## Type 1 Error Rate

### Description

Computes the exact family wise type 1 error rate of a basket trial .

### Usage

toer(
design,
theta1 = NULL,
n,
lambda,
epsilon,
tau,
logbase = 2,
prune = FALSE,
results = c("fwer", "group"),
...
)

## S4 method for signature 'OneStageBasket'
toer(
design,
theta1 = NULL,
n,
lambda,
epsilon,
tau,
logbase = 2,
prune = FALSE,
results = c("fwer", "group"),
...
)


### Arguments

 design An object of class Basket created by setupBasket. theta1 Probabilities under the alternative hypothesis. If length(theta1) == 1, then this is a common probability for all baskets. If is.null(theta1) then the type 1 error rate under the global null hypothesis is computed. n The sample size per basket. lambda The posterior probability threshold. See details for more information. epsilon A tuning parameter that determines the amount of borrowing. See details for more information. tau A tuning parameter that determines how similar the baskets have to be that borrowing occurs. See details for more information. logbase A tuning parameter that determines which logarithm base is used to compute the Jensen-Shannon divergence. See details for more information. prune Whether baskets with a number of responses below the critical pooled value should be pruned before the final analysis. results Whether only the family wise error rate (option fwer) or also the rejection probabilities per group (option group) should be returned. ... Further arguments.

### Details

toer computes the exact family wise type 1 error rate and the exact rejection probabilities per group. The family wise type 1 error rate is the probability to reject at least one null hypothesis for a basket with theta1 = theta0. If all theta1 > theta0 then the family wise type 1 error rate under the global null hypothesis is computed. The rejection probabilities correspond to the type 1 error rate for baskets with theta1 = theta 0 and to the power for baskets with theta1 > theta 0.

If prune = TRUE then the baskets with an observed number of baskets smaller than the pooled critical value are not borrowed from. The pooled critical value is the smallest integer c for which all null hypotheses can be rejected if the number of responses is exactly c for all baskets.

This method is implemented for the class OneStageBasket.

### Value

If results = "fwer" then the family wise type 1 error rate is returned as a numeric value. If results = "group" then a list with the rejection probabilities per group and the family wise type 1 error rate is returned. If all theta1 > theta0 then the family wise type 1 error rate is calculated under the global null hypothesis. For baskets with theta1 = theta0 the rejection probabilities corresponds to the type 1 error rate, for baskets with theta1 > theta0 the rejection probabilities corresponds to the power.

### Methods (by class)

• OneStageBasket: Type 1 error rate for a single-stage basket design.

### Examples

design <- setupOneStageBasket(k = 3, theta0 = 0.2)
toer(design, n = 15, lambda = 0.99, epsilon = 2, tau = 0)