Biomedical Engineering Reference
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(a;b] means that the patient had a clinic visit at month a and no breast
retraction was detected at the visit, while at the very next visit at month
b, breast retraction was found to be present already. In particular, there are
5 patients for whom the breast retraction was detected at their first clinical
visits, meaning a = 0 and giving left-censored observations. Note that for
the right-censored observations, the observed intervals have the form (a;1).
Among others, one objective of the study was to compare the two treatments
through their effects on breast retraction.
We now establish some notation for Interval-censoring. Let T denote the
failure time of interest. When T is interval-censored, we use I = (L;R] to
denote the interval containing T. Using the notation, we see that current
status data correspond to the situation where either L = 0 or R = 1. Interval-
censoring also contains right-censoring and left-censoring as special cases and
if R = 1, we have a right-censored observation, while if L = 0 we obtain a
left-censored observation. Although most real interval-censored data are given
in the form I = (L;R], in the literature, some authors prefer to employ the
form fU;V;
1
= I(T < U);I
2
= I(U T < V )g with U < V to represent
interval-censored data. This means that a study subject is observed at two
random time points U and V , and T is known only to be smaller than U,
between U and V , or larger than V . One main advantage of the latter format
is that it is natural to impose assumptions on the censoring mechanism, as
discussed below.
In the analysis of failure time data, one basic and important assumption
that is commonly used is that the censoring mechanism is independent of or
noninformative about the failure time of interest. With respect to the formu-
lation I = (L;R], this means that
P(T tjL = l;R = r;L < T R) = P(T tjl < T r)
(Sun (2006); Oller et al. (2004)). It essentially says that, except for the fact
that T lies between l and r, which are the realizations of L and R, the interval
(L;R] (or equivalently its endpoints L and R) does not provide any extra
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