Fast and efficient QTL mapper for thousands of molecular phenotypes.

(a, b) Density plots of the k and n parameter ML estimates made from 100, 1K, 10K and 100K permutations on GEUV_EUR. (c) A scatter plot of the number of variant sites tested per gene (cis-window ±1Mb of the TSS) against the n parameter ML estimates made again from 100, 1K, 10K and 100K permutations on GEUV_EUR. (d, e) Quantile–Quantile plots of the best P-values obtained through 1000 permutations (observed) of the GEUV_EUR dataset against simulated P-values sampled from the fitted beta distributions (expected). Expected P-values are plotted against the observed ones for all genes pooled together in (d) and for each gene separately in panel (e). (f) The KS test −log10 P-values comparing observations and expectations for each gene. The red line shows the expected Bonferroni significance threshold when testing 13 703 genes

(a, b) Scatter plots of the adjusted P-values obtained from 1000 permutations via the direct method (in grey) and the beta approximation (in light blue) against those obtained through the standard permutation scheme with 100K permutations (a) or through the adaptive method with up to 1M permutations (b). All this was performed on the GEUV_EUR dataset. Adjusted P-values are plotted on both linear (a) and log (b) scales. Expected variation for 1000 permutations is shown by the 95% confidence intervals in red. (c) The equivalent number of permutations required by the direct permutation scheme to reach the same calibration as the beta approximation (from 1000 permutations) as a function of the adjusted P-value targeted. The dashed and solid gray lines show the expected accuracy of the adaptive permutation scheme that stops when 5 and 10 stronger null signals are found, respectively. (d) The sensitivity–specificity ratio of reasonable FastQTL runs (beta approximation or direct method with 50–5000 permutations) to recover an optimal eQTL set derived from 100 000 permutations. (e) The sensitivity–specificity ratio to recover the nine official eQTL sets released by the GTEx consortium using both Matrix eQTL (direct method) and FastQTL (beta approximation) with 100, 500 and 1000 permutations