Bagging Nearest-Neighbor Prediction independence Test: an efficient method for nonlinear dependence of two continuous variables

Testing dependence/correlation of two variables is one of the fundamental tasks in statistics. In this work, we proposed an efficient method for nonlinear dependence of two continuous variables (X and Y). We addressed this research question by using BNNPT (Bagging Nearest-Neighbor Prediction independence Test, software available at https://sourceforge.net/projects/bnnpt/). In the BNNPT framework, we first used the value of X to construct a bagging neighborhood structure. We then obtained the out of bag estimator of Y based on the bagging neighborhood structure. The square error was calculated to measure how well Y is predicted by X. Finally, a permutation test was applied to determine the significance of the observed square error. To evaluate the strength of BNNPT compared to seven other methods, we performed extensive simulations to explore the relationship between various methods and compared the false positive rates and statistical power using both simulated and real datasets (Rugao longevity cohort mitochondrial DNA haplogroups and kidney cancer RNA-seq datasets). We concluded that BNNPT is an efficient computational approach to test nonlinear correlation in real world applications.