  This paper applies risk analysis to medical problems, through the properties
of nonlinear responses (convex or concave). It shows 1) necessary relations
between the nonlinearity of dose-response and the statistical properties of the
outcomes, particularly the effect of the variance (i.e., the expected frequency
of the various results and other properties such as their average and
variations); 2) The description of "antifragility" as a mathematical property
for local convex response and its generalization and the designation
"fragility" as its opposite, locally concave; 3) necessary relations between
dosage, severity of conditions, and iatrogenics. Iatrogenics seen as the tail
risk from a given intervention can be analyzed in a probabilistic
decision-theoretic way, linking probability to nonlinearity of response. There
is a necessary two-way mathematical relation between nonlinear response and the
tail risk of a given intervention. In short we propose a framework to integrate
the necessary consequences of nonlinearities in evidence-based medicine and
medical risk management.
  Keywords: evidence based medicine, risk management, nonlinear responses
