of the LD correlation between SNPs on different chromosomes or more than d Mb distant is zero, even though, in a particular sample, the observed value is nonzero due to finite sample size. In our method, we set the LD correlation between distant SNPs to zero, because it is inappropriate to represent a randomly sampled correlation in the discovery sample by another randomly sampled correlation in the reference sample. In the conditional analysis, if a SNP to be tested is more than d Mb distant from all the top SNPs fitted in the model, we are therefore unable to model and adjust for the variability in the estimate of the SNP effect due to the sampling variation of correlations in the discovery sample. Thus, the conditional effect will be the same as the marginal effect, whereas the standard error of this SNP effect decreases as the residual variance is reduced because of the selected SNPs in the model. This signifies that test statistics will be inflated and the false positive rate will increase. This problem will be dramatically exacerbated if the discovery set is not very large, for example, coming from a single GWAS cohort, with there being a higher
