The method was originally outlined by Bernie Devlin and Kathryn Roeder in a 1999 paper.
[1] It involves using a set of anonymous genetic markers to estimate the effect of population structure on the distribution of the chi-square statistic.
The distribution of the chi-square statistics for a given allele that is suspected to be associated with a given trait can then be compared to the distribution of the same statistics for an allele that is expected not to be related to the trait.
[4] In theory, it takes advantage of the tendency of population structure to cause overdispersion of test statistics in association analyses.
[5] The genomic control method is as robust as family-based designs, despite being applied to population-based data.
[6] It has the potential to lead to a decrease in statistical power to detect a true association, and it may also fail to eliminate the biasing effects of population stratification.
[7] A more robust form of the genomic control method can be performed by expressing the association being studied as two Cochran–Armitage trend tests, and then applying the method to each test separately.
Often this will lead to an overestimation of the significance of an association but it depends on the way the sample was chosen.
[9] This kind of spurious association increases as the sample population grows so the problem should be of special concern in large scale association studies when loci only cause relatively small effects on the trait.
A method that in some cases can compensate for the above described problems has been developed by Devlin and Roeder (1999).
[10] It uses both a frequentist and a Bayesian approach (the latter being appropriate when dealing with a large number of candidate genes).
The frequentist way of correcting for population structure works by using markers that are not linked with the trait in question to correct for any inflation of the statistic caused by population structure.
[11] For the binary one, which applies to finding genetic differences between the case and control populations, Devlin and Roeder (1999) use Armitage's trend test and the
test for allelic frequencies If the population is in Hardy–Weinberg equilibrium the two statistics are approximately equal.
Under the null hypothesis of no population stratification the trend test is asymptotic
Marchini et al. (2004)[14] demonstrates by simulation that genomic control can lead to an anti-conservative p-value if this value is very small and the two populations (case and control) are extremely distinct.