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Activity Number: 29
Type: Contributed
Date/Time: Sunday, August 2, 2009 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #304906
Title: Composition Confidence Intervals Offer Better Coverage Than the Delta Method
Author(s): Paul Duty*+ and Nancy Flournoy
Companies: Montgomery College and University of Missouri-Columbia
Address: 51 Mannakee Street, Rockville, MD, 20850,
Keywords: confidence intervals ; coverage improvement ; Delta Method ; root compositions ; statistical theory ; dosage quantal estimation
Abstract:

Delta Method confidence intervals for functions of parameters, particularly nonlinear functions, are prone to either undercoverage or overcoverage. The Composition Method is a completely analytical approach that, with a well chosen composition, produces an asymmetric interval that adjusts for this nonlinearity. We study a family of confidence intervals we call root composition intervals. Analytical comparisons are made between root composition intervals and the Delta Method interval. We then show that given a sufficiently large sample, coverage for root composition intervals will be closer to the nominal coverage than coverage for the Delta Method interval. Finally, we compare coverage between some root composition intervals and the Delta Method interval for the quantal from a dose-response function.

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