Table 4. Over-dispersion factors and empirical type I errors for the association test without the correction of PS.

		Significance level
Study	Over-dispersion	0.05e	0.01e	0.001e
NHSca-NHScoa	1.005	0.0505	0.0100	0.0010
PLCOca-PLCOcob	1.025	0.0527	0.0110	0.0012
NHSca-PLCOcoc	1.062	0.0572	0.0120	0.0013
PLCOca-NHScod	1.090	0.0588	0.0127	0.0016

Note: The over-dispersion factor and empirical type I errors under various significant levels are estimated by applying the 1-df Wald test statistic without the correction of PS on the set of 241,238 genomic control SNPs. We assume all genomic control SNPs are disease unrelated.

^aNHSca-NHSco is the original NHS breast cancer study.

^bPLCOca-PLCOco is the original PLCO prostate cancer study.

^cNHSca-PLCOco is the reconstructed study with breast cancer cases from the NHS, and external controls from PLCO.

^dPLCOca-NHSco is the reconstructed study with prostate cancer cases from the PLCO, and external controls from NHS.

^eEmpirical type I error rates under the given significant level (assuming all genomic control SNPs are disease-unrelated).