ABSTRACT
National Institute of Allergy and Infectious Diseases, National Cancer Insti-
tute, Bethesda, Maryland, USA
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
13.2 Description of Interval-Censored Data and Assumptions for
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
13.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
13.2.2 Basic Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
13.2.3 Assessment of Simple Endpoints . . . . . . . . . . . . . . . . . . . . . . . . 349
13.2.4 Composite Endpoints and Interval Censoring . . . . . . . . . . . 351
13.2.5 Informative Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
13.3 Rank Tests for Interval-Censored Data . . . . . . . . . . . . . . . . . . . . . . . . . . 353
13.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
13.3.2 Practical Proposal: Ignoring Unscheduled Assessments . 354
13.3.3 Likelihood for Grouped Continuous Model . . . . . . . . . . . . . 355
13.3.4 Permutation-Based Rank Tests . . . . . . . . . . . . . . . . . . . . . . . . . 357
13.3.5 Score Tests with a High-Dimensional Nuisance
Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
346 Interval-Censored Time-to-Event Data: Methods and Applications
13.3.6 Multiple Imputation Approaches . . . . . . . . . . . . . . . . . . . . . . . . 360
13.3.7 Other Closely Related Methods . . . . . . . . . . . . . . . . . . . . . . . . . 361
13.4 Software: “Interval” R Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.4.1 Using the “Interval” R Package . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.4.2 Validation of the “Interval” Package . . . . . . . . . . . . . . . . . . . . . 365
13.5 Simulation with Regular Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
13.6 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
In this chapter we consider two-sample or k-sample rank tests for interval-
censored responses. As with right-censored responses, the most common type
of test is a logrank test or some weighted version of the logrank test such as
a generalization of the Wilcoxon rank sum test for censoring. We focus on
the tests available in the interval R package (Fay and Shaw, 2010) and the
tests proposed in Freidlin et al. (2007). We additionally show that the tests
of Zhao and Sun (2004) and Sun et al. (2005) calculated in the SAS macros
described in So et al. (2010) are closely related to tests available in the interval
R package. We focus on practical aspects of the analysis.
