| ldBands {Hmisc} | R Documentation |
This function computes and plots group sequential stopping boundaries
from the Lan-DeMets method with a variety of α-spending
functions using the ld98 program from the Department of
Biostatistics, University of Wisconsin written by DM Reboussin, DL
DeMets, KM Kim, and KKG Lan. Such stopping boundaries are
useful for early termination of clinical trials for safety problems or
for efficacy. Simple plot and print methods are
implemented. Simple sample size and minimally detectable effect sizes
given sample sizes may be obtained with a summary method if
power was specified to ldBands. Alternatively,
summary computes, for each look, the difference in means that
must be achieved to cross a boundary if n and sd are
specified, or the minimum difference in proportions and the odds ratios
that must be achieved to cross a boundary if n and pbar
are specified.
ldBands(n = length(times), times = NULL, alpha = 0.05, sided = 2,
alphaLower=alpha/2, alphaUpper=alpha/2,
information = NULL,
spending=c('OBrien-Fleming','Pocock','alpha*t^phi',
'Hwang-Shih-DeCani'),
phi=1,
spending2=c('OBrien-Fleming','Pocock','alpha*t^phi',
'Hwang-Shih-DeCani'),
phi2=phi,
truncate = Inf, power = NULL, pr = TRUE)
## S3 method for class 'ldBands':
print(x, ...)
## S3 method for class 'ldBands':
plot(x, xlab='Time', ylab='Z', actual=NULL,
type='b', labels=NULL, ...)
## S3 method for class 'ldBands':
summary(object, stdiff=NULL, n=NULL,
p1=NULL, p2=NULL, hr=NULL, events=NULL,
pbar=NULL, sd=NULL, ...)
## S3 method for class 'summary.ldBands':
print(x, ...)
n |
number of interim analyses. If times is given, is
automatically taken as the length of times.
For summary.ldBands, n is the sample size, to obtain
detectable standardized difference. |
times |
times at which interim analyses are done |
alpha |
overall α level for the multiple tests.
Default is 0.05. If sided=3 is the α-level
for the lower bounds, otherwise is the total α. |
sided |
set to 1 to use a one-sided test, 3 for
asymmetric two-sided bounds |
alphaLower |
α-level for lower bound if
sided=3. Defaults to α/2. When sided=3
alpha is recalculated from alphaLower+alphaUpper. |
alphaUpper |
α-level for upper bound if
sided=3. Defaults to α/2. |
information |
a vector of information times if different from
times. Used for computing covariances of test statistics. |
spending |
an α spending function. Default is
O'Brien-Fleming function. If sided=3 is the spending
function for the lower bounds. |
phi |
parameter for the third and fourth types of spending
functions (exponent of time for the third, default is 1) |
spending2 |
spending function for the upper bounds if
sided=3. Defaults to same spending function for lower
bounds. |
phi2 |
parameter for third and fourth spending functions if
sided=3. Default is phi. |
truncate |
a value at which to truncate Z critical values so that early looks will have some power without really affecting the overall α level. Default is no truncation. |
power |
A power for which to compute a drift parameter; useful in sample size calculations |
pr |
set to FALSE to supress the actual output of the
ld98 program |
x |
an object created by ldBands or summary.ldBands |
xlab |
x-axis label |
ylab |
y-axis label |
actual |
an optional list with two components: times and z values to add as points to the first plot |
type |
default is "b" causing both points and lines to be
drawn for boundaries. Use type="l" for example to suppress
drawing circles at points. |
labels |
an optional character vector to be used to label time
points corresponding to those generated by ldBands |
object |
an object created by ldBands |
stdiff |
standardized difference to detect |
p1 |
probability of event in group 1 |
p2 |
probability of event in group 2, to compare with p1
in order to obtain sample size for two-sample binomial |
hr |
hazard ratio to detect, to obtain needed number of events at end of study for either treatment arm using the logrank test |
events |
number of events per treatment arm at end of study, to obtain detectable hazard ratio |
pbar |
mean of actual probabilities of events in two treatment arms |
sd |
standard deviation of an observation |
... |
unused |
This function assumes that you have stored the ld98 executable
in a subdirectory that is in your system path. Obtain ld98
program from the URL given in the reference below.
The plot method makes two plots if power is specified, the
second containing exit and cumulative exit probabilities as a function
of time. If par(mfrow=c()) is not already set to something besides
c(1,1), par(mfrow=c(2,1)) is set temporarily.
A list of class "ldBands" with the following components. When
summary is used and n and either pbar or
sd are given, summary returns the same object returned
by ldBands but with possible components
diff.lower,diff.lower (needed difference means or proportions) and
or.lower,or.upper (needed odds ratios).
data |
a data frame containing the main calculations |
power |
power specified, if any |
drift |
drift calculated, if power specified |
type |
"boundaries" if power not specified,
"power" otherwise |
n |
number of interim analyses, for ldBands. For
summary is the number of observations per arm, and it must be
a vector with length equal to the number of looks if pbar or
sd are given. |
alpha |
input value of alpha |
sided |
1-3 |
alphaLower |
lower α |
alphaUpper |
upper α |
spending |
name of α spending function used |
phi |
parameter for spending function |
spending2 |
name of spending function for upper boundary.
Defaults to spending |
phi2 |
parameter for second spending function. Defaults to
phi but is ignored if spending2 is the first or second
type of spending function. |
truncate |
value at which Z statistics truncated (default
is Inf) |
Frank E Harrell Jr
Reboussin DM, DeMets DL, Kim K-M, Lan KKG (1996): Programs for computing group sequential boundaries using the Lan-DeMets method. http://www.medsch.wisc.edu/landemets
Reboussin DM, DeMets DL, Kim K, Lan KKG (2000): Computations for group sequential boundaries using the Lan-DeMets spending function method. Controlled Clinical Trials 21:190-207.
## Not run:
# Get boundaries for O'Brien-Fleming spending function, 5 looks, alpha=.05
b <- ldBands(5, pr=FALSE)
plot(b)
# Same but times are irregular, and information times are different than
# test times. Use Pocock spending function.
b <- ldBands(times= c(.4, .6, .8, .9, .95),
information=c(.42,.65,.83,.89,.94), spending='Pocock')
# Get power calculations
u <- ldBands(times=c(.4, .6, .8, .9, .95), power=.9)
u$drift # standardize difference * sqrt(n per arm)
# needed to provide power=.9
summary(u, n=50) # obtain detectable standardized difference
summary(u, p1=.4, p2=.5) # get sample size per arm, two-sample binomial
summary(u, hr=1.5) # get number of events per arm needed
# to detect a hazard ratio of 1.5
# Asymmetric boundaries with different spending functions, truncate
b <- ldBands(5, sided=3, spending='alpha*t^phi', phi=1, phi2=1.5,
alphaLower=.01, alphaUpper=.04, truncate=4)
b
plot(b)
# Compute differences in proportions and odds ratios needed to cross
# the boundaries, given a mean probability in two treatment arms of 0.1
# and given a vector of sample sizes per arm corresponding to the looks
s <- summary(b, n=seq(200,1000,by=200), pbar=.1)
s
d <- s$data
plot(d$n, d$or.lower, xlab='N Per Arm',
ylab='Critical Odds Ratio', type='b',
ylim=range(d$or.lower, d$or.upper), log='y')
lines(d$n, d$or.upper, type='b')
abline(h=1, lty=2)
## End(Not run)