Practical Methods for Bounding Test Size with an Internal Pilot Design

• Activity Number: 176
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Christopher S. Coffey*+ and Keith E. Muller
• Companies: University of Alabama, Birmingham and University of North Carolina, Chapel Hill
• Keywords: internal pilots ; sample size re-estimation ; linear models ; study design

Abstract

For linear models with Gaussian errors, internal pilot designs use a fraction of the data to re-estimate the error variance and adjust the final sample size. Such designs increase power (if original variance value too small) or reduce expected sample size (if original value too large). However, the approach may inflate test size. Coffey and Muller (2001) found that a "bounding" test, consisting of a design-specific adjustment to the critical value used for hypothesis testing, is particularly appealing because it guarantees control of test size while still providing most of the advantages of internal pilot designs. Unfortunately, computational complexities make the bounding method difficult to use. We describe new analytic forms for the distributions at the heart of internal pilot theory. All results apply to any univariate linear model with fixed predictors and Gaussian errors, not just the two group t-tests considered by most authors. The simple new forms lead to many useful results. Most importantly, calculations for example studies illustrate that the new results make the bounding method practical by dramatically reducing computation times.