Page 44 - Special Topic Session (STS) - Volume 1

STS353 H. Zhao et al.
center may share similar medical environment and thus their failure times
may tend to be correlated with each center serving as a cluster. Furthermore,
the cluster size, the number of subjects from a center, could be different from
one center to another and may contain some relevant information about the
failure time of interest. Similar data can occur in a dental study concerning all
teeth of an individual (Zhang and Sun, 2010) and such an example will be
discussed below in details.
For the analysis of clustered failure time data, a commonly used approach
is the marginal model approach in which estimation is usually carried out
based on estimating equations-based (GEE) procedures. One major
advantage of these methods is their robustness against the misspecification
of the correlation structure and also it is relatively easy to use as one can
leave the association structure to be arbitrary (Williamson et al., 2003). On
the other hand, it is apparent that such methods can be less efficient and
more importantly, it is difficult to take into account the informative cluster
size. Corresponding to these, we present a within-cluster resampling (WCR)
method when the failure time of interest follows a class of linear
transformation models (Fine et al., 1998; Zhang et al., 2005). One advantage
of these models is their flexibility as they include many commonly used
models such as he proportional hazards model and the proportional odds
model as special cases. The WCR method uses a single observation to
represent each cluster and is a cluster-based approach (Hoffman et al., 2001;
Cong et al., 2007; Chen et al., 2016; Chen et al., 2017). Like the GEE-based
methods, the new method can be easily implemented and leave the
correlation structure arbitrary, and in the meantime, it still works or is valid
when the cluster size is informative.

2. Methodology
Consider a failure time study consisting of clusters and subjects

within cluster . For subject in cluster , let denote the failure time of

interest and suppose that there exists a −dimensional vector of categorial
covariates denoted by , = 1, … , = 1, … , . Some comments on the
,

covariates will be given below. Let = + ⋯ + and assume that
1

follows the linear transformation model given by

( ) = + (1)
0

0

In the above, (∙) denotes an unknown strictly increasing function, is a
0
0
vector of unknown regression parameters, and denotes a random error

assuming to have a completely known distribution function . An advantage
of the model above is its flexibility as it includes some commonly used
models as special cases. For example, it gives the Cox model if () = 1 −
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