Biomedical Engineering Reference
In-Depth Information
most of them assume or apply only to the situation where the observation
scheme or censoring mechanism is the same for study subjects in different
groups. However, this may not be true in, for example, some drug develop-
ment studies. In other words, the assessment times or schedules that yield
censored intervals for the endpoints of interest may be different for subjects
given different treatments or treatment dependent. One example in which this
can be easily appreciated is current status data. In this case, the censoring is
represented by a single variable and the variable may follow different distri-
butions for subjects in different treatment groups. A specific field where this
often happens is tumorgenicity experiments, where the failure time of interest
is usually the time to tumor onset and the censoring variable is the death or
sacrifice time. If the tumor under study is between lethal and nonlethal, as
usually the case, the two variables are then related. Among others, Sun (1999)
considered this problem and developed a nonparametric test procedure that
allows treatment-dependent censoring variables. More research is definitely
needed for such problems.
As mentioned above, most of the existing nonparametric test procedures
for interval-censored data are direct generalizations of the ones for right-
censored data. Also as discussed above, one difference between the two types
of data is the counting process approach, which is a key tool for the develop-
ment and asymptotic studies of statistical procedures for right-censored data,
but in general not available for interval-censored data. As a consequence, the
asymptotic behavior of the test procedures above are generally unknown and
the permutation approach is often applied to determine the p-value of a hy-
pothesis test. Some exceptions include the test procedures proposed by Sun
et al. (2005) and Zhao et al. (2008), who derived the asymptotic distributions
of the test statistics under the null hypothesis. A limitation for both the per-
mutation approach and the results given in Sun et al. (2005) and Zhao et al.
(2008) is that they require the same censoring mechanism for the subjects in
different treatment groups. Also, because the asymptotic behavior of all pro-
 
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