Practical Issues on Using Weighted Logrank Tests with Interval-Censored Events in Clinical Trials - Interval-Censored-Time-to-Event Data: Methods and Applications - page 349

depends on z if , we have assessment-treatment dependence (ATD). The case
of CIA with ATD could occur if one treatment may cause (either by design
or through some unforseen effect of the treatment) different probabilities of
missing scheduled or making additional unscheduled assessments, and those
probabilities are independent of the event Xi. if . This could occur, for example,
in a trial where patients receive either a treatment that requires weekly ad-
ministration of an intravenous (IV) drug or a drug that can be taken orally
by the patient. The patients who receive the IV drug would meet with study
nurses or doctors weekly while the patients who receive the oral drug would
meet with study nurses or doctors only at the regularly scheduled assessment
times. For the patients who receive IV drug, it may be more likely that they
would be assessed at more time points because they will be at the doctor's
oce more often to receive treatment. In contrast, it requires an extra trip
to the doctor's oce for the assessment of patients who are receiving oral
treatment, so they may be more likely to miss an assessment visit.
For regular assessments, each subject has the same set of possible assess-
ments; but for irregular assessment times, we allow each subject to have their
own set of assessment times, so the assessments for any particular subject need
not have any assessment times in common with any of the other subjects. We
use the same terminology (TIA, CIA, and ATD) for irregular assessment times.
There are some special cases that have been studied in the literature. If
k if = 1 for all i (where ki if is the number of assessments for patient i), then the
responses are called Case I interval-censored or current status data. If ki if = 2
for all i, then the responses are called Case II interval-censored. If k if = k > 2
for all i, then the responses are called Case k interval-censored. If we have
no restrictions on the ki, if , then the data are known as \mixed-case" interval-
censoring (see, for example, Schick and Yu, 2000). In this chapter we are not
concerned with exactly observed observations, although all the results for this
chapter hold if we allow exactly observed events at x to be represented using