Biomedical Engineering Reference
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(2011), and Zhang and Sun (2010a). Specifically, Kim (2010) and Zhang and
Sun (2010a) discussed a set of clustered interval-censored data in which the
cluster size may be related to the failure times of interest and developed some
methods for their regression analysis. Xiang et al. (2011) also considered the
regression problem but focused on the data that may involve cured subjects,
as discussed in the previous section. It is apparent that many other issues
could occur related to clustered interval-censored data as with right-censored
data and a lot of research remains to be done.
1.7
Analysis of Competing Risks Interval-Censored Data
One faces competing risks analysis when there exist several possible distinct
failures or failure types and one only observes the failure that occurs the first.
It is easy to see that the underlying structure behind competing risks data is
similar to that behind multivariate failure time data as one has to deal with
several related failure times together for both cases. On the other hand, as
described above, multivariate failure time data assume that all failure times
can be observed if there is no censoring, while for competing risks data, one
observes only the time to the first failure and all other failures are censored.
A simple example of competing risks data is given by a medical study on the
patients who can die from one disease with several related causes or several
related diseases.
For competing risks data, the quantities of interest include the cause-
specific hazard function and the cumulative incidence function. In the case of
right-censored data, a large literature has been established (Kalbfleisch and
Prentice (2002); Kevin and Moeschberger (2003)). For example, under the
proportional hazards competing risks model, methods have been developed to
easily estimate regression parameters using the partial likelihood approach.
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