Recommended confidence intervals for two independent binomial proportions
@article{Fagerland2015RecommendedCI,
title={Recommended confidence intervals for two independent binomial proportions},
author={Morten Wang Fagerland and Stian Lydersen and Petter Laake},
journal={Statistical Methods in Medical Research},
year={2015},
volume={24},
pages={224 - 254}
}The relationship between two independent binomial proportions is commonly estimated and presented using the difference between proportions, the number needed to treat, the ratio of proportions or the odds ratio. Several different confidence intervals are available, but they can produce markedly different results. Some of the traditional approaches, such as the Wald interval for the difference between proportions and the Katz log interval for the ratio of proportions, do not perform well unless…
Figures and Tables from this paper
100 Citations
Confidence intervals for the difference between independent binomial proportions: comparison using a graphical approach and moving averages.
- MathematicsPharmaceutical statistics
- 2014
It is found that the score-based methods on the whole have the best two-sided coverage, although they have slight deficiencies for confidence levels of 90% or lower, and the Brown-Li 'Jeffreys' method appears to perform reasonably well, and in most situations, it has better one-sided Coverage than the widely recommended alternatives.
Recommended tests and confidence intervals for paired binomial proportions.
- MathematicsStatistics in medicine
- 2014
The practical application of statistical methods for the analysis of paired binomial proportions using data from a recently published study of airway reactivity in children before and after stem cell transplantation and a matched case-control study of the association between floppy eyelid syndrome and obstructive sleep apnea-hypopnea syndrome are illustrated.
Confidence interval of difference of proportions in logistic regression in presence of covariates
- MathematicsStatistical methods in medical research
- 2018
Four procedures for analyzing the data are presented, and it is shown that, among the four methods studied, the resampling method based on the exact distribution function yields a coverage rate closest to the nominal.
Equal-tailed confidence intervals for comparison of rates.
- MathematicsPharmaceutical statistics
- 2017
Methods that are found to be robust for a wide range of applications in the analysis of rates are described, including a new stratified score method based on the t-distribution, suitable for use in either a fixed effects or random effects analysis.
Score confidence intervals and sample sizes for stratified comparisons of binomial proportions.
- MathematicsStatistics in medicine
- 2020
The efficient score tests are rederive, which reveals their theoretical relationship with the contrast-based score tests, and provides a basis for adapting the method by using other weighting schemes.
Approximate confidence intervals for a linear combination of binomial proportions: A new variant
- MathematicsCommun. Stat. Simul. Comput.
- 2017
A new adjustment for constructing an improved version of the Wald interval for linear combinations of binomial proportions, which addresses the presence of extremal samples is proposed, which performed better for some evaluation measures.
Generalized Confidence Intervals and Fiducial Intervals for Some Epidemiological Measures
- MathematicsInternational journal of environmental research and public health
- 2016
The overall conclusion is that the proposed methodologies based on generalized pivotal quantities and fiducial quantities provide an accurate and unified approach for the interval estimation of the various epidemiological measures in the context of binary outcome data with or without covariates.
Power evaluation of asymptotic tests for comparing two binomial proportions to detect direct and indirect association in large-scale studies
- MathematicsStatistical methods in medical research
- 2017
Comparisons of the power functions of three popular asymptotic tests show that when the design is balanced between the two binomials, the three tests are equivalent in terms of power, but when theDesign is unbalanced, differences in power can be substantial and the choice of the most powerful test also depends on the value of the parameters of the two compared binomial.
Confidence Intervals for Relative Risk by Likelihood Ratio Test
- Computer Science
- 2018
It is proposed to include in the comparison the alternative method of the Wilks confidence interval based on the likelihood ratio tests, and the procedure and R code for constructing such confidence intervals are described.
Several Proportions or Probabilities
- Mathematics
- 2013
We discuss the Multi-hypergeometric and Multinomial distributions and their properties with the focus on exact and large sample inference for comparing two proportions or probabilities from the same…
References
SHOWING 1-10 OF 61 REFERENCES
Confidence intervals for a ratio of two independent binomial proportions.
- Mathematics, Computer ScienceStatistics in medicine
- 2008
An approximate Bayesian interval is derived and its frequency properties are superior to all of the non-iterative confidence intervals considered, which have performance characteristics that are very similar to the computationally intensive score method.
Test-based exact confidence intervals for the difference of two binomial proportions.
- MathematicsBiometrics
- 1999
Test-based methods of constructing exact confidence intervals for the difference in two binomial proportions are proposed and it is shown that a large improvement can be achieved by using the standardized Z test with a constrained maximum likelihood estimate of the variance.
Confidence intervals for the ratio of two binomial proportions
- Mathematics
- 1984
Sometimes the ratio of two binomial proportions is the parameter of major interest, for instance as the risk ratio in a two-group cohort study (Fleiss, 1973) or as the likelihood ratio for a…
Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures
- Mathematics
- 2000
Abstract The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower…
Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions
- MathematicsComput. Stat. Data Anal.
- 2007
Confidence Limits for the Ratio of Two Binomial Proportions Based on Likelihood Scores: Non-Iterative Method
- Mathematics
- 1995
The interval estimation of the ratio of two binomial proportions based on the score statistic is superior over other methods. Iterative algorithms for calculating the approximate confidence interval…
Interval estimation for the difference between independent proportions: comparison of eleven methods.
- MathematicsStatistics in medicine
- 1998
Two new approaches which also avoid aberrations are developed and evaluated, and a tail area profile likelihood based method produces the best coverage properties, but is difficult to calculate for large denominators.
On logit confidence intervals for the odds ratio with small samples.
- Mathematics, Computer ScienceBiometrics
- 1999
Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf…
Fully specified bootstrap confidence intervals for the difference of two independent binomial proportions based on the median unbiased estimator.
- MathematicsStatistics in medicine
- 2009
An estimate of the risk difference based on median unbiased estimates (MUEs) of the two group probabilities is proposed and a corresponding confidence interval is derived using a fully specified bootstrap sample space.
Two-sided confidence intervals for the single proportion: comparison of seven methods.
- MedicineStatistics in medicine
- 1998
Criteria appropriate to the evaluation of various proposed methods for interval estimate methods for proportions include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use.

















