However, population structure is actually a fixed effect (i.e. its effect as a function of genetic ancestry is the same for all samples), and spurious associations might result if it is modeled as a random effect based on overall covariance, particularly in the case of unusually differentiated markers. Modeling population structure as a fixed effect provides a higher level of certainty in correcting for stratification, but requires running PCA (or a similar method) to infer the genetic ancestry of each sample34. If family structure is present, inferring genetic ancestry via PCA is a challenge, because family relatedness may lead to artifactual PCs19. A possible solution is to compute PCs using SNP loadings inferred from a set of unrelated samples, either using a different set of samples than those in the disease study or using an unrelated subset of samples from the disease study35. This is likely to be sufficient when the set of unrelated samples used is very large relative to the magnitude of population structure effects. However, unless sample sizes are very large, PCs computed from external SNP loadings
