baskexact (version 1.0.1)

weights_jsd: Weights Based on the Jensen-Shannon Divergence

Description

Weights Based on the Jensen-Shannon Divergence

Usage

weights_jsd(design, ...)
# S4 method for OneStageBasket
weights_jsd(
  design,
  n,
  lambda,
  epsilon = 1.25,
  tau = 0.5,
  logbase = 2,
  prune = FALSE,
  globalweight_fun = NULL,
  globalweight_params = list(),
  ...
)
# S4 method for TwoStageBasket
weights_jsd(design, n, n1, epsilon = 1.25, tau = 0, logbase = 2, ...)

Value

A matrix including the weights of all possible pairwise outcomes.

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.

Methods (by class)

• weights_jsd(OneStageBasket): Jensen-Shannon Divergence weights for a single-stage basket design.

• weights_jsd(TwoStageBasket): Jensen-Shannon Divergence weights for a two-stage basket design.

Details

weights_jsd calculates the weights used for sharing information between baskets based on the Jensen-Shannon divergence (JSD). 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. This is identical to how the weights are calculated in weights_fujikawa, however when Fujikawa's weights are used the prior information is also shared.

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.

Examples

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