Biomedical Engineering Reference
In-Depth Information
14.1
Introduction
In survival studies, one of the main goals is to compare the survival of indi-
viduals in different treatment groups. For the problem, when right-censored
failure time data are available, the well-known logrank test is a powerful and
widely used method and is available in major statistical software packages
such as SAS and S-Plus. For interval-censored survival data, which arise nat-
urally from studies in which there is a periodic follow-up, several authors
have discussed this problem. For example, Peto and Peto (1972) considered
the two-sample comparison problem under Lehmann-type alternatives. In this
case, the comparison problem reduces to a score test, which they referred to as
the logrank test for interval-censored data. Finkelstein (1986) later took a re-
gression approach and developed a score test under the proportional hazards
model when the covariates are treatment indicators. This score test allows
k-sample treatment comparisons and is a generalization of the logrank test.
Following Finkelstein (1986), Sun (1996) studied the same problem without
assuming the proportional hazards model and developed a nonparametric test
using the idea behind the logrank test for right-censored data. However, it
does not reduce to the logrank test in the case of right-censored data. Also,
it may not have the right size and good power if the proportion of strictly
interval-censored observations is small. Zhao and Sun (2004) improved this
test by making adjustments to the observed failure and risk numbers so that
the resulting test has a higher power and reduces to the logrank test when
right-censored data are available. Other existing test procedures for interval-
censored data can be found in Sun (1998). Given that most existing test proce-
dures for interval-censored data are ad hoc methods with unknown properties
and/or the variance estimation of the test statistic is complicated, Sun et al.
(2005) proposed a new class of generalized logrank tests for interval-censored
data without exact observations and established their asymptotic properties.
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