Biomedical Engineering Reference
In-Depth Information
8.7
Bibliography
As has been argued in Section 8.1, interval-censored data arise naturally in
many epidemiological applications, including any study setting whereby sub-
jects are repeatedly screened for the onset of a disease. Such studies yield
interval-censored data because the time-to-event of interest will generally only
be known to lie between two neighboring monitoring times. Various examples
of interval-censored data can be found, for example, in de Gruttola and La-
gakos (1989), Brookmeyer and Goedert (1989), Bacchetti (1990), Gentleman
and Geyer (1994), and Jewell et al. (2003).
The simplest example of interval-censoring on a time-to-event T consists
of marginal current status data, in which only pairs of the form (V;I(T V ))
are observed at a single monitoring time V . For example, in the context of
a cross-sectional study conducted for the sake of studying the age at onset
distribution, this single monitoring time might be the participant's age, and it
might only be known whether or not disease onset occurred prior to this age.
Carcinogenicity experiments ending with animal sacrifices at a fixed point in
time also yield similar data. The nonparametric maximum likelihood estima-
tor of the marginal distribution of T under the assumption of independence
between T and V is given by the so-called Pool Adjacent Violator algorithm.
A theoretical study of this estimator is presented in Groeneboom and Wellner
(1992). If a time-dependent covariate process L is observed until the mon-
itoring time, then the collected data have an extended current status data
structure given by (V;I(T V ); L(V )), where
L(V ) is the history of the
process L up until time V . In this case, if we dene (T;L) as the full data,
then the coarsening at random assumption on the conditional distribution of
V given the full data allows the hazard of being monitored to be a function
of the observed history of process L. Under the coarsening at random as-
sumption, many features of the distribution of (T;L) are identied from the
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