Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 5

servable (Dinse and Lagakos (1983)). As a matter of fact, we only have the
exact measurement of the observation time, which is often the death or sac-
rifice time of the subject. Note that for the first example, current status data
occur due to the study design, while for the second case, they are often ob-
served because of our inability to measure the variable directly and exactly.
Sometimes we also refer to current status data as case I interval-censored
data and to the general case as case II interval-censored data (Groeneboom
and Wellner (1992)).
In practice or applications, interval-censored data can be easily confused
with grouped survival data. There is actually a fundamental difference be-
tween these two data structures although both usually appear in the form of
intervals. The grouped survival data can be seen as a special case of interval-
censored data and commonly mean that the intervals for any two subjects
either are completely identical or have no overlapping. In contrast, the in-
tervals for interval-censored data may overlap in any way. As a consequence
of this structure difference, statistical methods for grouped survival data are
much more straightforward than those for interval-censored data and will not
be discussed.
The main purpose of this chapter is to provide a review of the most recent
advances during recent years on several commonly concerned topics about the
analysis of interval-censored failure time data. For the topics that have not
seen much advancement in recent years, we give a brief summary and focus on
some existing problems or directions for future research. Before discussing the
specific topics, we give some further introduction in Section 1.2 by discussing
a real set of interval-censored data, the data structure or censoring mecha-
nism, and some differences between right-censored data and interval-censored
data. The topics covered include nonparametric estimation of a survival func-
tion in Section 1.3, nonparametric comparison of survival functions in Section
1.4, semiparametric regression analysis of univariate interval-censored data in
Section 1.5, the analysis of multivariate or clustered interval-censored data in