Group Sequential Boundary

Problem

Return the two-sided nominal z boundaries for a group sequential design with linear alpha spending. At information fraction t_k the cumulative spend is alpha*t_k, and the boundary at look k is the inverse standard normal CDF of 1 - (alpha_k - alpha_(k-1))/2. Return [] for empty or invalid input, non-increasing information fractions, or alpha outside (0, 1).

Hint

Linear spending implies equal increments of alpha at equally spaced looks.

Test cases

case 1

in: [[0.25,0.5,0.75,1],0.05]

expected: [2.4977054744123723,2.4977054744123723,2.4977054744123723,2.4977054744123723]

case 2

in: [[1],0.05]

expected: [1.9599639845400532]

case 3

in: [[0.5,1],0.1]

expected: [1.9599639845400532,1.9599639845400532]

case 4

in: [[0.5,0.4],0.05]

expected: []

case 5

in: [[],0.05]

expected: []

Starter codePython

import math
def group_sequential_boundary(information_fractions, alpha):
    # Your code here
    pass

5 test cases · run your code against them in the editor