Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 4

the prescheduled observations for a clinically observable change in disease or
health status may miss some observations and return with a changed status.
Accordingly, we only know that the true event time is greater than the last
observation time at which the change has not occurred and less than or equal to
the first observation time at which the change has been observed to occur, thus
giving an interval that contains the real (but unobserved) time of occurrence
of the change. The well-studied right-censored failure time data are a special
case of interval-censored data.
Another example of interval-censored data arises in the acquired immune
deficiency syndrome (AIDS) trials (De Gruttola and Lagakos (1989)) that,
for example, are interested in times to AIDS for human immunodeficiency
virus (HIV) infected subjects. In these cases, the determination of AIDS onset
is usually based on blood testing, which can be performed obviously only
periodically but not continuously. As a consequence, only interval-censored
data may be available for AIDS diagnosis times. A similar case is for studies
on HIV infection times. If a patient is HIV-positive at the beginning of a study,
then the HIV infection time is usually determined by a retrospective analysis
of his or her medical history. Therefore, we are only able to obtain an interval
given by the last HIV negative test date and the first HIV positive test date
for the HIV infection time.
An important special case of interval-censored data is the so-called current
status data (Jewell and van der Laan (1995); Sun and Kalbfleisch (1993)). This
type of censoring means that each subject is observed only once for the status
of the occurrence of the event of interest. In other words, we do not directly
observe the survival endpoint but instead, we only know the observation time
and whether or not the event of interest has occurred at the time. As a con-
sequence, the survival time is either left- or right-censored. One such example
is the data arising from cross-sectional studies on survival events (Keiding
(1991)). Another example is given by the tumorgenicity study and in this
situation, the time to tumor onset is usually of interest, but not directly ob-