Table 7.

Simulations with Sparse Genetic Architecture and Family 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	1.30E-03	1.60E-03	1.57	0.07	0.248	1.60E-03	47.46	0.73
LR + 4 PCs	1.20E-03	1.60E-03	1.53	0.07	0.248	1.60E-03	47.33	0.73
LR + cvBLUP	1.50E-03	9.00E-04	0.72	0.03	0.184	9.00E-04	35.81	0.49
LMM	2.00E-03	1.30E-03	0.98	0.05	0.249	1.30E-03	47.34	0.64
BOLT-inf	1.30E-03	9.00E-04	0.69	0.03	0.168	8.00E-04	33.39	0.44
BOLT-LMM	1.30E-03	9.00E-04	0.86	0.04	0.168	8.00E-04	64.13	0.79
LR + true genetic effect	1.70E-03	1.00E-03	1.14	0.05	0.250	1.00E-03	93.55	1.21

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 ${\chi }^2$.