ARTICLE
ABSTRACT
We consider the problem of interval estimation of the odds ratio. An asymptotic confidence interval is widely applied in economics, medicine, sociology, etc. Unfortunately, this confidence interval has a poor coverage probability, significantly smaller than the nominal confidence level. In this paper, a new confidence interval is proposed. Its construction requires only information on the sizes of samples and the sample odds ratio. The coverage probability of the proposed confidence interval is at least the nominal confidence level.
KEYWORDS
confidence interval, odds ratio
REFERENCES
Baumol, W. J., (2015). Macroeconomics: Principles and policy, Cengage Learning, Inc. Andrés, M.A., Mato, S.A., Tejedor, H.I., (2020). Pseudo-Bayesian test for the comparison of two proportions, Metron, 49 (1-4), pp. 151–162.
García-Pérez M.A, Nú´nez-Antón V. (2020) Asymptotic versus exact methods in the analysis of contingency tables: Evidence-based practical recommendations, Stat Methods Med Res., 29(9), pp. 2569–2582.
Cornfield, J., (1951). A Method of Estimating Comparative Rates from Clinical Data. Applications to Cancer of the Lung, Breast, and Cervix, JNCI: Journal of the National Cancer Institute, 11, pp. 1269–1275, DOI: 10.1093/jnci/11.6.1269.
Edwards, A.W.F., (1963). The Measure of Association in a 2×2 Table. Journal of the Royal Statistical Society, Ser. A. 126, pp. 109–114, DOI: 10.2307/2982448. Encyclopedia of Statistical Sciences, (2006). Wiley & Sons.
García-Pérez M.A., Nú´nez-Antón V., (2020) Asymptotic versus exact methods in the analysis of contingency tables: Evidence-based practical recommendations. Stat Methods Med Res., 29(9), pp. 2569–2582.
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, pp. 148–169.
Lawson, R., (2004). Small Sample Confidence Intervals for the Odds Ratio. Communications in Statistics - Simulation and Computation, 33, pp. 1095–1113, DOI: 10.1081/SAC- 200040691.
Morris, J.A., Gardner M.J., (1988). Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates. British Medical Journal, 296, pp. 1313–6, DOI: 10.1136/bmj.296.6632.1313.
McCullagh, P., (1980). Regression Models for Ordinal Data. Journal of the Royal Statistical Society, Ser. B. 42, pp. 109–142.
Neyman, J. (1934). On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection. Journal of the Royal Statistical Society, 97, pp. 558–625.
Thomas, D.G., (1971). Algorithm AS-36: exact confidence limits for the odds ratio in a 2×2 table. Applied Statistics, 20, pp. 105–110.
Wang, W., Shan G., (2015) Exact Confidence Intervals for the Relative Risk and the Odds Ratio. Biometrics, 71, pp. 985-995, DOI: 10.1111/biom.12360.
Zieliński, W., (2011) Comparison of confidence intervals for fraction in finite populations. Quantitative Methods in Economics, XII, pp. 177–182.
Zieliński, W., (2020a). A new exact confidence interval for the difference of two binomial proportions. REVSTAT-Statistical Journal, 18, pp. 521–530.
Zieliński,W., (2020b). A New Confidence Interval for the Odds Ratio: an Application to the Analysis of the Risk of Survival of an Enterprise. The 14th Professor Aleksander Zelia´s International Conference on Modelling and Forecasting of Socio-Economic Phenomena, pp. 185–191.
