# A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval

@article{Kawasaki2010APD, title={A Posterior Density for the Difference Between Two Binominal Proportions and the Highest Posterior Density Credible Interval}, author={Youhei Kawasaki and E. Miyaoka}, journal={Journal of the Japan Statistical Society. Japanese issue}, year={2010}, volume={40}, pages={265-275} }

The statistical inference concerning the difference between two independent binominal proportions has often been discussed in medical and statistical literature. This discussion is far more often based on the frequency theory of statistical inference than on the Bayesian theory. In this article, we propose the expression of the posterior probability density function (pdf) for the difference between two independent binominal proportions. In addition, we calculate the exact Highest Posterior… Expand

#### 10 Citations

A Bayesian non-inferiority test for two independent binomial proportions.

- Mathematics, Medicine
- Pharmaceutical statistics
- 2013

In drug development, non-inferiority tests are often employed to determine the difference between two independent binomial proportions. Many test statistics for non-inferiority are based on the… Expand

Confidence interval of difference of proportions in logistic regression in presence of covariates

- Mathematics, Medicine
- Statistical 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. Expand

Efficient computation for Bayesian comparison of two proportions

- Mathematics
- 2019

Abstract In Bayesian comparison of two proportions, the exact computation of the evidence involves evaluating a generalized hypergeometric function. Several agreeing, but not identical, expressions… Expand

A Bayesian equivalency test for two independent binomial proportions

- Mathematics, Medicine
- Journal of biopharmaceutical statistics
- 2016

A new index is proposed that suggests the equivalency of binomial proportions, which is constructed based on the Bayesian framework and is applied to the results of actual clinical trials to demonstrate the utility of the index. Expand

ON SAMPLE SIZE DETERMINATION BASED ON A BAYESIAN INDEX OF NON-INFERIORITY FOR TWO INDEPENDENT BINOMIAL PROPORTIONS

- 2015

In drug development, non-inferiority tests are often employed to determine the difference between two independent binomial proportions. Many test statistics for non-inferiority are based on the… Expand

Methods for calculating credible intervals for ratios of beta distributions with application to relative risks of death during the second plague pandemic

- Mathematics, Medicine
- PloS one
- 2019

A novel method of calculating Bayesian credible intervals for a ratio of beta distributed random variables is shown to quantify uncertainty of relative risk estimates for these two epidemics which are considered in a 2 × 2 contingency table framework. Expand

Effects of Green Tea Gargling on the Prevention of Influenza Infection: An Analysis Using Bayesian Approaches.

- Medicine
- Journal of alternative and complementary medicine
- 2017

The analysis of data obtained from a randomized trial on the prevention of influenza by gargling with green tea suggests that green tea gargling can be an additional preventive measure for use with other pharmaceutical and nonpharmaceutical measures and indicates the need for additional studies to confirm the effect of green tea Gargling. Expand

Bayesian approach for assessing noninferiority in a three-arm trial with binary endpoint.

- Computer Science, Medicine
- Pharmaceutical statistics
- 2018

Bayesian implementation of noninferiority trials when primary outcome of interest is binary is considered, as it provides a path to integrate historical trials and current trial information via sequential learning. Expand

Heterogeneous Multi-Sensor Fusion With Random Finite Set Multi-Object Densities

- Computer Science, Engineering
- IEEE Transactions on Signal Processing
- 2021

This paper addresses the density based multi-sensor cooperative fusion using random finite set (RFS) type multi-object densities (MODs) with a novel heterogeneous fusion method to perform the information averaging among local RFS MODs. Expand

Distributed Multi-Sensor Fusion of PHD Filters With Different Sensor Fields of View

- Computer Science
- IEEE Transactions on Signal Processing
- 2020

Two novel approaches are devised to perform the weighted arithmetic average (WAA) fusion rule in a more robust way by employing a set of state-dependent fusion weights which are computed online online. Expand

#### References

SHOWING 1-10 OF 33 REFERENCES

Test-based exact confidence intervals for the difference of two binomial proportions.

- Mathematics, Medicine
- Biometrics
- 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. Expand

Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables.

- Mathematics, Medicine
- Biometrics
- 2005

This article investigates the performance, in a frequentist sense, of Bayesian confidence intervals for the difference of proportions, relative risk, and odds ratio in 2 x 2 contingency tables and recommends tail intervals over highest posterior density (HPD) intervals, for invariance reasons. Expand

Interval estimation for the difference between independent proportions: comparison of eleven methods.

- Mathematics, Medicine
- Statistics 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. Expand

Approximate confidence intervals for one proportion and difference of two proportions

- Mathematics
- 2002

Constructing a confidence interval for a binomial proportion or the difference of two proportions is a routine exercise in daily data analysis. The best-known method is the Wald interval based on the… Expand

Unconditional Confidence Interval for the Difference between Two Proportions

- Mathematics
- 2003

Summary In applied statistics it is customary to have to obtain a one- or two-tail confidence interval for the difference d ¼ p2 � p1 between two independent binomial proportions. Traditionally, one… Expand

On small-sample confidence intervals for parameters in discrete distributions.

- Medicine, Mathematics
- Biometrics
- 2001

This paper illustrates for a variety of discrete problems, including interval estimation of a binomial parameter, the difference and the ratio of two binomial parameters for independent samples, and the odds ratio. Expand

Bayesian analysis of a 2×2 contingency table with dependent proportions and exact sample size

- Mathematics
- 2008

Abstract In the analysis of a 2×2 contingency table with dependent proportions, several measures used are based on the two conditional probabilities, π1| 1 and π1| 2, and the marginal probabilities,… Expand

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… Expand

Confidence intervals for two sample binomial distribution

- Mathematics, Engineering
- 2005

This paper considers confidence intervals for the difference of two binomial proportions. Some currently used approaches are discussed. A new approach is proposed. Under several generally used… Expand

Exact tests for equality of two proportions: Fisher × Bayes

- Mathematics
- 1985

Yates (1984) using theoretical and philosophical arguments claims to have proved that the Fisher exact test for comparing the proportions of two binomial experiments is the best exact test. The… Expand