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et al. (2012). Extensions to more general forms of interval-censoring, as well
as models incorporating covariate information, should also be possible.
3.7
Current Status Data with Outcome Misclassification
There has been recent interest in the analysis of current status data where
outcomes may be misclassified. McKeown and Jewell (2010) discuss a number
of biomedical and epidemiological studies where the current status of an in-
dividual, say a patient, is determined through a test which may not have full
precision. In this case, the real current status is perturbed with some prob-
ability depending on the sensitivity and specificity of the test. We use their
notation for this section. So, let T be the event time and C the censoring time.
If perfect current status were available, we would have a sample from the dis-
tribution of (Y;C), where Y = 1(T C). Consider now the misclassication
model that arises from the following specifications:
P( = 1 j Y = 1) = and P( = 0 j Y = 0) = :
The probabilities ; are each assumed greater than 0.5, as will be the case
for any realistic testing procedure. The observed data f
i
;C
i
g
i=1
is a sample
from the distribution of (;C). Interest lies, as usual, in estimating F, the
distribution of T. The log-likelihood function for the observed data is
X
X
l
n
(F) =
i
log( F(C
i
) + (1 )) +
(1
i
) log ( F(C
i
)) ;
i=1
i=1
where = +1 > 0. McKeown and Jewell provide an explicit characteriza-
tion of F, the MLE, in terms of a max-min formula. From the existing results
in the monotone function literature, it is clear that in
1=3
( F(t
0
)F(t
0
)) is dis-
tributed asymptotically like a multiple ofZ, so they resort to the construction
of confidence intervals via the m out of n bootstrap. More recently, Sal y Rosas
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