DISCRIMINANT DIAGNOSTICS WITH INCOMPLETE SYMPTOMATICS

Diagnostics by means of the linear discriminant function X = ∑pi=1bixi requires a knowledge of all the p symptoms that are arguments of this function. However, some responses are often missing. One may overcome this difficulty by constructing two acceptance zones whose boundaries depend on the number of the utilized symptoms. One of the two alternatives is accepted if the “incomplete” sum Xp−j = ∑p−ji=1bixi, j being the symptom number counted from the end of the list, crosses one of the boundaries. Otherwise the next symptom must be enlisted. Formulae defining the boundaries of the acceptance zones and the percentage of the patients whose diagnosis requires not more than p‐j symptoms are given. When the sum Xp−1 remains in the indifferent zone one may obtain the full discriminant function by replacing the missing data xi with the mean value xi. The increase of the probability of misclassification due to this procedure is calculated.