Efficient estimation of relative risk, odds ratio and their logarithms for rare events

Sequential estimators are proposed for the relative risk, odds ratio, log relative risk or log odds ratio of a dichotomous attribute in two populations. The estimators take the same number of observations from each population, and guarantee that the relative mean-square error for the relative risk or odds ratio, or the mean-square error for their logarithmic versions, is less than a given target. The efficiency of the estimators, defined in terms of the Cram\'er-Rao bound, is high when the considered attribute is rare or moderately rare.