Following Chapman et al. [59], we assumed that the test statistic from a case-control trend test of association follows a non-central chi-square distribution with 1 d.f. and non-centrality parameter η = (n−1)r 2 H, where n is the sample size, r 2 is the LD between the causal SNP and it's tag SNP on the GWAS genotyping panel, and H is the proportion of variation explained by the SNP if it were typed directly. In a case-control setting, , where Π is the proportion of cases in the total sample, p is the frequency of causal alleles in controls and in the general population (assuming a rare disease), p′ is the frequency of causal alleles in cases ( where θ is the allelic relative risk or odds ratio assuming a rare disease), and is the causal allele frequency in the study as a whole. We simulated sets of 100,000 X 1 values from a Normal distribution with mean = √η 1 and variance = 1, where η 1 is the presumed non-centrality parameter from the GWAS study (n = 1734,
