Biomedical Engineering Reference
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by applying one step of the iterative convex minorant algorithm starting from
the true ; while an asymptotic equivalence between the MLE and the toy
estimator is conjectured, it remains to be proved. Simulation studies show
that the MSE of the MLE is smaller than that of the pseudo-MLE (unsur-
prisingly) when the underlying counting process is Poisson. A natural query
in the context of the above discussion is the behavior of the LRS for testing
a hypothesis of the form (t
0
) =
0
using the full Poisson likelihood ratio
statistic. This has not been studied either computationally or theoretically.
Once again, one is tempted to postulateDup to a constant, but whether
one gets an asymptotically pivotal quantity in the mixed-case model with this
alternative statistic is unclear.
Thus, there are three conceivably different ways of constructing CIs via
likelihood ratio inversion for F(t
0
) in the mixed-case model. The first is based
on the the true likelihood ratio for this model, the second on the pseudo-
likelihood method of Sen and Banerjee (2007), and the third on the full Pois-
son likelihood; in the last two cases, we think of mixed-case interval-censored
data as panel count data from a counting process. As of now, the second
method is the only one that has been implemented and theoretically validated
and appears to be the only asymptotically pivotal method for nonparametric
estimation of F in the mixed-case model. However, there is need to investigate
the other two approaches, as these may produce alternative and, potentially,
better pivots in the sense that inversion of such pivots may lead to sharper
confidence intervals as compared to the pseudo-LRS-based ones.
3.4
Current Status Data with Competing Risks
The current status model in its simplest form, as discussed above, deals with
failure of an individual or a system but does not take into account the cause
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