Biomedical Engineering Reference
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likelihood estimator (NPMLE) of the survival distribution were first obtained
by Groeneboom (1987) (but see also Groeneboom and Wellner (1992)) and
involved techniques radically different from those used in classical survival
analysis with right-censored data.
In what follows, I emphasize the following: the development of asymptotic
likelihood ratio inference for current status data and its implications for esti-
mating monotone functions in general, an area I worked on with Jon Wellner
at the turn of the century and then on my own and with graduate students,
extensions of these methods to more general forms of interval-censoring, the
technical challenges that come into play when there are multiple observation
times on an individual and some of the (consequently) unresolved queries in
these models, the recent developments in the study of current status data un-
der competing risks, the development of smoothed procedures for inference in
the current status model, adaptive estimation for current data on a grid, cur-
rent status data with outcome misclassification, and semiparametric modeling
of current status data.
3.2
Likelihood-Based Inference for Current Status Data
Consider the classical current status data model. Let fT
i
;U
i
g
i=1
be n i.i.d.
pairs of non-negative random variables where Ti
i
is independent of Ui.
i
. One
can think of Ti
i
as the (unobserved) failure time of the i-th individual, that
is, the time at which this individual succumbs to a disease or an infection.
The individual is inspected at time Ui
i
(known) for the disease/infection and
one observes
i
= 1fT
i
U
i
g, their current status. The data we observe are
therefore f
i
;U
i
g
i=1
. Let F be the distribution function of T and G that of
U. Interest lies in estimating F. Let t
0
be an interior point in the support
of F; assume that F and G are continuously differentiable in a neighborhood
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