Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 21

(2004)). An example of such data is provided by AIDS studies concerning the
AIDS incubation time, defined as the time from HIV infection to AIDS diag-
nosis. In these situations, it is often the case that both the HIV infection time
and the AIDS diagnosis time are right- or interval-censored. One of the early
works on the analysis of doubly censored data is given by the seminal paper
of De Gruttola and Lagakos (1989) and following their work, many authors
also considered their analysis. For more references on the topic, readers are
referred to Sun (2004), Sun (2006), and Zhang and Sun (2010b).
In Section 1.2, we discussed the independent or noninformative assump-
tion for interval-censored data, and all of the methods discussed so far were
developed under this assumption. It is obvious that sometimes this assump-
tion may not hold. A simple example for this is clinical studies with periodic
follow-ups. In this case, informative censoring-intervals could occur if the pa-
tients make more clinical visits when they feel worse. Zhang and Sun (2010b)
gave several references on the analysis of informatively interval-censored data,
but the topic remains mainly untouched. As with informatively right-censored
data, a key part for their analysis is to describe or model the relationship be-
tween the failure time variable of interest and the censoring variables, which
is clearly generally very dicult given the limited information available.
So far the focus has been on interval-censoring alone without other com-
plications or factors causing incompleteness of the observed data. It is easy to
see that interval-censoring may occur together with other complications. For
example, interval-censored failure time data could occur together with longitu-
dinal data and in this case, one problem of interest is to make inference about
the relationship between or jointly model the concerned failure time variable
and the longitudinal variable (Finkelstein et al. (2010); Lee et al. (2011)). An-
other example is the interval-censored data on a multi-state model, which can
naturally occur in a disease progression study with periodic follow-ups (Chen
et al. (2010)).
Of course, interval-censoring can also occur together with truncation