Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 36, Issue 9-12, Pages 2143-2157Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610920601143634
Keywords
adaptive designs; power; sample size re-estimation
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Funding
- NATIONAL CANCER INSTITUTE [P01CA047982, R01CA095749] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES [P30AI050410] Funding Source: NIH RePORTER
- NCI NIH HHS [R01 CA095749, P01 CA047982] Funding Source: Medline
- NIAID NIH HHS [P30 AI050410] Funding Source: Medline
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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.
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