Table 1. Effectiveness of different approaches in correcting for stratification.
We list the λGC (Genomic Control lambda) of each method for normally differentiated (FST = 0.01) and unusually differentiated (Δ = 0.6) markers in Simulation 1 and Simulation 2. In each case, λGC was computed as the median χ2(1 dof) statistic (restricting to the subclass of markers tested) divided by 0.455. EIGENSTRAT corrects for population structure (Simulation 1), EMMAX and ROADTRIPS correct for family structure and for population structure at normally differentiated markers (FST = 0.01), and EMMAX+PCs corrects for family structure and for population structure at normally or highly differentiated markers (FST = 0.01 or Δ = 0.6). We note that the approach of ref. 30 is immune to all of these confounders, implying a value of λGC=1.00 for each column of the table.
| Simulation 1, FST = 0.01 |
Simulation 1, Δ = 0.6 |
Simulation 2, FST = 0.01 |
Simulation 2, Δ = 0.6 |
|
|---|---|---|---|---|
| Armitage trend | 1.40 | 48.4 | 1.57 | 48.3 |
| EIGENSTRAT | 1.00 | 1.00 | 1.17 | 1.14 |
| EMMAX* | 1.00 | 2.05 | 1.01 | 1.62 |
| EMMAX* + PCs | 1.00 | 1.02 | 1.01 | 1.01 |
| ROADTRIPS | 1.00 | 48.4 | 1.00 | 48.3 |
EMMAX can use either the IBS or Balding-Nichols estimate of the kinship matrix33. Results for IBS are displayed in the table, and results for Balding-Nichols are 1.00, 1.91, 1.00, 1.28 for EMMAX and 1.00, 1.03, 1.00, 0.99 for EMMAX + PCs.