Similarity Coefficients of Normal Distributions in Selecting the Optimal Treatments

In the current research, we aim to define a new form of the similarity coefficient to compare the resemblance grade of two Gaussian density functions. We aim to assess the method utility on a theoretical model. The density functions are stated for a biological marker “survival length”, observed in three groups of patients, suffering from a hypothetical disease. The first group consists of patients who are not treated, whereas we recommend 2 possible treatment methods for the second and the third group, respectively. All the “survival length” assumptions of the model (mean values and standard deviations) are made to exclude the equivocal conclusion, regarding a selection of the better treatment. At the first stage, we apply the measure of similarity to populations: survival among untreated patients contra survival among patients after Treatment 1. Another similarity coefficient estimates a relation between populations: survival among untreated patients versus survival among patients after Treatment 2. The lower value of the coefficient points out the more effective treatment. In order to simplify calculations, proposed in the definition of a similarity coefficient, we approximate the Gaussian curve by a specially designed polynomial, known as the π-function.