Besides the choice of the kinship matrix, the estimation of variance parameters is also a crucial part of the EMMAX approach. In our analysis of the NFBC data, we show that estimating these parameters under the null hypothesis does not lead to appreciable bias in the association P values. The example of rheumatoid arthritis and type 1 diabetes in the WTCCC data set, in contrast, reveals the difficulties encountered by EMMAX when there are SNPs explaining a large fraction of phenotypic variance. In such cases, we show that estimating variance parameters conditionally on the SNPs with stronger effects alleviates these concerns.
