However, higher interaction odds ratios can arise if the causal variant and marker have differing MAF. As an example, the marker rs10235235 observed at the CYP3A locus15 has MAF 0.09 in women of European ancestry and odds ratios for breast cancer of 0.979 (95% CI: 0.915–1.047) and 0.906 (95% CI: 0.864–0.950) in women with age at menarche ≤12 years and >12 years, respectively. This gives an interaction odds ratio of 1.08 (95% CI: 0.990–1.176) (the original study used a finer categorization of age at menarche, leading to a significant interaction). Assume that the marker and causal variant have the maximum correlation given their MAFs (i.e., D’ = 1). Treating the odds ratios as risk ratios, we can use the approach shown in Table 2 to solve for the causal risk ratios on disease and on exposure that lead to the observed marker risk ratios, given a fixed causal MAF. For causal MAF of 0.05, the observed marker effects can arise from causal risk ratio 0.831 on disease and 0.116 on exposure. This seems unlikely because such a strong effect (0.116 = 1 / 8.62) would probably be detected by a linkage study, but this region was not identified in the largest linkage scan for age at menarche.29 Similarly, a causal MAF of 0.01 implies a causal risk ratio of 0.155 (= 1 / 6.45) on disease and 0.208 on exposure, which again seems strong considering the lack of evidence of linkage to breast cancer in this region. However, a causal MAF of 0.02 implies causal risk ratios of 0.577 (= 1 / 1.73) on disease and 0.187 (= 1 / 5.36) on exposure, which is more plausible. Therefore, our observed marker interaction is compatible with a low-frequency causal variant with strong main effects but no interactions. Although common SNPs are generally expected to tag common causal variants,30 the possibility of a low-frequency causal variant suggests caution in claiming a gene-environment interaction in this case.