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Education And Debate Complexity science

Complexity and clinical care

BMJ 2001; 323 doi: (Published 22 September 2001) Cite this as: BMJ 2001;323:685

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Non linearity in medicine : a problem or an opportunity ?

Dear sir,

The paper by Wilson & Holt (1) raises some fundamental issues on the
inherent mathematical properties of medical data and underlines the
rational basis for a truly revolutionary approach to their analysis and

In the past century we have witnessed a steady increase in the quantity
and quality of collected, analysed and published medical data. This trend,
which has been particularly evident in the last 40 years, has been driven
also by the spectacular development of digital document management systems
and electronic literature databases. If we consider the body of medical
literature as evidence of the amount of medical data processed all over
the world, it is clear that the growth has been exponential.
The number of currently published medical journals is estimated to be
around 20,000 and is still increasing due also to the advent of e-
publishing. This figure is at strong discrepancy with the scenario of the
first decades of 1900 when the number of medical journals was in the order
of a few dozens, mirroring the difficulties associated with systematic
data collection and the lack of knowledge of the basic rules of clinical
epidemiology, a discipline that was founded only in the '50s. At the time,
the application of statistics to the medical field was in its infancy and
this is not surprising since many techniques were originally developed for
different fields like agriculture and only subsequently applied to the
medical setting.

In fact the most powerful and well established statistical methods were
developed in the first half of the past century when the size as well as
the understanding of figures coming from clinical observations was rather
limited and certainly negligible in comparison with today. These methods
are still widely used today to analyse medical data and are indeed
considered as standard tests by the regulatory agencies.
It is noteworthy that all these methods rely on the basic assumption that
medical variables are normally distributed and, more importantly, that
they are linear in nature .

The reasons underlying this belief are quite easy to understand: on the
one hand linear models are undoubtedly more user friendly as compared to
non-linear ones which require stronger theoretical assumptions in the pre-
analysis phase; on the other hand the limited historical exposure of
physicians to medical data has led them to assume that biological
phenomena share the linear laws that govern physical systems and that have
their grounds in Newtonian mechanics .

The issue of non-linearity of medical data has very rarely been raised in
literature. Clearly epidemiologists and statisticians devoted to the
medical field are quite happy with linear techniques, since they have been
trained from the beginning with them; physicians and other health
professionals, due to their proverbial poor mathematical competence, are
also happy, provided that statisticians and regulatory agencies do not
think differently.

However, persisting in the linear approach is not without danger: if, for
instance, for two given variables a correlation coefficient of 0.018 is
calculated under the linear hypothesis and a P-value of 0.80 is added, a
relationship between the two is ruled out. Revisiting the relationship
between these two variables through the non-linear approach could change
the situation dramatically since fuzzy and smooth interactions may
determine significant effects through a complex multifactorial interplay.

There is now the reason to ask a fundamental question: is the mathematics
used in medicine what it should be?
It is perhaps useful to remind ourselves that nowadays research and
practice in medicine, diagnosis and therapy have become formidable due to
the contribution of physics with all its complex mathematics behind .

We should start to systematically address the analyses of our non-linear
and complex systems with a different kind of approach. In my view the use
of artificial neural networks, evolutionary algorithms and other systems
of "knowledge discovery in data bases" should be supported and encouraged.
The cooperation with "bio" mathematicians keen on complex adaptive systems
should be strongly advocated in the interest of the community and of the
quality of health care delivery.

Competing interests: No competing interests

27 September 2001
Enzo Grossi
Medical Director , European Medical Affairs, Bracco Imaging
Folli 50 20134 Milano