An Analytical Comparison of the Principal Component Method and the Mixed Effects Model for Association Studies in the Presence of Cryptic Relatedness and Population Stratification

The principal component method and the mixed effects model represent two popular approaches to controlling for population structure and cryptic relatedness in genetic association studies. There are only a handful of studies comparing their performance. These studies are typically based on simulation studies and the results are therefore limited in their applicability. In this paper, we conduct an analytical comparison of these two approaches in the presence of cryptic relatedness and population structure in terms of their validity and efficiency. In the presence of cryptic relatedness, we show that both methods are valid, but the mixed effects model is more powerful for detecting association. In the presence of population structure, however, we show that both methods can be invalid. The biases and variances of the estimates from the two methods are compared. Examples and simulation studies are provided to demonstrate the conclusions.