Fuzzy gating and the problem of screening

The problem of population screening is very important for medical statistics. It allows one to analyze the expression of certain parameters in the population of healthy persons, in order to compare it to the expression of these parameters in the persons with a specific disease. If a parameter is expressed differently in ill and healthy persons, then this parameter may serve as a pointer to the disease, especially in its earlier stages. While the analysis of given parameters in people with the established diagnosis does not represent many difficulties, the analysis of the general population is not easily carried out. The problem is that the general population contains both ill and healthy people. The population of healthy people is said to be 'contaminated' by the noise-subpopulation of ill people. The resulting statistical parameters are, therefore, biased and in order to find their correct values one needs to cancel out the input of the noise. In this paper we propose a new method to cancel out the noise, based on the theory of fuzzy sets. We assume that an auxiliary parameter is measured simultaneously and it is used to separate the subpopulations. If two subpopulations (the data and the noise) form clearly distinguished clusters in respect to this auxiliary parameter, one creates a gate and throws out the events outside the gate assuming that they are noise. However, when the clusters overlap, this procedure is no longer useful, and it is this particular situation for which we have developed fuzzy gating. In addition to the fact that the gate is fuzzified, a specifically designed algorithm is applied to compute the probability density functions for both subpopulations. Our algorithm gives a very high precision and is very robust as to the level of noise and the type of distributions.