Page 72 - Contributed Paper Session (CPS) - Volume 6

CPS1810 Jin-Jian Hsieh et al.
formulated a semiparametric median residual life regression model based on
a accelerated failure time regression model. Jeong, Jung and Costantino (2008)
used a simple approach to estimate the median residual lifetime, which
applied the technique by inverting a function of the Kaplan-Meier estimators.
Jung, Jeong and Bandos (2009) applied the inverse probability weight method
for log-linear quantile residual life regression model. Ma and Yin (2010)
suggested a general class of semiparametric median residual life models.
However, quantile residual life regression has not been studied for semi-
competing risks data yet. Based on this motivation, we study the quantile
residual life regression for semi-competing risks data in this article. This article
investigates the quantile residual life regression based on semi-competing risk
data. Because the non-terminal event time is dependently censored by the
terminal event time, the inference on the non-terminal event time is not
available without extra assumption. Therefore, we assume the non-terminal
event time and the terminal event time follow an Archimedean copula. Then,
we apply the inverse probability weight technique to constructing an
estimating equation of quantile residual life regression coefficients.

2. Methodology
In this paper, we study quantile residual life regression based on semi-
competing risk data. Assume that s the non-terminal event time and is
the terminal event time. In addition, may be dependently censored by . Let
be the right censoring time which is assumed to be independent of (, )
given covariates. Therefore, the observed variables are {( , , , ), =

1, . . . , }, where = ∧ ∧ , = ( ≤ ∧ ), = ∧ , = ( ≤

), ∧ is the minimum operator and (·) is the indicator function, which is
called as semi-competing risks data. With covariates, we usually investigate
the relationship between the response and covariates via regression model.
However, the quantile residual life regression model can provide a more
intuitive interpretation in medical or other related research. Suppose |
defines the − quantile residual life function at time . Then, | =
−quantile( − | ≥ ) satisfies the relation ( − ≥ | | ≥ ) =

1 − , which is equivalent to ( ≥ + | ) = (1 − )( ≥ ). It can

be more clearly aware of the impact in test drug or clinical trial. Then, we
consider the log-linear quantile residual life model as:

− {log( − )| ≥ , } = | 0 , (1)
0

0

where |0 is a vector of the quantile regression coefficients, and is a vector

of discrete covariates for a subject . Because is dependently censored by
, it is necessary to specify the relationship between and . In this paper, we
assumed that and follow an copula model.
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