Sample Size Software for the Supremum Log-Rank
The algorithm used
for computing sample size for the supremum log-rank is described in
detail in the technical report "A sample size formula for the supremum
log-rank statistic" by Kevin Hasegawa Eng and Michael R. Kosorok, which
can be downloaded by clicking here. We recommend
reading this thoroughly before using the software described below. As part
of this package, the function surv.Rtest for computing the supremum weighted
log-rank and its p-value is included. The family of weights used are the
G(rho,gamma) class (Harrington and Fleming, 1982 Biometrika). An optional
argument enables computation of the usual weighted log-rank.
To incorporate the software into R,
insert the code obtained
by clicking here into
R. To do this in a unix
environment, place this code in a file (named, for example, "renyi.r")
in a subdirectory. In that subdirectory, begin
R and type the following
command: source("renyi.r"). This procedure will create the functions
sup.r, sup.inverse, cnorm, sup.g, sup.G, surv.Rtest and KM.left.
The function sup.r computes the quantity R described in the above
technical report. This quantity times the sample size based on the regular
log-rank statistic will give the sample size required for the
supremum log-rank. The arguments required by sup.r are alpha
(the two-sided type I error) and beta (the type II error). The function
sup.r calls the following functions:
- The function sup.inverse computes the
critical values for the supremum in absolute value of Brownian motion.
The only argument required for this function is the type I error alpha.
- The function cnorm computes the area to the right of z under
a standard normal density. It is more accurate than the
R function pnorm.
The only required argument is z.
- The function sup.G computes the value of the function G(x)
defined in the above technical report. The only required
argument is x.
- The function sup.g computes the derivative of G(x). The only
required argument is x.
The function surv.Rtest computes the supremum weighted log-rank test
and its p-value, along with the non-supremum weighted log-rank test if
requested. Tied values are allowed, and the variance is calculated
correctly for ties. The p-values have not been adjusted for ties, but
the computed p-values will be conservative in the presence of ties (and
asymptotically exact when no ties are present). The required arguments
are time (the event times), delta (the
censoring indicators) and group (treatment indicators which must take on the
values 1 or 2 only). No missing values are allowed. Optional arguments
are rho and gamma (both with default value 0) which are the powers of
the left-continuous pooled Kaplan-Meier estimator S(t-) and
1-S(t-), respectively. Another optional argument is the logical
logrank (with default value F) which indicates whether the usual weighted
logrank is also to be calculated (with the same weight function used in
the supremum version). The final optional argument is the error permitted
for the supremum p-value (with default 1.0e-8). The function surv.Rtest
calls the following function:
- The function KM.left is called by surv.Rtest to calculate the weights
if either rho or gamma (optional arguments for surv.Rtest) are non-zero.
The required arguments are time and delta.