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:

Or install the development version from GitHub:

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] 0.02676826
```

`p1`

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] 0.0231528
```

With `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] 0.976372
```

`pow`

has the same parameters as `toer`

.