AC-PCoA: Adjustment for confounding factors using principal coordinate analysis

Confounding factors exist widely in various biological data owing to technical variations, population structures and experimental conditions. Such factors may mask the true signals and lead to spurious associations in the respective biological data, making it necessary to adjust confounding factors accordingly. However, existing confounder correction methods were mainly developed based on the original data or the pairwise Euclidean distance, either one of which is inadequate for analyzing different types of data, such as sequencing data.In this work, we proposed a method called Adjustment for Confounding factors using Principal Coordinate Analysis, or AC-PCoA, which reduces data dimension and extracts the information from different distance measures using principal coordinate analysis, and adjusts confounding factors across multiple datasets by minimizing the associations between lower-dimensional representations and confounding variables. Application of the proposed method was further extended to classification and prediction. We demonstrated the efficacy of AC-PCoA on three simulated datasets and five real datasets. Compared to the existing methods, AC-PCoA shows better results in visualization, statistical testing, clustering, and classification.Author summary: With today’s unprecedented amount of data, researchers are challenged by the need to enhance meaningful signals without the interference of unwanted confounders hidden inside the data. Data visualization is an important step toward exploring and explaining data in order to intuitively identify the dominant patterns. Principal coordinate analysis (PCoA), as a visualization tool, allows flexible ways to define pairwise distances and project the samples into lower dimensions without changing the distances. However, when visualizing large-scale biological datasets, the true patterns are often hindered by unwanted confounding variations, either biologically or technically in origin. To eliminate these confounding factors and recover underlying signals, we proposed a method called Adjustment for Confounding factors using Principal Coordinate Analysis, or AC-PCoA, and showed that it significantly outperforms existing methods in visualization through three simulation studies and five real datasets. We further showed that the low-dimensional representations given by AC-PCoA provide promising results in statistical testing, clustering, and classification as well.