Since symmetry is an idealized phenomenon and asymmetry is more typical for real problems, e.g. noncompatible bivariate conditioning, skewed errors, asymmetric KL divergences for non-normal distributions, development of proper methods for medical applications can be of great interest both for theory and practice. I will illustrate this importance by several examples from Health Sciences. We can take as examples data from bivariate relationships between cholesterol and blood pressures in cardiology risk preventive studies and studies on relationships between several quantitative measures for bone mineral density. I will illustrate several paradoxes of statistical inference for the typical measures of dependence, like correlation coefficient prevalently used for measuring the association between cholesterols and blood pressures. This sever over-symmetrization prevents medical discoveries completely fundamental for proper treatment of e.g. hypertension for older patients. Thus, in general employing measures of linear association (e.g. correlation) may ignore the asymmetric and hierarchical levels of dependence. I will discuss on the importance of proper statistical invariants.