Simultaneous confidence intervals for comparing binomial parameters

Alan Agresti, Matilde Bini, Bruno Bertaccini, Euijung Ryu

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or "exact" small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52).

Original languageEnglish (US)
Pages (from-to)1270-1275
Number of pages6
JournalBiometrics
Volume64
Issue number4
DOIs
StatePublished - Dec 1 2008

Fingerprint

Simultaneous Confidence Intervals
Biometrics
confidence interval
Statistics
Confidence Intervals
Proportion
Odds Ratio
odds ratio
Score Statistic
Bonferroni
Relative Risk
Coverage Probability
relative risk
biometry
methodology
Small Sample
Categorical or nominal
Pairwise
statistics
Simulation Study

Keywords

  • Bonferroni method
  • Difference of proportions
  • Odds ratio
  • Score test
  • Studentized range distribution
  • Tukey multiple comparisons

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this

Simultaneous confidence intervals for comparing binomial parameters. / Agresti, Alan; Bini, Matilde; Bertaccini, Bruno; Ryu, Euijung.

In: Biometrics, Vol. 64, No. 4, 01.12.2008, p. 1270-1275.

Research output: Contribution to journalArticle

Agresti, Alan ; Bini, Matilde ; Bertaccini, Bruno ; Ryu, Euijung. / Simultaneous confidence intervals for comparing binomial parameters. In: Biometrics. 2008 ; Vol. 64, No. 4. pp. 1270-1275.
@article{4cb38b94274f4bb9a16bf2d0e80cf1b5,
title = "Simultaneous confidence intervals for comparing binomial parameters",
abstract = "To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or {"}exact{"} small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52).",
keywords = "Bonferroni method, Difference of proportions, Odds ratio, Score test, Studentized range distribution, Tukey multiple comparisons",
author = "Alan Agresti and Matilde Bini and Bruno Bertaccini and Euijung Ryu",
year = "2008",
month = "12",
day = "1",
doi = "10.1111/j.1541-0420.2008.00990.x",
language = "English (US)",
volume = "64",
pages = "1270--1275",
journal = "Biometrics",
issn = "0006-341X",
publisher = "Wiley-Blackwell",
number = "4",

}

TY - JOUR

T1 - Simultaneous confidence intervals for comparing binomial parameters

AU - Agresti, Alan

AU - Bini, Matilde

AU - Bertaccini, Bruno

AU - Ryu, Euijung

PY - 2008/12/1

Y1 - 2008/12/1

N2 - To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or "exact" small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52).

AB - To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or "exact" small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52).

KW - Bonferroni method

KW - Difference of proportions

KW - Odds ratio

KW - Score test

KW - Studentized range distribution

KW - Tukey multiple comparisons

UR - http://www.scopus.com/inward/record.url?scp=56049098181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56049098181&partnerID=8YFLogxK

U2 - 10.1111/j.1541-0420.2008.00990.x

DO - 10.1111/j.1541-0420.2008.00990.x

M3 - Article

C2 - 18266891

AN - SCOPUS:56049098181

VL - 64

SP - 1270

EP - 1275

JO - Biometrics

JF - Biometrics

SN - 0006-341X

IS - 4

ER -