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Approximate Interval Estimation of the Ratio of Binomial Parameters: A Review and Corrections for Skewness
Abstract
Various methods for finding confidence intervals for the ratio of binomial parameters are reviewed and evaluated numerically. It is found that the method based on likelihood scores (Koopman, 1984, Biometrics 40, 513-517; Miettinen and Nurminen, 1985, Statistics in Medicine 4, 213-226) performs best in achieving the nominal confidence coefficient, but it may distribute the tail probabilities quite disparately. Using general theory of Bartlett (1953, Biometrika 40, 306-317; 1955, Biometrika 42, 201-203), we correct this method for asymptotic skewness. Following Gart (1985, Biometrika 72, 673-677), we extend this correction to the case of estimating the common ratio in a series of two-by-two tables. Computing algorithms are given and applied to numerical examples. Parallel methods for the odds ratio and the ratio of Poisson parameters are noted.
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Citations
Cites
Some Methods for Strengthening the Common χ 2 Tests
Cochran, W. G. (1954) · Biometrics · doi:10.2307/3001616 · Cited by 3,718
Cited by
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007) · Behavior Research Methods · doi:10.3758/bf03193146 · Cited by 65,971
Farrington, C. P., & Manning, G. (1990) · Statistics in Medicine · doi:10.1002/sim.4780091208 · Cited by 657
OptimalCutpoints: An R Package for Selecting Optimal Cutpoints in Diagnostic Tests
López-Ratón, M., Rodríguez-Álvarez, M. X., Suárez, C. C., & Sampedro, F. G. (2014) · Journal of Statistical Software · doi:10.18637/jss.v061.i08 · Cited by 548
The interplay of Bayesian and frequentist analysis
Bayarri, M. J., & Berger, J. O. (2004) · Statistical Science · doi:10.1214/088342304000000116 · Cited by 525
Confidence intervals for a binomial proportion
Vollset, S. E. (1993) · Statistics in Medicine · doi:10.1002/sim.4780120902 · Cited by 477
Metadata
- Authors
- Gart, J. J., & Nam, J.-M.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1988-06
- Volume
- 44
- Issue
- 2
- Pages
- 323
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W1974215045
- Cited by
- 189
- References
- 1
- FWCI
- 4.38
- Type
- journal article
- Language
- en
- Open access
- closed
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