Luke J. O’Connor

Luke J. O'Connor, Alkes L. Price

Genome-wide association studies (GWAS) have emerged as a rich source of genetic clues into disease biology, and they have revealed strong genetic correlations among many diseases and traits. Some of these genetic correlations may reflect causal relationships. We developed a method to quantify causal relationships between genetically correlated traits using GWAS summary association statistics. In particular, our method quantifies what part of the genetic component of trait 1 is also causal for trait 2 using mixed fourth moments $E(α_1^2α_1α_2)$ and $E(α_2^2α_1α_2)$ of the bivariate effect size distribution. If trait 1 is causal for trait 2, then SNPs affecting trait 1 (large $α_1^2$) will have correlated effects on trait 2 (large $α_1α_2$), but not vice versa. We validated this approach in extensive simulations. Across 52 traits (average $N=331$k), we identified 30 putative genetically causal relationships, many novel, including an effect of LDL cholesterol on decreased bone mineral density. More broadly, we demonstrate that it is possible to distinguish between genetic correlation and causation using genetic association data.

Luke O'Connor, Muriel Médard, Soheil Feizi

A latent space model for a family of random graphs assigns real-valued vectors to nodes of the graph such that edge probabilities are determined by latent positions. Latent space models provide a natural statistical framework for graph visualizing and clustering. A latent space model of particular interest is the Random Dot Product Graph (RDPG), which can be fit using an efficient spectral method; however, this method is based on a heuristic that can fail, even in simple cases. Here, we consider a closely related latent space model, the Logistic RDPG, which uses a logistic link function to map from latent positions to edge likelihoods. Over this model, we show that asymptotically exact maximum likelihood inference of latent position vectors can be achieved using an efficient spectral method. Our method involves computing top eigenvectors of a normalized adjacency matrix and scaling eigenvectors using a regression step. The novel regression scaling step is an essential part of the proposed method. In simulations, we show that our proposed method is more accurate and more robust than common practices. We also show the effectiveness of our approach over standard real networks of the karate club and political blogs.