The Use of the Linear Mixed Model in Human Genetics

We give a short but detailed review of the methods used to deal with linear mixed models (restricted likelihood, AIREML algorithm, best linear unbiased predictors, etc.), with a few original points. Then we describe three common applications of the linear mixed model in contemporary human genetics: association testing (pathways analysis or rare variants association tests), genomic heritability estimates, and correction for population stratification in genome-wide association studies. We also consider the performance of best linear unbiased predictors for prediction in this context, through a simulation study for rare variants in a short genomic region, and through a short theoretical development for genome-wide data. For each of these applications, we discuss the relevance and the impact of modeling genetic effects as random effects.