One-tailed asymptotic inferences for the relative risk: A comparison of 63 inference methods

Two-tailed asymptotic inferences for the ratio R=p_2/p₁ of two independent proportions have been well covered in the published literature. However, not very much has been written about one-tailed asymptotic inferences. This paper evaluates 63 different methods for realizing such inferences (hypothesis tests and confidence intervals). In general it is noted that: (a) the one-tailed inferences require at least 80 observations per sample, compared to the 40 observations necessary for two-tailed inferences; (b) the traditional methods do not perform well; (c) the methods selected for each case are not always the same; and (d) the optimal method is the ‘approximate adjusted score’ method (ZA1 in this paper), which is not always reliable, or ‘Peskun´s score’ method (ZP0 in theis paper), which is always reliable but is very conservative. The two selected methods provide an confidence interval that is obtained through an explicit formula.