Over-dispersion factor (and the empirical type I error under the significant level of 0.05) for association tests with adjustment for various numbers of PCs.

Note: The over-dispersion factor (and the empirical type I error under the significant level of 0.05) are estimated by applying the 1-df Wald test statistic with the adjustment for selected PCs on the set of 241,238 genomic control SNPs.aPLCOca-PLCOco is the original PLCO prostate cancer study.bPLCOca-NHSco is the reconstructed study with prostate cancer cases from the PLCO, and external controls from NHS.cNHSca-NHSco is the original NHS breast cancer study.dNHSca-PLCOco is the reconstructed study with breast cancer cases from the NHS, and external controls from PLCO.eThose PCs were chosen by the proposed permutation procedure for the correction of PS. The selected sets of PCs for individual analyses (from left to right) are: 1st PC; 1st, 2nd, and 4th PCs; 2nd PC; and 1st, 2nd, and 3rd PCs. The PCs were ordered according to their corresponding eigenvalues备注：本研究针对241238个基因组对照单核苷酸多态性（Single Nucleotide Polymorphism, SNP）位点集合，采用经选定主成分（Principal Component, PC）校正的1自由度沃尔德（Wald）检验统计量，估算过度离散因子与0.05显著性水平下的经验I型错误率。 a. PLCOca-PLCOco 为原始PLCO前列腺癌研究。 b. PLCOca-NHSco 为重构研究，其前列腺癌病例源自PLCO队列，外部对照源自NHS队列。 c. NHSca-NHSco 为原始NHS乳腺癌研究。 d. NHSca-PLCOco 为重构研究，其乳腺癌病例源自NHS队列，外部对照源自PLCO队列。 e. 上述主成分通过本研究提出的置换程序选取，用于群体分层（Population Stratification, PS）校正。各单次分析选取的主成分集合（按从左至右顺序）依次为：第1主成分；第1、2、4主成分；第2主成分；以及第1、2、3主成分。主成分依据其对应的特征值进行排序。