Abstract
In order to measure the association between an exposure variable X and an outcome variable Y , we introduce the effect-control sampling design and we consider the family of symmetric association measures. Focusing on the case of binary exposure and outcome variables, a general estimator of such measures is proposed and its asymptotic properties are also discussed. We define an allocation procedure for a stratified effect-control design, which is optimal in terms of the variance of such an estimator. Finally, small sample behavior is investigated by Monte Carlo simulation for a measure belonging to the family, which we believe particularly interesting as it possess the appealing property of being normalized.
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References
Agresti, A.: A survey of exact inference for contingency tables. Stat. Sci. 7(1), 131–153 (1992)
Borgoni, R., Marasini, D., Quatto, P.: Effect-control sampling and odds ratio, ITACOSM 2009, Siena, (2009)
Edwards, A.W.F.: The measure of association in 2 ×2 table. JRSS A 126(1), 109–114 (1963)
Good, I.J., Mittal, Y.: The amalgamation and geometry of two-by-two contingency tables. Ann. Stat. 15(2), 694–711 (1987)
Haberman, S.J.: A warning on the use of chi-squared statistics with frequency tables with small expected cell counts. J. Am. Stat. Assoc. 83, 555–560 (1988)
Jewell, N.P.: Statistics for Epidemiology. Chapman&Hall/CRC, New York (2004)
Lachin, J.M.: Biostatistical Methods: The Assessment of Relative Risks. Wiley, New York (2000)
Landenna, G.: Fondamenti di statistica descrittiva. il Mulino, Bologna (1994)
Lehmann, E.L.: Elements of Large-Sample Theory. Springer, New York (2001)
Mehta, C.R., Patel, N.R., Gray, R.: Computing an exact confidence interval for the common odds ratio in several 2 by 2 contingency tables. J. Am. Stat. Assoc. 80, 969–973 (1985)
Mehta, C.R., Patel, N.R., Senchaudhuri, P.: Importance sampling for estimating exact probabilities in permutational inference. J. Am. Stat. Assoc 83, 999–1005 (1988)
Woolf, B.: On estimating the relation between blood group and disease. Ann. Hum. Genet. 19, 251–253 (1955)
Zelen, M.: The analysis of several 2 × 2 contingency tables. Biometrika 58, 129–137 (1971)
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Borgoni, R., Marasini, D., Quatto, P. (2013). Symmetric Association Measures in Effect-Control Sampling. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds) Advances in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35588-2_24
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DOI: https://doi.org/10.1007/978-3-642-35588-2_24
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