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## Supplementary Material 

## Simulation 

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 

<img src='content_image/312947.jpg'>

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 

<img src='content_image/312946.jpg'>

For eQTL data, we simulated a response variable, Y as a mixture of Gaussians 

<img src='content_image/312945.jpg'>

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. 

## 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 

<img src='content_image/312944.jpg'>

