Exact confidence intervals for the relative risk and the odds ratio

Biometrics

Volumn 71, Issue 4, 2015, Pages 985-995

  Wang, Weizhen ^a,b   Shan, Guogen ^c  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

^b WRIGHT STATE UNIVERSITY   (United States)

^c UNIVERSITY OF NEVADA   (United States)

Author keywords

Binomial distribution; Coverage probability; Multinomial distribution; Set inclusion

Indexed keywords

BINOMIAL DISTRIBUTION; CONFIDENCE INTERVAL; COVERAGE PROBABILITIES; EXACT CONFIDENCE INTERVAL; MATCHED-PAIR DESIGN; MULTINOMIAL DISTRIBUTIONS; ODD RATIOS; RELATIVE RISKS; SET INCLUSION;

PROBABILITY DISTRIBUTIONS;

BIOMETRY; COMPARATIVE STUDY; CONFIDENCE INTERVAL; DATA ACQUISITION; NUMERICAL MODEL; PROBABILITY; RISK ASSESSMENT;

BINOMIAL DISTRIBUTION; BIOMETRY; CLINICAL TRIAL (TOPIC); CONFIDENCE INTERVAL; HUMAN; ODDS RATIO; PROCEDURES; RISK; SAMPLE SIZE; STATISTICAL ANALYSIS; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA;

BINOMIAL DISTRIBUTION; BIOMETRY; CLINICAL TRIALS AS TOPIC; CONFIDENCE INTERVALS; HUMANS; MATCHED-PAIR ANALYSIS; MODELS, STATISTICAL; ODDS RATIO; RISK; SAMPLE SIZE;

EID: 84955366933     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/biom.12360     Document Type: Article

References (29)

1. Agresti, A. (2002). Categorical Data Analysis, 2nd ed., New York: John Wiley & Sons, Inc.
2. Agresti, A. and Coull, B. A. (1998). Approximate is better than exact for interval estimation of binomial proportions. The American Statistician 52, 119-126.
3. Agresti, A. and Min, Y. (2001). On small-sample confidence intervals for parameters in discrete distributions. Biometrics 57, 963-971.
4. Bentur L., Lapidot M., Livnat G., Hakim F., Lidroneta-Katz C., Porat I., et al. (2009). Airway reactivity in children before and after stem cell transplantation. Pediatric Pulmonology 44, 845-850.
5. Bol'shev, L. N. (1965). On the construction of confidence limits. Theory of Probability and its Applications 10, 173-177 (English translation).
6. Brown, L. D., Cai, T. T., and DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Sciences 16, 101-133.
7. Buehler, R. J. (1957). Confidence intervals for the product of two binomial parameters. Journal of the American Statistical Association 52, 482-493.
8. Chan, I. S. F. and Zhang, Z. (1999). Test-based exact confidence intervals for the difference of two binomial proportions. Biometrics 55, 1202-1209.
9. Casella, G. and Berger, R. L. (1990). Statistical Inference. Belmont, CA: Duxbury Press.
10. Chen, J. (1993). The order relations in the sample spaces and the confidence limits for parameters. Advances in Mathematics 22, 542-552.
11. Essenberg, J. M. (1952). Cigarette smoke and the incidence of primary neoplasm of the lung in albino mice. Science 116, 561-562.
12. Gart, J. J. (1971). The comparison of proportions: A review of significance tests, confidence intervals, and adjustments for stratification. Review of the International Statistical Institute 39, 148-169.
13. Goodman, L. A. (1985). The analysis of cross-classified data having ordered and/or unordered categories: Association models, correlation models, and asymmetry models for contingency tables with or without missing entries. The Annals of Statistics 13, 10-69.
14. Huwang, L. (1995). A note on the accuracy of an approximate interval for the binomial parameter. Statistics & Probability Letters 24, 177-180.
15. Li, Z., Taylor, J. M. G., Nan, B. (2010). Construction of confidence intervals and regions for ordered binomial probabilities. The American Statistician 64, 291-298.
16. Lin, Y., Newcombe, R. G., Lipsitz, S., and Carter, R. E. (2009). Fully specified bootstrap confidence intervals for the difference of two independent binomial proportions based on the median unbiased estimator. Statistics in Medicine 28, 2876-2890.
17. Lloyd, C. J. and Kabaila, P. (2003). On the optimality and limitations of Buehler bounds. Australian and New Zealand Journal of Statistics 45, 167-174.
18. McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society. Series B 42, 109-142.
19. Parzen, M., Lipsitz, S., Ibrahim, J., and Klar, N. (2002), An estimate of the odds ratio that always exists. Journal of Computational and Graphical Statistics 11, 420-436.
20. Santner, T. J. and Snell, M. K. (1980). Small-sample confidence intervals for p1-p2 and p1/p2 in contingency tables, Journal of the American Statistical Association 75, 386-394.
21. Shan, G. and Wang, W. (2013). ExactCIdiff: An R package for computing exact confidence intervals for the difference of two proportions. The R Journal 5, 62-70.
22. StatXact 10th release of the most popular exact statistics analysis software (2013). Cytel Inc. 675 Massachusetts Avenue, Cambridge, MA 02139.
23. Thomas, D. G. (1971). Algorithm AS-36: Exact confidence limits for the odds ratio in a 2×2 table. Applied Statistics 20, 105-110.
24. Wang, W. (2006). Smallest confidence intervals for one binomial proportion. Journal of Statistical Planning and Inference 136, 4293-4306.
25. Wang, W. (2010). On construction of the smallest one-sided confidence interval for the difference of two proportions. The Annals of Statistics 38, 1227-1243.
26. Wang, W. (2012). An inductive order construction for the difference of two dependent proportions. Statistics & Probability Letters 82, 1623-1628.
27. Wang, W. (2013). A note on bootstrap confidence intervals for proportions. Statistics & Probability Letters 83, 2699-2702.
28. Wang, W. and Zhang, Z. (2014). Asymptotic infimum coverage probability for interval estimation of proportions. Metrika 77, 635-646.
29. Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association 22, 209-212.