Comparison of relative risk, attributable risk and logistic response procedures for 2×2×2 andc 2×2×2 contingency tables

Summary

A numerical evaluation was made on three different χ² statistics in order to compare mutagenic risk frequencies between two experimental groups in a 2×2×2 contingency table andc 2×2×2 contingency tables. The three methods involve 1) a relative risk approach, 2) an attributable risk approach and 3) a logistic response approach. A relatively large difference was observed among χ² statistics in the three approaches using actual data under the hypothesis that there is no difference between the two groups under scrutiny. With regard to approximate power, it appears that approaches 2) and 3) give fairly stable results. Approach 1) has greater power if there is a small difference in the control groups. It was confirmed that the approximate power of approach 1) is extremely large when the difference in the relative risk frequencies between the two groups under contrast is constant and each relative risk frequency is small.