Inferring causal pathways among three or more variables from steady-state correlations in a homeostatic system

Abstract

Cross-sectional correlations between two variables have limited implications for causality. We show here that in a homeostatic system with three or more inter-correlated variables, it is possible to make causal inferences from steady-state data. Every putative pathway between three variables makes a set of differential predictions that can be tested with steady state data. For example, among 3 variables, A, B and C, the coefficient of determination, [Formula] is predicted by the product of [Formula] and [Formula] for some pathways, but not for others. Residuals from a regression line are independent of residuals from another regression for some pathways, but positively or negatively correlated for certain other pathways. Different pathways therefore have different prediction signatures, which can be used to accept or reject plausible pathways. We apply these principles to test the classical pathway leading to a hyperinsulinemic normoglycemic insulin-resistant, or pre-diabetic state using four different sets of epidemiological data. Currently, a set of indices called HOMA-IR and HOMA-{beta} are used to represent insulin resistance and glucose-stimulated insulin response by {beta} cells respectively. Our analysis shows that if we assume the HOMA indices to be faithful indicators, the classical pathway must in turn, be rejected. Among the populations sampled, the classical pathway and faithfulness of the HOMA indices cannot be simultaneously true. The principles and tools described here can find wide application in inferring plausible regulatory mechanisms in homeostatic systems based on epidemiological data.