glrt { New R Package for Analyzing Interval-Censored Survival Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 378

Later, Zhao et al. (2008) developed a similar class of generalized logrank tests

for interval-censored data allowing exact observations.
While treatment comparison software for right-censored data is commonly

found, software for interval-censored data is generally rare. Recently, Fay and

Shaw (2010) published the R package interval, whose function ictest con-
ducts the two generalized logrank tests of Sun (1996) and Finkelstein (1986)

and some weighted logrank tests. So et al. (2010) developed SAS macros for

conducting score-function-based tests and the generalized tests of Sun et al.

(2005) and Zhao et al. (2008). In this chapter we introduce a new R package

named glrt (version 1.0) developed by Zhao and Sun (2010). This package

conducts four different types of generalized logrank tests. In Section 14.2, we

introduce basic notation and review the methodology of the involved general-

ized logrank tests. The main functions of the package and the input require-

ments and output are introduced in Section 14.3. For illustration, two data

sets are analyzed using the four types of test procedures in Section 14.4. We

conclude with some remarks in Section 14.5.

14.2 Generalized Logrank Tests for Comparing Survival

Functions

14.2.1 Basic Notation

Consider a survival study involving a total of n independent subjects from

k different treatment groups with nl Ti subjects from group l; l = 1; ;k.
Obviously, P Ti, n Ti = n. Let T Ti represent the survival time of interest and zi Ti
the k-vector of treatment indicators for the i-th subject, i = 1;:::;n. If subject

i is from treatment group l, zi Ti has a one at the l-th position and zero elsewhere.
Assume that, instead of observing Ti, Ti , we observe f(L Ti ;R Ti ]; z Ti ;i = 1; ;ng,
where (L Ti ;R Ti ] is an interval to which Ti Ti belongs. As special cases, Ti Ti is exactly