  As biomedical sciences discover new layers of complexity in the mechanisms of
life and disease, mathematical models trying to catch up with these
developments become mathematically intractable. As a result, in the grand
scheme of things, mathematical models have so far played an auxiliary role in
biomedical sciences. We propose a new methodology allowing mathematical
modeling to give, in certain cases, definitive answers to systemic biomedical
questions that elude empirical resolution. Our methodology is based on two
ideas: (1) employing mathematical models that are firmly rooted in established
biomedical knowledge yet so general that they can account for any, or at least
many, biological mechanisms, both known and unknown; (2) finding model
parameters whose likelihood-maximizing values are independent of observations
(existence of such parameters implies that the model must not meet regularity
conditions required for the consistency of maximum likelihood estimator). These
universal parameter values may reveal general patterns (that we call natural
laws) in biomedical processes. We illustrate this approach with the discovery
of a clinically important natural law governing cancer metastasis.
Specifically, we found that under minimal, and fairly realistic, mathematical
and biomedical assumptions the likelihood-maximizing scenario of metastatic
cancer progression in an individual patient is invariably the same: Complete
suppression of metastatic growth before primary tumor resection followed by an
abrupt growth acceleration after surgery. This scenario is widely observed in
clinical practice and supported by a wealth of experimental studies on animals
and clinical case reports published over the last 110 years. The above most
likely scenario does not preclude other possibilities e.g. metastases may start
aggressive growth before primary tumor resection or remain dormant after
surgery.
