weights_fujikawa {baskexact}

Weights Based on Fujikawa et al.'s Design

Description

Weights Based on Fujikawa et al.'s Design

Usage

weights_fujikawa(design, ...)

## S4 method for signature 'OneStageBasket'
weights_fujikawa(
  design,
  n,
  lambda,
  epsilon = 1.25,
  tau = 0.5,
  logbase = 2,
  prune = FALSE,
  globalweight_fun = NULL,
  globalweight_params = list(),
  ...
)

## S4 method for signature 'TwoStageBasket'
weights_fujikawa(design, n, n1, epsilon = 1.25, tau = 0, logbase = 2, ...)

Arguments

design

An object of class Basket created by setupOneStageBasket or setupTwoStageBasket.

...

Further arguments.

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. If this is TRUE then lambda is also required and if globalweight_fun is not NULL then globalweight_fun and globalweight_params are also used.

globalweight_fun

Which function should be used to calculate the global weights.

globalweight_params

A list of tuning parameters specific to globalweight_fun.

n1

The sample size per basket for the interim analysis in case of a two-stage design.

Details

weights_fujikawa calculates the weights used for sharing information between baskets based on the proposal by Fujikawa et al. (2020). The weight for two baskets i and j is found as (1 - JSD(i, j))^\varepsilon where JSD(i, j) is the Jensen-Shannon divergence between the individual posterior distributions of the response probabilities of basket i and j. Note that Fujikawa's weights also share the prior information between the baskets.

A small value of epsilon results in stronger borrowing also across baskets with heterogenous results. If epsilon is large then information is only borrowed between baskets with similar results. If a weight is smaller than tau it is set to 0, which results in no borrowing.

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.

The function is generally not called by the user but passed to another function such as toer and pow to specificy how the weights are calculated.

Value

A matrix including the weights of all possible pairwise outcomes.

Methods (by class)

• weights_fujikawa(OneStageBasket): Fujikawa-weights for a single-stage basket design.

• weights_fujikawa(TwoStageBasket): Fujikawa-weights for a two-stage basket design.

References

Fujikawa, K., Teramukai, S., Yokota, I., & Daimon, T. (2020). A Bayesian basket trial design that borrows information across strata based on the similarity between the posterior distributions of the response probability. Biometrical Journal, 62(2), 330-338.

Examples

design <- setupOneStageBasket(k = 3, p0 = 0.2)
toer(design, n = 15, lambda = 0.99, weight_fun = weights_fujikawa)