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The importance of the relative risk in comparison of 2 X 2 tables has long been recognized. Bartlett 1935 proposed both large and small sample tests for testing the hypothesis of the constancy of the relative risk between two tables and Norton 1945 extended the large sample test to the general case of several 2 X 2 tables. More recently, Cornfield 1956 developed a procedure for making multiple comparisons among several relative risks by finding various simultaneous confidence intervals. All these tests involve iterative computational techniques. This paper is concerned with the point and interval estimation of the common relative risk for several 2 X 2 tables. Either these tables are assumed to have equal relative risks or they have passed one of the aforementioned homogeneity tests. It is shown that the point and interval estimates based on the simple addition of the corresponding elements of the tables are not, in general, appropriate and may, in fact, yield badly misleading interpretations. Consistent and efficient estimators of the common relative risk are presented, together with their associated confidence intervals. Two numerical examples are given. Some of the issues dealt with in this paper have been previously considered by other authors. Mantel and Haenszel 1959 and Cornfield and Haenszel 1960 have also warned against the use of the pooled estimator discussed in sections 3 and 4. Mantel and Haenszel have gone on to propose various methods of combining heterogeneous relative risks from segments of a population into a single summary relative risk. Woolf 1955 used one of the point and interval estimators derived in sections 6 and 7 in dealing with the problem of combining homogeneous relative risks.
John J. Gart (Sat,) studied this question.