Browse > Article
http://dx.doi.org/10.5351/KJAS.2012.25.3.435

Evaluating Interval Estimates for Comparing Two Proportions with Rare Events  

Park, Jin-Kyung (International Vaccine Institute)
Kim, Yong-Dai (Department of Statistics, Seoul National University)
Lee, Hak-Bae (Department of Applied Statistics, Yonsei University)
Publication Information
The Korean Journal of Applied Statistics / v.25, no.3, 2012 , pp. 435-446 More about this Journal
Abstract
Epidemiologic studies frequently try to estimate the impact of a specific risk factor. The risk difference and the risk ratio are generally useful measurements for this purpose. When using such measurements for rare events, the standard approaches based on the normal approximation may fail, in particular when no events are observed. In this paper, we discuss and evaluate several existing methods to construct confidence intervals around risk differences and risk ratios using Monte-Carlo simulations when the disease of interest is rare. The results in this paper provide guidance how to construct interval estimates of the risk differences and the risk ratios when no events are detected.
Keywords
Bayesian probability interval; confidence interval; rare events; risk ratio; risk difference;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Koopman, P. A. R. (1984). Confidence limits for the ratio of two binomial proportions, Biometrics, 40, 513-517.   DOI   ScienceOn
2 Louis, T. A. (1981). Confidence intervals for a binomial parameter after observing no successes, The Amer- ican Statistician, 35, 154-154.
3 Mee, R. W. (1984). Confidence bounds for the difference between two probabilities, Biometrics, 40, 1175- 1176.
4 Miettinen, O. S. and Nurminen, M. (1985). Comparative analysis of two rates, Statistics in Medicine, 4, 213-226.   DOI   ScienceOn
5 Newcombe, R. G. (1998a). Two-sided confidence intervals for the single proportion: Comparison of seven methods, Statistics in Medicine, 17, 857-872.   DOI   ScienceOn
6 Newcombe, R. G. (1998b). Interval estimation for the difference between independent proportions: Comparison of eleven methods, Statistics in Medicine, 17, 873-890.   DOI
7 Noether, G. E. (1957). Two confidence intervals for the ratio of two probabilities and some measures of effectiveness, Journal of the American Statistics Association, 52, 36-45.   DOI   ScienceOn
8 Santner, T. S. and Snell, M. K. (1980). Small-sample confidence intervals for p1 - p2 and p1=p2 in 2$\times$2 contingency tables, Journal of the American Statistical Association, 75, 386-394.
9 Walter, S. D. (1975). The distribution of Levin's measure of attributable risk, Biometrika, 62, 371-375.   DOI   ScienceOn
10 Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference, Journal of the American Statistical Association, 22, 209-212.   DOI   ScienceOn
11 Aitchison, J. and Bacon-Shone, J. (1981). Bayesian risk ratio analysis, The American Statistician, 35, 254-257.
12 Bickel, P. J. and Doksum, K. A. (1977). Mathematical Statistics: Basic Ideas and Selected Topics, Holden- Day.
13 Beal, S. L. (1987). Asymptotic confidence intervals for the difference between two binomial parameters for use with small samples, Biometrics, 43, 941-950.   DOI
14 Berger, R. L. and Boos, D. D. (1994). P Values maximized over a confidence set for the nuisance parameter, Journal of the American Statistical Association, 89, 1012-1016.
15 Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (1995). Bayesian Data Analysis, Chapman & Hall.
16 Chan, Ivan S. F. (1998). Exact tests of equivalence and efficacy with a non-zero lower bound for comparative studies, Statistics in Medicine, 17, 1403-1413.   DOI
17 Ewell, M. (1996). Comparison methods for calculating confidence intervals for vaccine efficacy, Statistics in Medicine, 15, 2379-2392.   DOI
18 Gart, J. J. and Nam, J. M. (1988). Approximate interval estimation of the ratio of binomial parameters: A review and corrections for skewness, Biometrics, 44, 323-338.   DOI   ScienceOn
19 Katz, D., Baptista, J., Azen, S. P. and Pike, M. C. (1978). Obtaining confidence intervals for the risk ratio in cohort studies, Biometrics, 34, 469-474.   DOI   ScienceOn