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Activity Number:
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123
- The Early Bird Catches the Worm: Sequential Decision-Making as a Framework in Time of COVID-19 Pandemic
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Type:
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Invited
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Date/Time:
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Monday, August 8, 2022 : 10:30 AM to 12:20 PM
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Sponsor:
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Caucus for Women in Statistics
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Abstract #320343
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Title:
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Effects of Early Stopping Options on an Exponential Family Distribution
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Author(s):
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Nancy Flournoy* and Sergey Tarima
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Companies:
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University of Missouri and Division of Biostatistics, Medical College of Wisconsin
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Keywords:
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Group Sequential Designs;
UMP interim hypothesis tests;
Mixtures;
Truncated Distributions;
Adaptive Designs;
Likelihood inference for adaptive designs
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Abstract:
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Interim testing has grown in popularity to permit the possibility of early stopping. Much theoretical effort has focused on characterizing and controlling type I error rates under conditions that ensure the normality of parameter estimates. Using simple two and three stage experiments for illustration, we draw on Tarima and Flournoy (2019 Statistical Papers & 2021 Metrika https://rdcu.be/cyGfb) to demonstrate that sigma fields are not nested when early stopping options are introduced. We show that the components of the likelihood conditional on reaching a stage are the subdensites of interim test statistics first described by Armitage et. al (1969) and now commonly used to create stopping boundaries. Working directly with the natural convolutions induced by multiple testing on the adapted support permits useful tractable characterizations of adapted events with fewer than usual assumptions. To illustrate the usefulness of this framework we show that sequential likelihood ratio tests derived from one-parameter exponential family random variables are UMP for any given alpha-spending function with pre-determined stage-specific sample sizes (no asymptotics or normality required).
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Authors who are presenting talks have a * after their name.
