Supplementary Material Simulation The effect size at a selected SNP To calculate the bias in figure 7, we compared the estimated effect size at the sampled SNP to the true effect at that SNP , ie not at the causal SNP. If the causal SNP is S and the selected SNP is T , then the underlying relative risk at T is simplest to calculate in a haploid system, which is equivalent to assuming Hardy Weinberg equilibrium. Given 31 ρ ′ = ρ ( S, T ) $^{√}$π$_{S}$ π$_{T}$ (1 − π$_{S}$ )(1 − π$_{T}$ ) Y = √ 0 . 7 Z + √ 0 . 3 X P$_{S}$ =        π$_{1}$ π$_{0}$ haplotype carries risk allele 1 − π$_{1}$ 1 − π$_{0}$ haplotype carries protective allele allele. π$_{1}$ = rπ$_{0}$ 1 − π$_{0}$ + rπ$_{0}$ . Once a “causal variant” SNP, S , was selected, control haplotypes were sampled randomly and case haplotypes sampled conditional on the allele carried at S . For a disease model with relative risk r , and given the minor (risk) allele at S has frequency π$_{0}$ , in controls, the frequency in cases is Therefore when sampling case haplotypes, we over-sample haplotypes carrying the risk allele and under sample those carrying the protective allele by using sampling probabilities proportional to For eQTL data, we simulated a response variable, Y as a mixture of Gaussians where Z was sampled from a standard Gaussian and X is the count of the minor allele at the causal SNP. Thus, X would explain 30% of the variance of Y , or 30% of the simulated eQTL, independent of minor allele frequency.