Block network mapping approach to quantitative trait locus analysis

Abstract

Background: Advances in experimental biology have enabled the collection of enormous troves of data on genomic variation in living organisms. The interpretation of this data to extract actionable information is one of the keys to developing novel therapeutic strategies to treat complex diseases. Network organization of biological data overcomes measurement noise in several biological contexts. Does a network approach, combining information about the linear organization of genomic markers with correlative information on these markers in a Bayesian formulation, lead to an analytic method with higher power for detecting quantitative trait loci?

Results: Block Network Mapping, combining Similarity Network Fusion (Wang et al., NM 11:333-337, 2014) with a Bayesian locus likelihood evaluation, leads to large improvements in area under the receiver operating characteristic and power over interval mapping with expectation maximization. The method has a monotonically decreasing false discovery rate as a function of effect size, unlike interval mapping.

Conclusions: Block Network Mapping provides an alternative data-driven approach to mapping quantitative trait loci that leverages correlations in the sampled genotypes. The evaluation methodology can be combined with existing approaches such as Interval Mapping. Python scripts are available at http://lbm.niddk.nih.gov/vipulp/ . Genotype data is available at http://churchill-lab.jax.org/website/GattiDOQTL .

Keywords: Bayes’ theorem; Interval mapping; QTL mapping.

Fig. 1

Flowchart outlining the major parts of the BNM algorithm

Fig. 2

Flowchart outlining the Hierarchical Clustering algorithm

Fig. 3

Flowchart outlining the algorithm steps to obtain the ratio in Eq. 5

Fig. 4

Power and FDR as a function of Effect Size. Power and FDR of the BNM algorithm (blue) and IM from the R/qtl package (red) with increasing effect sizes. Each point corresponds to the Power (a-c) or FDR (d-f) within a group of 4000 data points with an average effect size in the x-axis. We show the power and FDR at three P-value (for IM) and R-value (for BNM) thresholds: 0.001 and 0.146 (a, d), 0.03 and 0.322 (b, e), and 0.05 and 0.383 (c, f). These P-value, R-value pairs are matched so that they have the same FDR averaged over all points (see Additional file 1: Figure S2)

Fig. 5

ROC curves as a function of Effect Size. ROC curves for IM (blue) and BNM (red) within 6 groups of 3800 data points with average effect sizes 0.108±0.065,0.309±0.077,0.555±0.101,0.892±0.140,1.403±0.239 and 2.582±1.00

Fig. 6

Power and FDR as a function of Sample Size. Power and FDR of the BNM algorithm (blue) and IM from the R/qtl package (red) with increasing effect sizes. Each point corresponds to the Power (a-c) or FDR (d-f) within a group of 2000 data points with an average effect size in the x-axis. We show the power and FDR at P-value = 0.05 (for IM) and the matching BNM R-value such that IM and BNM have the same FDR averaged over all points (see Fig. 7). In (a,d) we use all the mice (Nmice = 742) and three samples of 500 phenotypes from the 1000 simulated phenotypes; the FDR matching R-value = 0.362 (see Fig. 7 a). In (b, e) we use three samples of randomly selected 600 mice out of the 742 mice available; the FDR matching R-value = 0.492 (see Fig. 7 b). In (c, f) we use three samples of randomly selected 400 mice out of the 742 mice available; the FDR matching R-value = 0.281 (see Fig. 7 c). The plots are the means over the three samples in each case, and the errorbars are the standard deviations from the mean in each case

Fig. 7

False Discovery Rate variability. The average false discovery rates (y-axis) are the mean over the three samples of the average over the FDRs within each of the 76 effect size groups in Fig. 6 at different P-value (for IM (blue)) or R-value (for BNM (red)) thresholds (x-axis). In (a) we take the average FDR over the points in Fig. 6 d for each of the three samples. The plot is mean over the three samples and the errorbars are the standard deviation from the mean. Similarly we take the average over the points in Fig. 6 e (b), and Fig. 6 f (c). In (d) we replot all together the results for BNM (red plots in (a-c)). In (e) we replot all together the results for IM (blue plots in (a-c)

Fig. 8

Neutrophil SNP Signals. For each chromosome we show 1 - R-value of each SNP (y-axis). The x-axis shows the location of each SNP in Mb. The horizontal red dotted line denotes the threshold value above which signals are detected