Practical Issues on Using Weighted Logrank Tests with Interval-Censored Events in Clinical Trials - Interval-Censored-Time-to-Event Data: Methods and Applications - page 346

13.2.1 Overview

For concreteness consider an HIV vaccine trial where subjects are assessed

at baseline and those found to be HIV-negative (and found to meet all other

inclusion criteria) are randomized to an experimental HIV vaccine or placebo.

The endpoint is time from randomization (which we suppose happens imme-

diately after the baseline assessment) until HIV is detectable in the blood.

We do not observe the time until the endpoint, but only observe that it falls

between the last HIV-negative blood sample and the first HIV-positive blood

sample. This assumes that once the event has occurred, it will be able to be

observed at the next assessment (so, for example, no one is spontaneously

cured of HIV and we assume that the assay has perfect sensitivity and speci-

ficity). We are interested in detecting differences in survival distributions of

the time until endpoint (HIV is first detectable in blood) between vaccinated

and placebo subjects.

An essential property of any test of treatment effect is that the test is

valid, that is, the size of the test is not larger than the nominal level. So it
would seem that we should not allow different assessment distributions for

the different treatments, which we will call assessment-treatment dependence

(ATD), because those differences might affect the validity of the test. In fact,

we will show by simulation that there are some kinds of ATD that do not

destroy the validity of some tests.

For estimating the survival distribution from one sample, there are some

minimum assumptions needed on the assessment distribution for identifiability

(Oller et al., 2007). We consider here only the more restrictive (but simpler

to describe) assumption of independent assessment. Under independent as-

sessment (or independent censoring), the process that causes a subject to be

assessed is independent of that subject's event time. For a study of time to

death with right-censoring, we often assume that the censoring is indepen-

dent of death. In that case, the independence assumption would be violated if

subjects drop out and are right-censored if they become very ill. This is infor-