Construction of a continuous stopping boundary from an alpha spending function
Related Experiment Video
Updated: Oct 9, 2026

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
Published on: December 10, 2012
1Department of Biostatistics, Harvard School of Public Health, Boston, Massachusetts 02115, USA. betensky@sdac.harvard.edu
Abstract:
Lan and DeMets (1983, Biometrika 70, 659-663) proposed a flexible method for monitoring accumulating data that does not require the number and times of analyses to be specified in advance yet maintains an overall Type I error, alpha. Their method amounts to discretizing a preselected continuous boundary by clumping the density of the boundary crossing time at discrete analysis times and calculating the resultant discrete-time boundary values. In this framework, the cumulative distribution function of the continuous-time stopping rule is used as an alpha spending function. A key assumption that underlies this method is that future analysis times are not chosen on the basis of the current value of the statistic. However, clinical trials may be monitored more frequently when they are close to crossing the boundary. In this situation, the corresponding continuous-time boundary should be used. Here we demonstrate how to construct a continuous stopping boundary from an alpha spending function. This capability is useful in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.
Related Concept Videos
Electrostatic Boundary Conditions
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Boundary Conditions: Lossless Lines
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Continuity of a Function
Properties of Continuous Functions
Area Between Curves: Problem Solving
Limits with Oscillating Discontinuities
