Construction of a continuous stopping boundary from an alpha spending function

Research output: Contribution to journalArticle

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, α. 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 also in the design of clinical trials. We use the Beta-Blocker Heart Attack Trial (BHAT) and AIDS Clinical Trials Group protocol 021 for illustration.

Original languageEnglish (US)
Pages (from-to)1061-1071
Number of pages11
JournalBiometrics
Volume54
Issue number3
DOIs
StatePublished - Sep 1 1998

Fingerprint

clinical trials
Clinical Trials
beta-adrenergic antagonists
cumulative distribution
Distribution functions
Continuous Time
myocardial infarction
Boundary Crossing
Statistics
Stopping Rule
Monitoring
Type I error
Cumulative distribution function
statistics
methodology
Boundary Value
Statistic
Discrete-time
monitoring
Attack

Keywords

  • Boundary crossing
  • Brownian motion
  • Discrete sequential boundary

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

Cite this

Construction of a continuous stopping boundary from an alpha spending function. / Betensky, Rebecca.

In: Biometrics, Vol. 54, No. 3, 01.09.1998, p. 1061-1071.

Research output: Contribution to journalArticle

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