For IRF4, the association becomes stronger after correcting for the north/south difference (Eigen statistic 1). However, when the second PC is considered the signal is greatly diminished. With the combined ESAIMs (north/south and north), the evidence for association is also greatly diminished by the EIGENSTRAT analysis and eliminated in the STRAT analysis. We examined different sets of ESAIMs including several different combinations of north/south ESAIMs and north-ESAIMs. The results were identical when 192 north/south ESAIMs or 384 north/south ESAIMs were used for the PC1 correction (data not shown). However, as expected based on our PCA results, decreasing the 1211 north-ESAIMs led to poorer PC2 correction and less complete correction of the false positive IRF4 association (see footnote Table 3). Together these results suggest the potential application of ESAIMs in association studies of candidate genes or in replication studies (see discussion).
