Table 2.

Example of robust association tests as applied to a schizophrenia dataset with 10 covariates

SNP	Z.add	Z.dom	Z.rec	P.add	P.dom	P.rec	Theoretical combined p	Bootstrap combined p	Integration error
1	0.910	−0.282	0.912	0.363	0.778	0.362	0.597	0.596	7.60E−05
2	0.424	0.482	1.034	0.672	0.630	0.301	0.500	0.509	4.32E−05
3	0.774	0.862	1.092	0.439	0.389	0.275	0.479	0.469	1.37E−04
4	1.826	−1.999	1.347	0.068	0.046	0.178	0.095	0.103	6.99E−04
5	1.888	−1.735	1.645	0.059	0.083	0.100	0.119	0.116	5.07E−04
6	0.656	−1.366	0.276	0.512	0.172	0.783	0.321	0.313	2.04E−04
7	1.023	−1.358	0.970	0.306	0.175	0.332	0.321	0.282	5.29E−04
8	1.379	−1.724	0.998	0.168	0.085	0.318	0.169	0.164	5.30E−04
9	1.242	−2.475	0.546	0.214	0.013	0.585	0.029	0.03	6.68E−04
10	2.055	−3.517	1.066	0.040	0.000437	0.286	0.001	0.002	1.38E−04
11	1.186	−1.009	0.946	0.236	0.313	0.344	0.416	0.422	4.97E−05
12	1.051	−0.756	0.955	0.293	0.450	0.340	0.497	0.481	5.69E−05
13	1.593	−0.800	1.728	0.111	0.424	0.084	0.166	0.169	1.98E−04
14	1.620	−0.741	1.885	0.105	0.459	0.059	0.120	0.098	2.74E−04
15	1.836	−1.319	1.678	0.066	0.187	0.093	0.134	0.118	2.51E−04
16	1.285	0.575	1.780	0.199	0.566	0.075	0.149	0.153	5.19E−04
17	−0.477	1.258	−0.070	0.634	0.209	0.944	0.377	0.366	2.38E−04
18	−1.575	1.742	−0.898	0.115	0.081	0.369	0.162	0.147	1.50E−04
19	−0.664	2.133	0.117	0.507	0.033	0.907	0.069	0.06	3.05E−04
20	−1.861	1.270	−1.676	0.063	0.204	0.094	0.128	0.108	4.23E−04

Z.add, Z.dom and Z.rec are the z-statistics under the additive, dominant and recessive models respectively. Similarly, P.add, P.dom and P.rec are the p-values under the three genetic models. Theoretical combined p is the p-value adjusted for multiple testing of different genetic models, obtained by the proposed analytic approach. Bootstrap combined p represents the same p-value obtained by 1,000 bootstraps. Integration error is the estimated error from computing the trivariate integral using mvtnorm