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

Cross-sectional correlations between two variables have limited implications for causality. We examine here whether it is possible to make causal inferences from steady-state data in a homeostatic system with three or more inter-correlated variables. 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, rAC2 is predicted by the product of rAB2 and rBC2 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 using appropriate null hypotheses. The type 2 error reduces with sample size but the nature of this relationship is different for different predictions. 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-β are used to represent insulin resistance and glucose-stimulated insulin response by β cells respectively. Our analysis shows that if we assume the HOMA indices to be faithful indicators, the classical pathway must in turn be rejected. In effect, among the populations sampled, the classical pathway and faithfulness of the HOMA indices cannot be simultaneously true. The principles and example shows that it is possible to infer causal pathways from cross sectional correlational data on three or more correlated variables.