Biomedical Engineering Reference
In-Depth Information
However, there exists little literature on general interval-censored data with
competing risks except some approaches developed for current status data.
For example, Jewell et al. (2003) considered the estimation problem of cumu-
lative incidence functions and developed several estimates. Groeneboom et al.
(2008a), (Groeneboom et al. (2008b)) and Maathuis and Hudens (2011) also
studied the nonparametric estimation problem and established some consis-
tency and local limiting distributions of the nonparametric maximum like-
lihood estimates of cumulative incidence functions. More recently, Sun and
Shen (2009) discussed regression analysis of current status data under the
proportional hazards competing risks model and developed the maximum like-
lihood estimation. Also, Barrett et al. (2011) discussed a set of competing risks
interval-censored data arising from a Cognitive Function and Aging Study and
performed a multi-state model-based analysis.
1.8
Other Topics and Concluding Remarks
There exist a number of other topics about interval-censored failure time data
that were not touched upon in the previous sections. These include the analysis
of doubly censored data, informatively interval-censored data and truncated
interval-censored data, as well as the implementation of the existing proce-
dures and software packages.
To this point, the failure time considered has been the time to the occur-
rence of a certain event or between a fixed starting time point, usually setting
to be zero, and the event time. A more general framework is to define the
failure time as the time between two related events whose occurrence times
are random variables and both could suffer censoring. If there is right- or
interval-censoring on both occurrence times, the resulting data are commonly
referred to as doubly censored data (De Gruttola and Lagakos (1989); Sun
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