Inflammation and Immune System Activation in Aging: A Mathematical Approach

Nikas, Jason B.

Mathematical modeling. Utilizing the final 36 most significant genes, I wanted to explore the possibility of developing -via mathematical modeling -a function that could identify as correctly as possible the age status (O or Y) of an unknown subject based on the expression of any combination of those 36 most significant genes. To that end, I randomly selected approximately 70% of the subjects [11/15 young subjects and 18/25 old subjects] that could be used only for the development phase of such function. In other words, a function could be developed only by the exclusive use of those 29 subjects. The remaining 11 subjects (4 young and 7 old ones) were designated unknown (test) subjects and were used solely for the purpose of validating any promising function generated in the development phase. This split into two fixed sets, whereby one is used only for training and the other only for validation, represents the simplest implementation of K-fold cross validation 45, 46 . A function was deemed promising in the development phase only if it exhibited a sensitivity $ 0.90 and a specificity $ 0.90 in connection with the 29 subjects of the development phase. Pertaining to the validation phase, and in connection with the 11 unknown subjects, a promising function would have to exhibit the same minimum classification accuracy (a sensitivity $ 0.90 and a specificity $ 0.90) in order to be accepted. I was able to generate one such function (F 1 -henceforward also referred to as super variable) that fulfilled all of the aforementioned criteria. Supplementary Fig. 1 shows the equation of F 1 as a function of 7 genes.