Summary
This paper gives a review of certain jackknife estimators of a common odds ratio in the situation of several 2×2 tables. These jackknife estimators are based on the classical Mantel-Haenszel estimator and on some asymptotically efficient noniterative estimators. Finite-sample results and asymptotic properties for increasing sample sizes, but a fixed number of tables are summarized. Some open problems in this field of research are indicated.
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References
ANSCOMBE, F.J. (1956). On estimating binomial response relations. Biometrika 43, 461–4.
ARVESEN, J.N. (1969). Jackknifing U-statistics. Ann. Math. Statist.. 40, 2076–100.
BRESLOW, N.E. (1981). Odds ratio estimators when the data are sparse. Biometrika 68, 73–84.
BRESLOW, N.E.; LIANG, K.Y. (1982). The variance of the Mantel-Haenszel estimator. Biometrics 38, 943–52.
DAVIS, L.J. (1985). Weighted averages of the observed odds ratios when the number of tables is large. Biometrika 72, 203–5.
DONNER, A.; HAUCK, W.W. (1986). The large-sample relative efficiency of the Mantel-Haenszel estimator in the fixed-strata case. Biometrics 42, 537–45.
FLEISS, J.L.; DAVIES, M. (1982). Jackknifing functions of multinomial- frequencies, with an application to a measure of concordance. Am. J. Epidemiol.. 115, 841–5.
GÄNSSLER, P.; STUTE, W. (1977). Wahrscheinlichkeitstheorie. Springer-Verlag, Berlin.
GART, J.J. (1962). On the combination of relative risks. Biometrics 18, 601–10.
GART, J.J.; ZWEIFEL, J.R. (1967). On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika 54, 181–7.
GASTWIRTH, J.L.; GREENHOUSE, S.W. (1987). Estimating a common relative risk: application in equal employment. J.Am. Stat. Assoc.. 82, 38–45.
GUILBAUD, O. (1983). On the large-sample distribution of the Mantel-Haenszel odds ratio estimator. Biometrics 39, 523–5.
HALDANE, J.B.S. (1955). The estimation and significance of the logarithm of a ratio of frequencies. Ann. Hum. Genet.. 20, 309–11.
HAUCK, W.W. (1979). The large sample variance of the Mantel-Haenszel estimator of a common odds ratio. Biometrics 35, 817–9.
HAUCK, W.W. (1989). Odds ratio inference from stratified samples. Commun. Stat., Theory Methods 18, 767–800.
HAUCK, W.W.; ANDERSON, S.; LEAHY, F.J. III (1982). Finite-sample properties of some old and some new estimators of a common odds ratio from multiple 2×2 tables. J.Am. Stat. Assoc.. 77, 145–52.
HITCHCOCK, S.E. (1962), A note on the estimation of the parameters of the logistic function, using the minimum logit χ2 method. Biometrika 49, 250–2.
JEWELL, N.P. (1984). Small-sample bias of point estimators of the odds ratio from matched sets. Biometrics 40, 421–35.
MANTEL, N.; HAENSZEL, W. (1959). Statistical aspects of the analysis of data from retrospective studies of disease. J. Nat. Cancer Inst.. 22, 719–48.
McKINLAY, S.M. (1975). The effect of bias on estimators of relative risk for pair-matched and stratified samples. J. Am. Stat. Assoc.. 70, 859–64.
McKINLAY, S.M. (1978). The effect of nonzero second-order interaction on combined estimators of the odds ratio. Biometrika 65, 191–202.
NURMNEN, M. (1981). Asymptotic efficiency of general noniterative estimators of common relative risk. Biometrika 68, 525–30.
O’GORMAN, T.W.; WOOLSON, R.F.; JONES, M.P.; LEMKE, J.H. (1988). A Monte Carlo study of three odds ratio estimators and four tests of association in several 2×2 tables when the data are sparse. Commun. Stat., Simulation Comput.. 17, 813–35.
PARR, W.C.; TOLLEY, H.D. (1982). Jackknifing in categorical data analysis. Aust. J. Stat.. 24, 67–79.
PIGEOT, I. (1989). Asymptotic properties of several jackknife estimators of a common odds ratio. Technical Report 89/10, Fachbereich Statistik der Universität Dortmund (submitted for publication).
PIGEOT, I. (1990a). A class of asymptotically efficient noniterative estimators of a common odds ratio. Biometrika 77, 420–3.
PIGEOT, I. (1990b). A jackknife estimator of a combined odds ratio. To appear in Biometrics.
PIGEOT, I. (1990c). A simulation study of estimators of a common odds ratio in several 2×2 tables. To appear in J. Statist. Comp. Simulation.
PIGEOT, I. (1990d). Asymptotic relative efficiency of some jackknife estimators of a common odds ratio. To appear in Biom. J...
SERFLING, R.J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
TARONE, R.E.; GART, J.J.; HAUCK, W.W. (1983). On the asymptotic inefficiency of certain noniterative estimators of a common relative risk or odds ratio. Biometrika 70, 519–22.
WOOLF, B. (1955). On estimating the relation between blood group and disease. Ann. Hum. Genet.. 19, 251–3.
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Pigeot, I. (1992). Jackknifing Estimators of a Common Odds Ratio from Several 2×2 Tables. In: Jöckel, KH., Rothe, G., Sendler, W. (eds) Bootstrapping and Related Techniques. Lecture Notes in Economics and Mathematical Systems, vol 376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48850-4_26
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DOI: https://doi.org/10.1007/978-3-642-48850-4_26
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