Constructing binomial confidence intervals with near nominal coverage by adding a single imaginary failure or success.

Abstract:

:In this paper we present a simple method for constructing (1- alpha)100 per cent confidence intervals for binomial proportions with near nominal coverage for all underlying proportion parameters on the unit interval. This new method uses, with a slight modification, the standard normal approximation technique taught in introductory statistics classes. Specifically, we first augment the observed binomial data with an imaginary failure to compute the lower bound and an imaginary success to compute the upper bound. By contrast, the Agresti-Coull method adds the same number of imaginary successes and failures to the observed data, yet it can still give somewhat subnominal coverage. As motivation, we discuss the relationship between this new method and the Clopper-Pearson exact method. We also present numerical calculations to illustrate the satisfactory performance of this new method compared with several common alternatives. Finally, we argue that for certain statistical applications, such as the design and analysis of clinical trials with adverse events, this new method represents a valuable complementary approach.

journal_name

Stat Med

journal_title

Statistics in medicine

authors

Borkowf CB

doi

10.1002/sim.2469

subject

Has Abstract

pub_date

2006-11-15 00:00:00

pages

3679-95

issue

21

eissn

0277-6715

issn

1097-0258

journal_volume

25

pub_type

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