Table 6.

Simulations with Sparse Genetic Architecture and Population Structure

Model	mean(${\beta }_0$)	se(${\beta }_0$)	mean(${\chi }_{Null}^2$)	se(${\chi }_{Null}^2$)	mean($\beta$)	se($\beta$)	mean(${\chi }^2$)	se(${\chi }^2$)
LR	−1.50E-03	2.30E-03	2.88	0.14	0.245	2.20E-03	46.30	0.90
LR + 4 PCs	−6.00E-04	1.30E-03	1.01	0.05	0.248	1.20E-03	46.57	0.66
LR + cvBLUP	−6.00E-04	1.10E-03	0.97	0.05	0.238	1.10E-03	54.76	0.78
LMM	−7.00E-04	1.20E-03	1.00	0.05	0.247	1.20E-03	55.22	0.76
BOLT-inf	−8.00E-04	1.00E-03	0.97	0.05	0.211	1.00E-03	52.78	0.73
BOLT-LMM	−8.00E-04	1.00E-03	1.02	0.05	0.211	1.00E-03	77.75	1.05
LR + true genetic effect	−2.30E-03	1.90E-03	3.65	0.17	0.247	1.90E-03	87.22	1.56

Mean and standard error for effect estimates and test statistics of association tests at 1000 null SNPs with true $\beta =0:{\widehat{\beta }}_0$ and ${\chi }_{Null}^2$; and at 1000 causal SNPs with an alternative hypothesis of true $\beta =0.25:\widehat{\beta }$ and ${\chi }^2$.