Confidence intervals for a ratio of two independent binomial proportions

Several large-sample confidence intervals for the ratio of independent binomial proportions are compared in terms of exact coverage probability and width. A non-iterative approximate Bayesian interval is derived and its frequency properties are superior to all of the non-iterative confidence intervals considered. The approximate Bayesian interval, which is very easy to compute, has performance characteristics that are very similar to the computationally intensive score method. Two sample size determination formulas are presented, one for desired absolute precision and the other for desired relative precision.

[1]  P. A. R. Koopman,et al.  Confidence intervals for the ratio of two binomial proportions , 1984 .

[2]  R. Peto,et al.  Beta blockade during and after myocardial infarction: an overview of the randomized trials. , 1985, Progress in cardiovascular diseases.

[3]  E. B. Wilson.  Probable Inference, the Law of Succession, and Statistical Inference , 1927 .

[4]  A. E. Maxwell,et al.  Analysing Qualitative Data , 1962 .

[5]  John J. Gart,et al.  The bias and higher cumulants of the logarithm of a binomial variate , 1986 .

[6]  S. Walter.  The distribution of Levin's measure of attributable risk , 1975 .

[7]  Alan Agresti,et al.  Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures , 2000 .

[8]  R. Newcombe.  Logit Confidence Intervals and the Inverse Sinh Transformation , 2001 .

[9]  S P Azen,et al.  OBTAINING CONFIDENCE INTERVALS FOR THE RISK RATIO IN COHORT STUDIES , 1978 .

[10]  J J Gart,et al.  Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness. , 1988, Biometrics.

[11]  Alan Agresti,et al.  Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables , 2005, Biometrics.

[12]  A. Brix.  Bayesian Data Analysis, 2nd edn , 2005 .

[13]  A. Agresti.  Categorical data analysis , 1993 .

[14]  S Lemeshow,et al.  Sample size requirements for studies estimating odds ratios or relative risks. , 1988, Statistics in medicine.