A Powerful Correlation Method for Microbial Co-Occurrence Networks

Motivation: Network interpretation using correlations has several known difficulties. Firstly, the data structure has discrete counts with an excess of zeros creating non-normal non-continuous data. Secondly, correlations, often used as similarity measures in network inference, are not causal. Thirdly, there is a masking effect of mutualism on commensalism and competition on amensalism in ecological networks that interfere with interpretation (Faust and Raes, 2012). More explicitly, the symmetric nature of correlations (cor(X,Y)=cor(Y,X)) can mask the affect of the asymmetric ecology relationship (commensalism and amensalism). We aim to solve the third issue which may speed up targeted drug therapies or disease diagnosis based on specific relationships in gut microbiomes. Methods: We apply a non-symmetric correlation method, Gini Correlations which should serve as a better classifier of ecological relationships revealing a fuller picture of microbiomes. First, create simulated correlated and independent Zero-Inflated Negative Binomial data. Second, validate Gini correlations by comparing Gini with Pearson Spearman and Kendall correlations; calculate false positive rate, true positive rate, accuracy, ROC, AUC after applying Benjamini-Hochberg (1995) multiple testing correction. Simulation Result: Gini is consistent and out performs other methods for small sample sizes of 10 and 25 producing consistently low false positive rates across 64+ simulation settings as well as consistently high accuracy rates. When sample size is increased to 50 Gini performs as well as other methods. Real Data Result: For well-defined microbial communities Gini correlations found novel biologically and medically relevant relationships. However, Gini's ability to unmask non-symmetric ecological relationships is yet to be determined