An analytical comparison of the principal component method and the mixed effects model for genetic association studies

The principal component method and the mixed effects model represent two popular approaches for controlling for population structure and cryptic related-ness in genetic association studies. There are quite few studies comparing their performance. However, these comparisons are typically conducted using simulation studies and their implications are therefore limited. We report an analytical study of these two approaches in the presence of cryptic relatedness and population structure in terms of their validity and efficiency. We show that in the presence of cryptic relatedness, both methods are valid but the mixed effects model is more powerful. In the presence of population structure, both methods can be invalid and be conservative or anti-conservative. Conditions under which they are valid are provided. These conclusions are demonstrated through examples and simulation studies.