Practical methods for bounding type I error rate with an internal pilot design

Christopher S Coffey; John A Kairalla; Keith E Muller

doi:10.1080/03610920601143634

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Practical methods for bounding type I error rate with an internal pilot design

Journal article

Peer reviewed

Practical methods for bounding type I error rate with an internal pilot design

Christopher S Coffey, John A Kairalla and Keith E Muller

Communications in statistics. Theory and methods, Vol.36(11), pp.2143-2157

2007

DOI: 10.1080/03610920601143634

PMCID: PMC3867302

PMID: 24363489

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https://www.ncbi.nlm.nih.gov/pmc/articles/3867302View

Open Access

Abstract

New analytic forms for distributions at the heart of internal pilot theory solve many problems inherent to current techniques for linear models with Gaussian errors. Internal pilot designs use a fraction of the data to re-estimate the error variance and modify the final sample size. Too small or too large a sample size caused by an incorrect planning variance can be avoided. However, the usual hypothesis test may need adjustment to control the Type I error rate. A bounding test achieves control of Type I error rate while providing most of the advantages of the unadjusted test. Unfortunately, the presence of both a doubly truncated and an untruncated chi-square random variable complicates the theory and computations. An expression for the density of the sum of the two chi-squares gives a simple form for the test statistic density. Examples illustrate that the new results make the bounding test practical by providing very stable, convergent, and much more accurate computations. Furthermore, the new computational methods are effectively never slower and usually much faster. All results apply to any univariate linear model with fixed predictors and Gaussian errors, with the t-test a special case.

Combinatorics

Experimental Design

Mathematics

Statistics

Combinatorics. Ordered structures

Designs and configurations

Distribution theory

Exact sciences and technology

General topics

Probability and statistics

Probability theory and stochastic processes

Sciences and techniques of general use

Details

Title: Subtitle: Practical methods for bounding type I error rate with an internal pilot design
Creators: Christopher S Coffey - Department of Biostatistics, University of Alabama at Birmingham, Birmingham, Alabama, United States
John A Kairalla - Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina, United States
Keith E Muller - Division of Biostatistics, Department of Epidemiology and Health Policy Research, University of Florida, Gainesville, Florida, United States
Resource Type: Journal article
Publication Details: Communications in statistics. Theory and methods, Vol.36(11), pp.2143-2157
DOI: 10.1080/03610920601143634
PMID: 24363489
PMCID: PMC3867302
NLM abbreviation: Commun Stat Theory Methods
ISSN: 0361-0926
eISSN: 1532-415X
Publisher: Taylor & Francis
Language: English
Date published: 2007
Academic Unit: Biostatistics
Record Identifier: 9984214820602771

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