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7 can be regarded as a lower bound. As an informal comparison, Figure?10 also displays the results of a more standard MR-type GWAS analysis. For a P-value of 10?8 and all 12,454 subjects, MR returned six SNPs, five of which were GIANT-identified markers, and four were exact matches with SNPs selected by our L1 algorithm (Figure?10). With a P -value cutoff of 5��10?8 and all subjects, MR returned 13 markers, 10 of which were GIANT-identified, and 7 of which were identical to the L1 -selected markers. Figure 10 Map of SNPs associated with height, as identified by the GIANT Consortium meta-analysis, L1 -penalized regression, and standard GWAS. Pemetrexed Base-pair distance is given by angle, and chromosome endpoints are demarcated by dotted lines. Starting from 3 o��clock ... The presence of a phase Selleck GSK690693 transition is not necessarily restricted to L1 algorithms, but rather may represent a deeper phenomenon in signal recovery. Other methods may show a similar phase transition��although CS theory suggests that, among convex optimization methods, those within the L1 class are closest to the optimal combinatorial L0 search. We conducted additional analyses to test whether a phase transition at a critical sample size could also be observed when our height data were analyzed using the MR approach commonly used in GWAS. In these simulations we varied the P -value threshold for genome-wide significance. As measures of selection are potentially subject to a phase transition, we examined the PPV* and the adjusted median P -value (��P?value*). The latter measure was defined to be the median P -value among those SNPs surviving the P -value cutoff, divided by the cutoff itself; the normalization was necessary to remove the dependence on the choice of cutoff. As shown in Figure?11, the P -value threshold 10?8 yielded EPZ004777 solubility dmso very few selected SNPs, and in fact, none were returned at sample sizes smaller than approximately 8,000. However, ��P?value* was mostly close to zero in the region of Figure?11B corresponding to n>8,000 and P?value