 95% confidence intervals (CP%) and
the mean squared error (MSE). The results are shown in Tables 1. We denote
the method by Jung et al. (2009) as the old method. The mean squared error
of our method is smaller than the old method. In particular, the bias of of
1
our method is smaller than the old method and the standard error of of our
1
method is smaller than the old method. The average of estimated standard
deviation of our method is reasonably close to the empirical standard
deviation, and the coverage probabilities of the 95% confidence interval are
close to 95%.

4. Discussion and Conclusion
This paper investigates the quantile residual life regression based on semi-
competing risk data. Because is dependently censored by , we can’t make
inference on without extra assumption. Therefore, we assume that (T,D)
follow an Archimedean copula. To check the copula assumption, we can apply
the checking approach by Hsieh, Wang, and Ding (2008). Then, we apply the
inverse probability weight technique to constructing an estimating equation
of | 0 , ( | 0 ) = 0. But, ( | 0 ) may not be continuous in | 0 . Thus, we

apply the generalized solution approach to overcoming this problem. From
the simulation studies, it shows the performance of the proposed method is
good. When the covariates are continuous, we can group it as categorical
variables or handle it with smoothing technique, which is treated as a future
work.

References
1. Gelfand, A. E. and Kottas, A. (2003). Bayesian Semiparametric
Regression for Median Residual Life. Scandinavian Journal of Statistics,
30, 651-665.
2. Hsieh, J. J., Ding, A. A., Wang, W., and Chi, Y. L. (2013). Quantile
regression based on semicompeting risks data. Open Journal of
Statistics, 3, 12-26.
3. Hsieh, J. J. and Hsiao, M. F. (2015). Quantile Regression Based on A
Weighted Approach under Semi-Competing Risks Data. Journal of
Statistical Computatiion and Simulation, 85, 27932807.
4. Hsieh, J. J. and Wang, H. R. (2017). Quantile regression based on
counting process approach under semi-competing risks data. Accepted
by Annals of the Institute of Statistical Mathematics.
5. Hsieh, J. J., Wang, W and Ding, A. A. (2008). Regression analysis based
on semi-competing risks data. Journal of Royal Statistic Society, Series
B, 70, 3-20.
6. Jeong, J. H. Jung, S. H. and Costantino, J. (2008). Nonparametric
Inference on Median Residual Life Function. Biometrics, 64, 157-163.

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