A previous study recommended use of pedigree-based (prior) kinship coefficients because of the theoretical justification for the test statistic [Thornton and McPeek, 2007]. While we have not studied the asymptotic properties for the corrected χ2 test based on estimated kinships, as shown in the simulation study, p-values are uniformly distributed under the null hypothesis, so that the corrected χ2 test based on estimated kinships is useful in practice and is also applicable to testing associations. We believe the corrected χ2 test with estimated kinships would be more appropriate for reducing the false positive rate if there is background correlation among individuals beyond what is reflected in the known pedigree structures. Especially among cases, individuals are more likely to share their ancestral background and to be genetically similar to one another than are controls [Voight and Pritchard, 2005]. Estimated kinship coefficients would also be more appropriate for adjusting an unbalance of relatedness between the case and control group. We believe that the proposed approach will provide a practical tool for association studies to reduce false positive results caused by the cryptic relatedness beyond a known or unknown genealogy.
