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Improving interval estimation of binomial proportions.

X H Zhou1, C M Li, Z Yang

  • 1VA Puget Sound Health Care System, Seattle, WA 98108, USA. azhou@u.washington.edu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 15, 2008
PubMed
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This study introduces a novel confidence interval for binomial proportions using Edgeworth expansion. The new method demonstrates competitive finite-sample performance compared to existing intervals in clinical studies.

Area of Science:

  • Statistics
  • Biostatistics

Background:

  • Accurate confidence intervals for binomial proportions are crucial in statistical inference.
  • Existing methods like Wilson, Agresti-Coull, and Jeffreys intervals have limitations in certain scenarios.

Purpose of the Study:

  • To propose a new confidence interval for the binomial proportion.
  • To provide theoretical justification for the new interval.
  • To compare its performance against established intervals.

Main Methods:

  • The proposed interval utilizes the Edgeworth expansion of a logit transformation of the sample proportion.
  • Finite-sample performance was evaluated using coverage probabilities and expected lengths.
  • Comparison was made against Wilson, Agresti-Coull, and Jeffreys intervals.

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Main Results:

  • The new confidence interval offers a theoretically justified approach.
  • Its finite-sample performance is competitive with existing best intervals.
  • Illustrative examples from two clinical studies are provided.

Conclusions:

  • The proposed Edgeworth expansion-based confidence interval is a valuable addition to the methods for estimating binomial proportions.
  • It shows promise for application in real-world clinical research.