Biomedical Engineering Reference
In-Depth Information
H
0
: f(0) = 0 against its complement based on an observation of a sample path
of X. Thus, the null hypothesis constrains a monotone function at a point,
similar to what we have considered thus far. Wellner (2003) shows that an ap-
propriately defined likelihood ratio statistic for this problem is given precisely
byDusing Cameron{Martin{Girsanov's theorem followed by an integration
by parts argument.
On the methodological front, a detailed investigation of the likelihood
ratio-based intervals in comparison to other methods for current status data
was undertaken in Banerjee and Wellner (2005), and their behavior was seen
to be extremely satisfactory. Among other things, the simulations strongly
indicate that in a zone of rapid change of the distribution function, the like-
lihood ratio method is significantly more reliable than competing methods
(unless good parametric fits to the data were available). As subsequent in-
vestigation in the current status and closely related models has shown, if the
underlying distribution function is expected to be fairly erratic, the likelihood
ratio inversion method is generally a very reliable choice.
3.3
More General Forms of Interval-Censoring
With current status data, each individual is tested only once to ascertain
whether the event of interest has transpired. However, in many epidemiological
studies, there are multiple follow-up times for each individual and, in fact,
the number of follow-up times may vary from individual to individual. Such
models are called mixed-case interval-censoring models, a term that seems
to have originated in the work of Schick and Yu (2000), who dealt with the
properties of the NPMLE in these models. In this section I describe to what
extent the ideas of the previous section for current status data extend to
mixed-case interval-censoring models and what challenges remain. It turns
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