Page 71 - Contributed Paper Session (CPS) - Volume 6

CPS1810 Jin-Jian Hsieh et al.

Quantile residual life regression based on semi-
competing risks data
Jin-Jian Hsieh, Jian-Lin Wang
Department of Mathematics, National Chung Cheng University Chia-Yi, Taiwan, R.O.C.

Abracts
This paper investigates the quantile residual life regression based on
semicompeting risk data. Because the terminal event time dependently
censors the non-terminal event time, the inference on the non-terminal event
time is not available without extra assumption. Therefore, we assume that the
non-terminal event time and the terminal event time follow an Archimedean
copula. Then, we apply the inverse probability weight technique to construct
an estimating equation of quantile residual life regression coefficients. But, the
estimating equation may not be continuous in coefficients. Thus, we apply the
generalized solution approach to overcome this problem. Since the variance
estimation of the proposed estimator is difficult to obtain, we use the
bootstrap resampling method to estimate it. From simulations, it shows the
performance of the proposed method is good.

Keywords
Archimedean copula model; Bone marrow transplant data; Dependent
censoring; Quantile residual life regression; Semi-competing risks data.

1. Introduction
Quantile regression can provide covariate effects for different quantile,
which is more robust than ordinary least squares regression. Quantile
regression was originally introduced by Koenker and Bassett (1978), and it has
been widely investigated by many literatures, such as Powell (1984, 1986),
Ying, Jung and Wei (1995), Portnoy (2003), Peng and Huang (2008) for
censored data. Peng and Fine (2009) studied quantile regression for
competing risks data, which constructs the model based on conditional
quantiles with the cumulative incidence function. Hsieh et al. (2013), Hsieh and
Hsiao (2015), and Hsieh and Wang (2017) studied quantile regression for semi-
competing risks data based on the inverse probability weight technique, a
weighted approach, and the counting process approach, respectively. In many
medical research, the residual life is of interest. The residual life of a patient
can be prolonged by a medical treatment. The quantile residual life regression
also has been widely investigated by many literatures, such as Gelfand and
Kottas (2003), Jeong, Jung and Costantino (2008), Jung, Jeong and Bandos
(2009) and Ma and Yin (2010) for censored data. Gelfand and Kottas (2003)

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