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The Use of the Cross-Ratio in Aetiological Surveys

Published online by Cambridge University Press:  05 September 2017

Abstract

The use of the cross-ratio as a measure of association in a 2×2 table is closely related to Bartlett's (1935) definition of interaction in a higher-order table. Inference about aetiological associations from case-control studies is most naturally done in terms of the cross-ratio, as a measure of relative risk. Standard methods of statistical analysis, for the comparison and combination of relative risks and for matched pairs, are reviewed, and some new results noted.

Type
Part IX — Biomathematics and Epidemiology
Copyright
Copyright © 1975 Applied Probability Trust 

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References

Bartlett, M. S. (1935) Contingency table interactions. J. R. Statist. Soc. Suppl. 2, 248252.Google Scholar
Brown, D. T. (1959) A note on approximation to discrete probability distributions. Information and Control 2, 386392.Google Scholar
Cornfield, J. (1951) A method of estimating comparative rates from clinical data. Applications to cancer of the lung, breast and cervix. J. Nat. Cancer Inst. 11, 12691275.Google ScholarPubMed
Cornfield, J. (1956) Some aspects of retrospective studies. J. Chron. Dis. 11, 523534.Google Scholar
Cox, D. R. (1958) Two further applications of a model for binary regression. Biometrika 45, 562565.Google Scholar
Cox, D. R. (1970) The Analysis of Binary Data. Methuen, London.Google Scholar
Darroch, J. N. (1974) Multiplicative and additive interaction in contingency tables. Biometrika 61, 207214.CrossRefGoogle Scholar
Doll, R. and Hill, A. B. (1950) Smoking and carcinoma of the lung. Preliminary report. Br. Med. J. 2, 739748.Google Scholar
Edwards, A. W. F. (1963) The measure of association in a 2 × 2 table. J. R. Statist. Soc. A 126, 109114.Google Scholar
Gart, J. J. (1962a) Approximate confidence levels for the relative risk. J. R. Statist. Soc. B 24, 454463.Google Scholar
Gart, J. J. (1962b) On the combination of relative risks. Biometrics 18, 601610.Google Scholar
Gart, J. J. (1971) The comparison of proportions: a review of significance tests, confidence intervals and adjustments for stratification. Rev. Inst. Internat. Statist. 39, 148169.Google Scholar
Gart, J. J. and Zweifel, J. R. (1967) On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika 54, 181187.Google Scholar
Good, I. J. (1963) Maximum entropy for hypothesis formulation especially for multidimensional contingency tables. Ann. Math. Statist. 34, 911934.CrossRefGoogle Scholar
Lancaster, H. O. (1969a) The Chi-squared Distribution. Wiley, New York.Google Scholar
Lancaster, H. O. (1969b) Contingency tables of higher dimensions. Bull. Inst. Internat. Statist. 43, 143151.Google Scholar
Lindley, D. V. (1964) The Bayesian analysis of contingency tables. Ann. Math. Statist. 35, 16221643.Google Scholar
Macmahon, B. and Pugh, T. F. (1970) Epidemiology. Principles and Methods. 2nd ed. Little, Brown, Boston.Google Scholar
Mantel, N. and Haenszel, W. (1959) Statistical aspects of the analysis of data from retrospective studies of disease. J. Nat. Cancer Inst. 22, 719748.Google Scholar
Plackett, R. L. (1969) Multidimensional contingency tables: a survey of models and methods. Bull. Inst. Internat Statist. 43, 133142.Google Scholar
Seigel, D. G. and Greenhouse, S. W. (1973) Validity in estimating relative risk in case-control studies. J. Chron. Dis. 26, 219225.Google Scholar