The fuzzy nature of health and disease

Health and illness, with the exception of extreme and well defined clinical conditions, are vague and not well defined concepts. They are useful in common language and for naive classifications, but too coarse for risk assessment and diagnostic modelling. Although fuzzy logic is naturally more appropriate to reach these aims, we think it's important, in order to rise its acceptance in the whole medical community, to explore its connections and implications with the more popular probabilistic reasoning, showing at the same time the intrinsic limits of the latter. We have focused a subset of 4,563 male subjects sampled from REALAB project data base (Grossi et al 2005). In this project we were able to define the presence and the absence of illness just on basic laboratory tests information properly processed with an original multivariate recursive algorithm. For every subject we calculated a mean disease score as the average forecast of different logistic models, being this score an estimate of the probability to belong to the REALAB illness class. Subjects were sampled following a survey design able to create subjects strata representing the full range of disease scores. Then the data were processed using the fanny methods (Kaufman and Rousseeuw, 1990), a fuzzy clustering technique which build up 5 clusters taking as input data only the disease score for each subject. Then we calculated 5deg and 95deg percentiles for each laboratory parameter within each cluster and compared their values across them. We observed substantial and coherent differences between clusters, appearing those differences related to the increasing rate of diseased subjects. In spite of explorative nature of our study, the results seem to point out the good ability of a common fuzzy clustering methods in mapping probability measures in a coherent fuzzy cluster structure. This supports the reliability of mathematical application of fuzzy reasoning to improper binary constrained concepts as health and illness