Practical Issues on Using Weighted Logrank Tests with Interval-Censored Events in Clinical Trials - Interval-Censored-Time-to-Event Data: Methods and Applications - page 352

13.3 Rank Tests for Interval-Censored Data

13.3.1 Overview

In this section we describe several rank tests for interval-censored data that

have been proposed in the literature. Section 13.3.2 describes a simple ap-

proach described by Freidlin et al. (2007) where all subjects have the same

assessment schedule, the unscheduled assessments are ignored, the data are

treated as right-censored, and the usual logrank test is applied. The method

effectively forces independent assessments of the assessments that are not ig-

nored, and because of this can be used even in cases were the unscheduled

assessments are informative. The method of Freidlin et al. (2007) cannot be

used with irregular assessments; for that situation we can use the methods

described in Sections 13.3.3 through 13.3.7. Section 13.3.3 sets up a semi-

parametric likelihood where two special cases are the proportional hazards

model and the proportional odds model. The CIA assumption allows use of
this likelihood. Then the score statistic is derived and is the sum of treatment

indicators times rank-like scores for interval-censored data. Section 13.3.4 cre-

ates permutation tests from those rank-like scores using either exact methods,

Monte Carlo approximations or asymptotic approximations. Section 13.3.5

creates score tests in the usual way from the semiparametric likelihood. The

problem is that the assumptions of the usual score test (a fixed number of nui-

sance parameters that maximize the likelihood when the associated derivative

is 0) do not always hold for interval-censored data. Section 13.3.6 creates tests

using multiple imputation. Here we discuss how the correction for the vari-

ance should not follow the usual multiple imputation-style correction (see,

for example, Rubin, 1987; Pan, 2000; Zhao and Sun, 2004), but should use

the within-cluster resampling-style correction as in Hoffman et al. (2001) and

Huang et al. (2008). Further, we discuss how the multiple imputation approach