Most powerful test sequences with early stopping options

Sergey Tarima () and Nancy Flournoy
Additional contact information
Sergey Tarima: Institute for Health and Equity, Medical College of Wisconsin
Nancy Flournoy: University of Missouri, 600 S State St.

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 4, No 4, 513 pages

Abstract: Abstract We extended the application of uniformly most powerful tests to sequential tests with different stage-specific sample sizes and critical regions. In the one parameter exponential family, likelihood ratio sequential tests are shown to be uniformly most powerful for any predetermined $$\alpha $$ α -spending function and stage-specific sample sizes. To obtain this result, the probability measure of a group sequential design is constructed with support for all possible outcome events, as is useful for designing an experiment prior to having data. This construction identifies impossible events that are not part of the support. The overall probability distribution is dissected into components determined by the stopping stage. These components are the sub-densities of interim test statistics first described by Armitage et al. (J R Stat Soc: Ser A 132:235–244, 1969) that are commonly used to create stopping boundaries given an $$\alpha $$ α -spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the probability anatomy together. The reduction of support caused by the adoption of an early stopping rule induces sequential truncation (not nesting) in the probability distributions of possible events. Multiple testing induces mixtures on the adapted support. Even asymptotic distributions of inferential statistics that are typically normal, are not. Rather they are derived from mixtures of truncated multivariate normal distributions.

Keywords: Adaptive designs; Adapted support; Group sequential designs; Local asymptotics; Interim hypothesis testing; Likelihood ratio tests (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00184-021-00839-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metrik:v:85:y:2022:i:4:d:10.1007_s00184-021-00839-w

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/184/PS2

DOI: 10.1007/s00184-021-00839-w

Access Statistics for this article

Metrika: International Journal for Theoretical and Applied Statistics is currently edited by U. Kamps and Norbert Henze

More articles in Metrika: International Journal for Theoretical and Applied Statistics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().