Most Powerful Test Sequences with Early Stopping Options
Sergey Tarima, Nancy Flournoy

TL;DR
This paper demonstrates that sequential likelihood ratio tests with early stopping are most powerful for one-parameter exponential family data, providing a detailed probability measure construction and analyzing the impact of early stopping on distribution support.
Contribution
It introduces a comprehensive probability measure framework for sequential tests with early stopping, revealing how support reduction affects distribution properties and asymptotic behavior.
Findings
Likelihood ratio tests are most powerful with early stopping in exponential family models.
Early stopping induces mixtures and truncation in the distribution of test statistics.
Asymptotic distributions become mixtures of truncated normals under local alternatives.
Abstract
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive 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 stage specific components. These components are sub-densities of interim test statistics first described by Armitage, McPherson and Rowe (1969) that are commonly used to create stopping boundaries given an -spending function and a set of interim analysis times. Likelihood expressions conditional on reaching a stage are given to connect pieces of the…
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