Hierarchical Association Coefficient Algorithm: New Method for Genome-Wide Association Study

Hierarchical association coefficient algorithm calculates the degree of association between observations and categories into a value named hierarchical association coefficient (HA-coefficient) between 0 for the lower limit and 1 for the upper limit. The HA-coefficient algorithm can be operated with stratified ascending categories based on the average of observations in each category. The upper limit refers to a condition where observations are increasingly ordered into the stratified ascending categories, whereas the lower limit refers to a condition where observations are decreasingly ordered into the stratified ascending categories. An HA-coefficient represents how close an observed categorization is to the upper limit, or how distant an observed categorization is from the lower limit. To demonstrate robustness and reliability, the HA-coefficient algorithm was applied to 3 different simulated data sets with the same pattern in terms of the association between observations and categories. From all simulated data sets, the same result was obtained, indicating that the HA-coefficient algorithm is robust and reliable.