and LD mean that evidence for association may peak at an alternative SNP even when the causal SNP is included in the genotyping panel, a bias which is more pronounced for weaker effects and smaller sample sizes (Supplementary Figure 6). Second, although it is well known that regression coefficients are unbiased estimates of population effects, this property does not hold after variable selection [Miller, 1984], an effect which has been referred to as “Winner’s curse” in genetics [Gring et al., 2001; Lohmueller et al., 2003]. Choosing SNPs on the basis of their significance or some other measure of strength of association induces a bias away from the null - i.e. coefficients of selected SNPs are expected to overestimate the true effect - and again the effect is more pronounced for smaller sample sizes and weaker effects (Supplementary Figure 7). These two biases mean that, in conditional testing, there is likely to be some residual association between the phenotype Y and the remaining genetic markers after conditioning on the selected SNP k ′ because (1) the conditioning SNP k ′ may not capture all the true association and (2) the estimated effect at the tested SNP k tends to be an overestimate. The result is very poor control of the type 1 error rate (Figure 1, track C1). Conditioning on the common causal variant rather than the most associated SNP (which is only possible in simulation studies) reduces the bias by removing the SNP selection problem, but does not eliminate it due to the overestimation of effect size (Figure 1, track C2). As seen in Supplementary Figure 8, Nica’s score tends towards to 1 for traits that share a causal variant and is uniformly distributed on [0 , 1] for distinct unlinked causal variants. Its distribution is increasingly skewed towards 1 as the LD between distinct causal variants increases. This makes sense if one considers that the case of two distinct variants in some LD lies partway between the extreme cases of distinct linked causal variants and a single common causal variant, which is equivalent to distinct causal variants in complete LD. The effect of using the most associated SNPs for testing compared with using the true causal SNPs is to reduce the skew towards higher rank scores as the r 2 between variants increases. Thus, Nica et. al ’s extension [Nica et al., 2010] is useful if searching for most likely colocalisation signals within a set, but as it avoids formally testing a null hypothesis, and because the scale against which to interpret the rank score is likely varies according to effect size, it does not provide a means to assess evidence for or against colocalisation at a given locus of interest. We show here that neither published method of SNP selection in proportional testing maintains control of the type 1 error rate (Figure 1, tracks P1, P2 and P3), although the bias is less extreme 10