For the primary simulation, two simulated haplotypes were randomly selected with replacement for each individual, and sufficient individuals were generated to simulate the desired number of cases and controls. Case/control status was designated based on the assigned risk, and equal numbers of cases and controls were selected for association testing. We tested all common variants in the genealogy for association with disease status, where common was defined by a minor allele frequency of 0.05 or greater. Thus we exclude any variant that is actually disease causing and focus on those that are generally represented directly or indirectly in the current genome-wide genotyping platforms [37]. Association tests were performed by comparing 1,000, 2,000, or 3,000 each of cases and controls, and we screened for common variants with p-values less than 10−8, a now-typical threshold for genome-wide significance [1]. We defined a single “simulation” as follows. A random gene genealogy was drawn with mutations distributed along the genealogy, and disease-causing mutations were assigned at random from those variants that were in the allowed frequency range. Then cases and controls were sampled as
