baskexact analytically calculates the operating characteristics of a
basket trial using the power prior design (
https://doi.org/10.48550/arXiv.2309.06988) and the
design of Fujikawa et al. (https://doi.org/10.1002/bimj.201800404).
Install the currenct CRAN version of baskexact:
install.packages("baskexact")Or install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("https://github.com/lbau7/baskexact")baskexact calculates the exact operating characteristics (type 1 error rate, power, expected number of correct decisions and expected sample size) of single-stage and two-stage basket trials with equal sample sizes using the power prior design and the design of Fujikawa et al.
At first, a design-object has to be created using either
setupOneStageBasket for a single-stage trial or
setupTwoStageBasket for a two-stage trial. For example:
library(baskexact) # the development version is used for the example
design <- setupOneStageBasket(k = 3, shape1 = 1, shape2 = 1, p0 = 0.2)k is the number of baskets, shape1 and
shape2 are the two shape parameters of the beta-prior of
the response probabilities of each basket and p0 is the
response probability under the null hypothesis. Note that currently only
common prior parameters and a common null response probability are
supported.
Use toer to calculate the type 1 error rate of a certain
design:
toer(
design = design,
p1 = NULL,
n = 15,
lambda = 0.99,
weight_fun = weights_cpp,
weight_params = list(a = 2, b = 2),
results = "group"
)
# $rejection_probabilities
# [1] 0.01401416 0.01401416 0.01401416
#
# $fwer
# [1] 0.02676826p1 refers to the true response probabilities under which
the type 1 error rate is computed. Since p1 = NULL is
specified, the type 1 error rates under a global null hypothesis are
calculated. n specifies the sample size per basket.
Currently only equal sample sizes are supported. lambda is
the posterior probability cut-off to reject the null hypothesis. If the
posterior probability that the response probability of the basket is
larger than p0 is larger than lambda, then the
null hypothesis is rejected. weight_fun specifies which
method should be used to calculate the weights. With
weights_cpp the weights are calculated based on a response
rate differences between baskets. In weight_params a list
of parameters that further define the weights is given. See Baumann et
al. (2024) for details. results specifies whether only the
family wise type 1 error rate (option fwer) or also the
basketwise type 1 error rates (option group) are
calculated.
To find the probability cut-off lambda such that a
certain FWER is maintained, use adjust_lambda, for example
to find lambda such that the FWER does not exceed 2.5%
(note that all hypotheses are tested one-sided):
adjust_lambda(
design = design,
alpha = 0.025,
p1 = NULL,
n = 15,
weight_fun = weights_cpp,
weight_params = list(a = 2, b = 2),
prec_digits = 4
)
# $lambda
# [1] 0.991
#
# $toer
# [1] 0.0231528With prec_digits it is specified how many decimal places
of lambda are considered. Use toer with
lambda = 0.9909 to check that 0.991 is indeed the smallest
probability cut-off with four decimals with a FWER of at most 2.5%. Note
that even when considering more decimal places the actual FWER will
generally below the nominal level (quite substantially in some cases),
since the outcome (number of responses) is discrete.
Use pow to calculate the power of the design:
pow(
design = design,
p1 = c(0.5, 0.5, 0.5),
n = 15,
lambda = 0.9942,
weight_fun = weights_cpp,
weight_params = list(a = 2, b = 2),
results = "group"
)
# $rejection_probabilities
# [1] 0.909585 0.909585 0.909585
#
# $ewp
# [1] 0.976372pow has the same parameters as toer.